math phd later in life

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• CAREER FEATURE
• 25 June 2024

How researchers navigate a PhD later in life

• Elizabeth Landau 0

Elizabeth Landau is a science writer based in Washington DC.

You can also search for this author in PubMed   Google Scholar

On a roll: Krista Bresock celebrates in her local skate park after graduating with a PhD in mathematics from West Virginia University, Morgantown, aged 41. Credit: Michael Germana

Krista Bresock sat crying in her professor’s office. She had to discuss one of five questions with her professor, in person. It was the concluding step of her final exam in functional analysis, the last course that she needed to complete for her PhD in mathematics. He’d shuffled a set of five cards, and she’d picked Card Number Two — corresponding to the one problem that she had not fully studied.

Unlike her fellow students studying intractable maths problems, Bresock was in her late thirties redoing coursework that she had failed years earlier. As a full-time maths teacher at West Virginia University (WVU) in Morgantown, she could find time to study only during nights and weekends.

“Problem Number Two was just collateral damage to being able to maintain this life of work full-time and be in grad school full-time,” Bresock remembers. She “fell to her knees” in relief when, a week later, she learnt she’d still got an A- in the course.

Many think of doctoral degrees as the domain of people in their twenties. Yet according to the US National Science Foundation, 17% of people who gained a PhD in science or engineering in the United States in 2022, the most recent year for which figures are available, were aged 36 or older . In some countries, including Colombia, Mexico, Portugal, South Korea, Iceland, Greece and Israel, the median age for entering a doctoral programme is 32 or higher, according to 2017 data from the OECD in Paris 1 .

Resources for mid-career scientists

A PhD requires a vast commitment of time and energy, often lasting five or more years. Stipends, when available, are often lower than salaries for other full-time jobs or professions. What’s more, students might have to move to another city, or even a different country, to attend their chosen course. Although difficult for any age group, those constraints can create different challenges for prospective students in their thirties, forties and beyond than for their younger colleagues.

At the same time, age often brings wisdom and self-confidence, qualities that can help older students to cope with a strenuous academic life. “The extra ten years that I was out doing other things gave me a lot of perspective and maturity to the way in which I think and live, and I think that was a big reason why I’ve succeeded,” says Peter Swanton, a 36-year-old graduate student working towards a doctoral degree in astrophysics at the Australian National University in Canberra.

Motivation is key

For Bresock, a doctoral degree represented “unfinished business”. She had struggled with alcohol and drug addiction from the age of 16, but hit a dangerous low point in early 2013, when she was a graduate student at WVU the first time round. She dropped out and checked herself into an in-patient programme, but still drank heavily afterwards. With the support of friends, family and Alcoholics Anonymous, she became sober in July 2013.

Bresock then taught maths at WVU, first as an adjunct and then as a full-time instructor, but she didn’t forget her incomplete doctorate. Finally, at the age of 37, she re-enrolled. “This little voice was like, ‘You have more to say. You have more to do. You have this thing sitting on the back burner that is kind of eating away at you,’” she says.

Despite her drive to finish the degree, motivating herself was “really hard sometimes”, she says, “because if I didn’t finish, no one would care: I would just not finish and still have this job and be fine.” One of her top tips for others looking to pursue a doctorate in mid-life is to fully understand and reflect on their motivations. If the goal is “more money”, that might not be enough, she says.

Before returning to his studies, Swanton held a variety of jobs, including hauling sugar cane, working in nightclub security and tutoring in secondary schools. He has this advice for anyone who’s considering a doctorate: make sure you’re “doing it because you love it”. For him, that has meant finding ways to combine telescopic investigations of cosmic objects, such as active galactic nuclei, with preserving folklore about the cosmos from the Gamilaraay, the people of his Aboriginal culture.

Peter Swanton, a 36-year-old graduate student in cultural astronomy at the Australian National University in Canberra, says that his previous work experience has given him the maturity to cope with the strains of academic life. Credit: Lannon Harley/ANU

Swanton’s heritage influences both his academic interests and the way in which he wants to communicate them. For example, the Gamilaraay language was originally a purely oral one. So, rather than just writing “a big block of text” for his dissertation, Swanton says that he would like to include elders and community members telling their own stories, and to bridge their knowledge with the Western understanding of the universe.

“My success has come down to finding something I am passionate about, and not concerning myself with future employability, which was the focus of my earlier attempts at academia and ultimately the reason why I didn’t succeed” at the time, he says.

Finding mentors

María Teresa Martínez Trujillo arrived at the Paris Institute of Political Studies to embark on a graduate programme in political science at the age of 32. Having spent her whole life up to that point in Mexico, she felt isolated from her classmates because of linguistic and cultural barriers, in addition to being the oldest student in her cohort. Martínez Trujillo had already had a career in the Mexican government, including working as an adviser to the secretary of the interior, yet she felt “less brave” than younger students, and had many more questions about reading materials.

She also felt ashamed about her lack of fluency in French. Over time, with the help of a therapist, she learnt to be less judgemental of herself and to overcome her impostor syndrome. Classmates helped her to proofread some of her assignments and she focused on improving her language skills.

Cultural and linguistic barriers left María Teresa Martínez Trujillo feeling isolated from her peers when she arrived from Mexico, aged 32, to embark on a graduate programme at the Paris Institute of Political Studies. Credit: Hiram Romero

Martínez Trujillo’s advisers — Hélène Combes and Gilles Favarel-Garrigues — were key for her as she dived into reading and fieldwork on the relationship between drug trafficking and the business world in Morelia, Mexico, for her master’s project. “They let me go to the ‘forest’ and spend time and lose myself,” she says, adding that when she felt lost or stuck, her advisers helped her to find her way.

Time and money

Finances often pose a problem for graduate students who don’t already have savings and support, including those who have worked previously. Even with tuition covered, and a stipend to help towards living expenses, making ends meet can be challenging, especially for students who have other financial responsibilities, such as providing for family members or maintaining a home.

Martínez Trujillo received a stipend, but she spent almost all of it on rent and didn’t want to ask her family for money. She worked as a nanny, consulted for a Mexican think tank and spent summers working in Mexico on friends’ projects. “I’d never have free days,” she says.

Bresock wishes she could have spent more time away from both work and studies. “I did a terrible job of that. Make sure you make time for yourself. That dissertation will still be there, if you go take a walk, or if you go swim or whatever, for an hour out of your life.”

Training: Data Analysis: Planning and Preparing

Like Bresock, Marc Gentile kept a full-time job while doing his PhD in astrophysics at the Swiss Federal Institute of Technology in Lausanne in his mid-to-late-fortiess. He needed to earn enough to support both himself and his wife, and to address other financial responsibilities.

“The top advice would be establishing effective work and study habits right from the start,” he says. “In my case, time was the most precious resource, and I had to be very well organized to make the most of it.”

Gentile would work on his doctoral assignments from 5 a.m. to 6 a.m. each weekday, before leaving for his day job. He would then read articles while commuting by train, and tackle more PhD tasks or further reading in the evenings. “I was told that I was, on average, more productive and better organized than most other, younger students, because you develop such skills when you work professionally,” he said.

Family matters

When Wendy Bohon walked across the stage to receive her doctorate in geology, she was nearly 38 years old and pregnant with twins. She wound up at Arizona State University in Tempe after beginning her career as an actor, and then becoming fascinated with earthquakes after one shook her apartment in 1999.

For her dissertation, Bohon conducted fieldwork in India on two large fault systems, focusing on how fast they had been moving, their intersections and their frequency of earthquakes — as well as the growth of mountains around them — over the past 34 million years. Today, she heads the Seismic Hazards and Earthquake Engineering branch of the California Geological Survey in Sacramento.

Wendy Bohon was nearly 38, and pregnant with twins, when she graduated from Arizona State University in Tempe with a PhD in geology. Credit: Linda Bohon

As a student, her desire to expand her family had put her in a different life stage from younger peers. She had met her husband, who already had a young daughter, while in her graduate programme. And whereas her classmates had wanted to avoid pregnancy, she had struggled to conceive. “That emotional disconnect and the difference in their reality and my reality — it was really tough,” she says. Ultimately, she and her husband chose to try the intensive process of in vitro fertilization, which Bohon mostly kept secret. At the same time, she was helping to co-parent her husband’s daughter, and the couple were given full custody of the girl when she was seven.

Bohon coped with parenting and finishing graduate school with the help of “a built-in village of people around who could step in to help us”. Other graduate students would play the card game UNO with the girl, or colour pictures with her. And Bohon’s mentor, along with the mentor’s husband, became the child’s godparents.

“In a lot of ways, it was easier to parent during my PhD, because my schedule was relatively flexible, so I could stay home with her when she was sick, or attend school functions,” Bohon says. What’s more, she adds, “having a kiddo that needed me helped me to set and keep healthier boundaries than I think I would have otherwise”.

Charlotte Olsen, a postdoctoral researcher in astrophysics at the New York City College of Technology, earned a PhD at the age of 42 and now investigates the factors that influence star formation and galaxy evolution. Olsen says that working on her doctorate presented challenges for her marriage. “I’m not gonna lie: grad school is really rough on a relationship,” she says — adding that, especially at the beginning, “it’s an incredibly stressful time”.

Among the responsibilities that older students might have is taking care of ageing parents. Olsen recalls that during her qualifying exams, she hadn’t heard from her mother, who was 76 years old at the time, for a while. She assumed that her mother wanted to give her space during that stressful time. Later, she found out that her mother’s appendix had ruptured, necessitating surgery and a stay in a hospital’s intensive-care unit.

Through it all, Olsen’s spouse was an invaluable source of emotional support. “Having somebody who is there with you along the way” helps a lot, she says.

What happens next?

Not everyone who gets a PhD stays in their field. Gentile, now 60, works as a data scientist for a Swiss television station. He had a postdoctoral research position for five years after graduation — but for several reasons, including financial ones, he could not find an academic job afterwards. “If I had really wanted to continue in astrophysics, then I would have had to move abroad; it’s difficult now,” he says.

Still, Gentile found the PhD experience rewarding and worthwhile. As well as acquiring problem-solving techniques, he learnt coding and data-science skills, such as machine learning and statistical methods. And he has used all of these in subsequent jobs, including his current one.

His graduate work also remains relevant. Some of the algorithms and software that he worked on during his PhD helped to inform the tools that scientists will use to analyse data from the European Space Agency’s Euclid observatory, which aims to explore dark energy and dark matter.

Bresock received a promotion at West Virginia University after earning her PhD in maths in December 2022, aged 41. Her dissertation examined how students understand the definite integral, a fundamental concept in calculus, when solving different kinds of problem.

Today, she has greater empathy for her own students because of her own struggles as a graduate student. Finishing her doctorate remains one of her most satisfying accomplishments, she says. “When people ask me what’s the biggest thing I’ve ever done in my life, it’s: get sober, and then, finish my PhD. That’s a close second.”

doi: https://doi.org/10.1038/d41586-024-02109-x

Organisation for Economic Co-operation and Development. Education at a Glance 2019: OECD Indicators (OECD, 2019).

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Is it possible to start a PhD in mathematics at the age of 29? [duplicate]

I graduated with a bachelor’s degree in mathematics. I was initially focused on branches in analysis like operator algebra. At the third year of my undergraduate study, I experienced a financial loss in my family. It was only a slight loss and would not influence the life and regular plans of my family. But at that time I was not mentally strong enough and I could not concentrate on study. I postponed two years to graduate, in 2020.

These days I am trying to apply for a master program in mathematics. My GPA is not top, but fair enough, and I also did my graduation thesis carefully. I applied for several programs in Europe and received the conditional admission of Uni of Göttingen, but my Toefl grade did not meet the requirements. This year I have prepared all the things and I am going to apply for several master’s programs in Germany.

I am currently interested in low-dimensional topology and want to select this area as my direction. But when I apply for a PhD, I am 29 years old, is it a huge disadvantage? I also referred to several persons working on geometric topology, and the time cost seems to be high. But I am still enthusiastic about mathematics and want to get a bread.

Anyone could give me some suggestions?

• gt.geometric-topology
• oa.operator-algebras
• 37 $\begingroup$ As far as I know it is not uncommon to start a PhD later in life, and 29 is not even that late. Age alone should not be much of a disadvantage. $\endgroup$ –  Wojowu Commented Feb 28, 2022 at 9:43
• 3 $\begingroup$ You may want to look at this thread. The "age gap" is somewhat smaller there but you should find some stories shared there encouraging! mathoverflow.net/q/59999/30186 $\endgroup$ –  Wojowu Commented Feb 28, 2022 at 9:44
• 5 $\begingroup$ This post is also tangentially related: Too old for advanced mathematics? And maybe you can find some related posts also on Academia . $\endgroup$ –  Martin Sleziak Commented Feb 28, 2022 at 9:46
• 5 $\begingroup$ Lefschetz started his PhD at age 33. So no age is too late. $\endgroup$ –  Kapil Commented Mar 1, 2022 at 12:03
• 4 $\begingroup$ @Brady, OK, but the question is whether it's possible to start a PhD in math at age 29. What's true for, say, sociology doesn't necessarily hold for Mathematics. $\endgroup$ –  Gerry Myerson Commented Mar 2, 2022 at 11:08

8 Answers 8

I don't think being 29 could ever be considered a disavantage on the intellectual or creative level to start a PhD. The comments below your question give you links to lists of famous mathematicians who were late starters. One famous example is Stephan Banach who wrote the equivalent of his master thesis at 28 and got the equivalent of what we call today a PhD at age 30.

I would nevertheless advise to be very careful on other aspects of a mathematician's carreer. Unfortunately, such a career is rarely based solely on talent and genius, unless you solve the equivalent of the Riemann hypothesis in your field. Financial and sociological issues are very important and might become more and more difficult to tolerate as you grow older.

If you plan to get a PhD and then move to industry and/or work for private companies, I guess (though I don't have a formal proof, only examples from friends and colleagues) that your professional life won't be any significantly different or harder than that of your colleagues who got their PhD a few years earlier than you. On the other hand, you have to know that there is an extremely fierce competition for jobs in academia.

It has now become standard to be on very unstable positions (called post-doc positions) for at least 3–4 years after the completion of your PhD. And sometimes up to 10 years! (I have seen that among younger colleagues.) During these years, you need to gain recognition from the bigwigs in your field, so that they can support your application for the next stage of your career: the tenure track position (which I will describe below). And that might be extremely difficult, even if you prove some big results.

I know someone who, as a PhD student, answered an implicit \footnote{added as per suggested by Dan Petersen} question of Serre (you might call it a conjecture ) on cohomological invariants of some finite groups. Instead of congratulating him for his results, Serre became mad at this guy, accused him of stealing his ideas, saying that "the main steps of the proof were already known to him, and that he was going to publish very soon a paper answering his own question." The guy was forced by Serre's affiliates to rewrite his paper and explicitly mention that his work contains no original contribution as "everything was already known to Serre" (but of course not published).

His career in abstact algebra, which should have certainly flourished in the best possible way, considering his brilliant debut, brutally stopped there. This guy was only 25 or 26 at the time, and was strong enough to start a new career in another field. I can't however imagine him doing the same if he was 36 (instead of 26).

But that is a single example, and obviously, most PhD don't end up like this. On the other hand, even if you succeed in having your peers acknowledge your work in a positive way and find some good post-doc positions, you still are in the middle of the jungle. Indeed, if you gain enough support from the bigwigs in your field, you can only upgrade from post-doc positions to a tenure track position.

While tenure track positions are certainly less insecure than post-doc positions, they still aren't permanent positions. They last between 5 to 10 years, and the same game has to be played again with the bigwigs: publish (a lot and frequently) on the subjects which they consider to be interesting, gain their recognition and ask them to support your application.

Then, finally, after 10 to 15 years of such a life (where you might have to move out places every 2 or 3 years), you may hope for a stable and permanent position. Which means that if you start your PhD at 29 and plan to work in the academia, you might secure a permanent position at 40 at the earliest. Granting the fact that you have been able to give plain satisfaction to the numerous bigwigs you will encounter during this 10 to 15 years period of time.

I do believe this is really an important issue to consider before getting bogged down in the academia. You really don't feel the same about those things whether you are in your late twenties or you come close to 40.

• 8 $\begingroup$ @Alex : I am certainly not tryng to discourage you from fulffilling your dreams. Mathematics is certainly worth devoting ones life to it. I am just trying to warn you that academia is far from being what it looks from this outside. It is a jungle! In my opinion, age only play a central role in some situations. When you are (very) young, you don't really care about job security and you recover very quickly from the humiliations the bigwigs may suject you to. I do believe that you become less and less able to tolerate such things when you get older. $\endgroup$ –  Libli Commented Feb 28, 2022 at 19:28
• 24 $\begingroup$ For those curious, this seems to be the paper referred to: arxiv.org/pdf/1112.6283.pdf . I do not understand why people like Serre do not understand that forcing (explicitly or implicitly) someone to write that makes you look like an enormous jerk. $\endgroup$ –  user2520938 Commented Mar 1, 2022 at 8:34
• 6 $\begingroup$ Regarding taking a PhD to industry: Be aware of the opportunity cost. Years invested in earning a PhD are years not spent building connections and industry-specific skillsets. (This is not to say a PhD-->industry is not worthwhile, but rather to be cognizant of the tradeoff.) $\endgroup$ –  Neal Commented Mar 1, 2022 at 14:31
• 10 $\begingroup$ I think the anecdote about Serre in this answer is inappropriate for many reasons: 1) It is a disparaging accusation against a person identified by his real name, made by an anonymous user. 2) It is based only on second-hand information about an incident which happened 10 years ago. 3) The student is easily identifiable from your description (see the comment of @user2520938), who would perhaps not like the affair to be dragged out in public, either. 4) It is not relevant to the question of whether it is a good idea to start a PhD at age 29. $\endgroup$ –  Dan Petersen Commented Mar 2, 2022 at 4:42
• 9 $\begingroup$ @DanPetersen : Life is full of unlikely events, sometimes very disappointing. I am sorry if this event involving Serre may shed some shadows on the naive picture of him you may have created for yourself. But the story happened exactly as I tell it. I was almost in first lines when it occured. $\endgroup$ –  Libli Commented Mar 2, 2022 at 10:04

I completed my PhD at the age of 32 which is not uncommon to Israelis. We often lose several years due to military service. So starting at 29 might be a bit late, but it is not a disaster. It is more about talent and commitment. Good luck.

• 12 $\begingroup$ Starting later in life, after having some life experiences can be a huge advantage. I witnessed many Israeli students doing their Ph.D thesis at Cornell, after completing their IDF time. They cut through their Ph.D work like a hot knife through butter. People going to grad school, straight out of the high school -> undergrad degree cycle, often get dizzy from the array of discussion and research topics, math's tangled history. $\endgroup$ –  Ryan Budney Commented Feb 28, 2022 at 18:31

This is/was certainly possible.

Proof : Reuben Hersh started a PhD after 30 (born in 1927, he defended his thesis in 1962 at the age of 35) after having been working a decade as a machinist. He eventually became a successful professor at the University of New Mexico. His scientific work ranges from hyperbolic PDEs to Probability and Philosophy.

• 5 $\begingroup$ Hersh’s experience 60 years ago shouldn’t count for much here. At the time, American academia was expanding, the academic job market was plentiful, and PhDs were quicker. That’s no longer true in the US, and I doubt it’s true in Germany. $\endgroup$ –  user44143 Commented Mar 1, 2022 at 15:41
• $\begingroup$ @MattF. The OP did not address the question of job market, but only that of feasibility of a PhD at the age of 29. Hersh's example shows that the answer is positive. $\endgroup$ –  Denis Serre Commented Mar 1, 2022 at 16:21
• $\begingroup$ Check out Hersh's published dissertation, esp. p. 321: jstor.org/stable/24900768 . Do you think someone today could get a PhD with a dissertation that "is virtually identical to" a paper only 18 pages long and described as "nothing but a straightforward use of Laplace and Fourier transformations"? I doubt it -- and that matters for someone today. $\endgroup$ –  user44143 Commented Mar 1, 2022 at 18:09
• 2 $\begingroup$ @MattF. Half (?) of the PhD theses in maths are either not cited, or forgotten after five years. That of R. Hersh is still a fundamental step in the theory of hyperbolic Initial Boundary Value Problem. Today, an advisor would ask the student (say R. Hersh grandchild) to elaborate around the 18 pages fundamental paper. It would extend to 100 pages, but the core of the thesis would remain about the same. $\endgroup$ –  Denis Serre Commented Mar 1, 2022 at 19:29
• $\begingroup$ Maybe the math would be no better! But adding another 80 pages would add another 6 months or year to the PhD. $\endgroup$ –  user44143 Commented Mar 2, 2022 at 16:38

Just another example: I graduated late, then worked 2 years outside university, then started my PhD, defended my thesis at 37, and at 47 I became associate professor. Since you ask this frequently: my field is dynamical systems.

It wasn't easy to catch up. I had to accept a few things which look cool in your 20s but uncomfortable in your 40s.

• $\begingroup$ Do your parents support this career? Is it not easy to overcome some anxiety of peer pressure in this process? $\endgroup$ –  Alex Commented Mar 1, 2022 at 14:16
• 2 $\begingroup$ I was lucky enough to work in very good and supportive teams. The difficult part was to move every 2 years or less and to wait my mid 40s to start building my own family. $\endgroup$ –  Paul Commented Mar 1, 2022 at 14:39

As a yes or no question, then certainly yes.

You are at a tiny disadvantage though, which you obviously know to be posing the question. And tiny disadvantages sometimes gradually get bigger, but sometimes they feeble into non-importance. Ultimately, it probably won't be the deciding factor. But it will manifest itself: on the professional level, it might mean you get judged negatively by some (short-sighted, and hopefully not many) professors/panel members; and on the personal level, it might mean you'll attach more importance to your family and financial status than you would have done a few years ago. No one knows how it will play out, but those will be the issues. That's all it is.

I don't know much but I can assure you that no one will be walking about thinking "omg they're just starting their phd". But you're right that (referring to one of your comments) it isn't that easy to overcome the social/peer pressure, but what should be easy anyway. Just make sure you're aware of it and have your approach to cope with it (and not just ignore it - I've seen too many people fail their Ph.D.'s not because they're mathematically incapable but because they don't know how to deal with the pressures involved). Anyway, pretty soon you'll talk to enough people to realise few people care about your age, they just care what maths you do.

Also, as a small personal supporting note cause no one likes getting rejected and it was that bit that made me catch your post: good that you avoided Goettingen, my supervisor there literally told me I was too old to go for a postdoc (at 28). So look at it as a bullet dodged, if it helps. (By the way, Mihailescu is at Goettingen and he didn't start his Ph.D. until he was aroud 40! (He's great by the way, incase this last paragraph is otherwise too negative.))

• $\begingroup$ 28 is common even if this is only the first post-doc…what I have realized is that being admitted to a master program is not difficult, it is a challenge whether I can find a supervisor afterwards. $\endgroup$ –  Alex Commented Mar 1, 2022 at 15:25
• $\begingroup$ it will be more difficult, but not terribly so (at all). there are plenty of posts here, on stackexchange, or on quora, about how to correctly approach a professor - learn about their research and if you find it interesting then tell them. you can't really fake this. and at that point they won't care about your age. (usually, but ye unfortunately there will be some cases where "at a tie" you could get marked down.) it's good to acknowledge that you're starting older, but that's where it ends - don't let it worry you. after that just focus on your mathematics. $\endgroup$ –  tomos Commented Mar 1, 2022 at 16:14
• $\begingroup$ Given what you say, why do you describe the disadvantage as tiny? Having less family time and less money are not tiny things for someone who has the values you suggest. $\endgroup$ –  user44143 Commented Mar 1, 2022 at 18:35
• $\begingroup$ i agree, i think i was just trying to say that the gap starts smaller and either gets bigger (if you miss out on things because you're judged too old, but you would have been fine and it would have been a chance to "catch up", or because as you say your family means you have less time for maths so your output decreases but that of your "competitors" doesn't) or gets neutralised early on (either through luck or being particularly good or particularly hard-working). but at the "beginning" there might not actually be that much difference between the candidates. $\endgroup$ –  tomos Commented Mar 1, 2022 at 19:23
• $\begingroup$ @tomos Thanks for your suggestions. Are you familiar with pure mathematics in Germany? I mean if there are comparatively abundant positions of phd there… $\endgroup$ –  Alex Commented Mar 1, 2022 at 19:53

I started my PhD at age 30, and don't feel my age was a significant obstacle. However, I believe almost no one should do a PhD, regardless of age.

• $\begingroup$ how come? if i may ask $\endgroup$ –  tomos Commented Mar 2, 2022 at 14:40
• $\begingroup$ There's nothing about an academic career that makes it worth staying extra years in school, taking one or more temporary positions, having little control over the city one lives in, just in the (possibly unlikely) hope that one will eventually find a tenure track position. Not to mention the fact that anyone capable of doing a PhD in a technical field could likely get a job in industry making 2x or 3x as much as a professor. $\endgroup$ –  Michael Benfield Commented Mar 2, 2022 at 17:15
• $\begingroup$ @tomos What he said is not comparatively unrealistic, if one has not set up a family or other burdens…No doubt pure maths requires strong brain muscle, and people are definitely the strongest in their young 20s, I acknowledge that…Different persons also have different stamina, and certain physical exercise could help maintain better. $\endgroup$ –  Alex Commented Mar 2, 2022 at 19:01

May be I live in another part of the world? I never asked this question to myself when I started my PhD from Mathematics Department and I was 29 at that time :)

I thought I was too young to do a PhD :D

• 1 $\begingroup$ Which field are you working in? $\endgroup$ –  Alex Commented Mar 1, 2022 at 12:18

I think the bottom line is that some things are easier if you start earlier, but that talent and quality will ultimately find a way and that these things are not determined by your physical age. If you have something original to say, you should still be able to say it regardless of your age.

Note that obtaining a PhD at a relatively old age is quite common for Israeli mathematicians and physicists. For example, if you need inspiration, Yuval Ne'eman started his PhD in physics aged 33. His main contribution (age 36) was his discovery of the classification of hadrons using $SU(3)$ flavour symmetry (known colloquially as the ''eightfold way''). This is a major achievement in twentieth-century physics.

• $\begingroup$ It's worth noting that Ne'eman's achievement was over sixty years ago: he was born in 1925, with the eight-fold way in 1961, and his related dissertation in 1962 ( proquest.com/docview/1812968444 ). $\endgroup$ –  user44143 Commented Mar 1, 2022 at 18:47
• 1 $\begingroup$ You are right. However, this does not contradict the fact that it is an interesting example of someone who started doing formal research relatively late in life but still made great advances. $\endgroup$ –  Hollis Williams Commented Mar 1, 2022 at 20:41

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How to Do a PhD Later in Life: A Primer on What to Expect

By Sara K. McBride

For many people, completing a PhD is a lifelong goal. However, not everyone can do one in their 20’s. Many of us have to wait until later in life to make the leap into this major commitment. It is critical to know what to expect when going in and some of the challenges and benefits of being a mid- or late-career student, which aren’t often talked about. I’d like to share my observations from both my personal experience as a late-30’s PhD student and those of my fellow PhD students in my program who ranged in age from early 20’s to age 70.

First, I need to say that, no matter what, you should avoid paying for your PhD on your own. There is a large number of fellowships and scholarships that will offer annual stipends and full tuition to incoming students. Self funding for 4-7 years is a huge responsibility. You don’t have to bear this cost alone if you seek fully funded PhD programs that support students financially.

Also, remember, take the bits of wisdom that are useful to you and leave the rest behind.

The Benefits

You’ve got different types of work experience. If you have had a lot of life experience, you can apply numerous skills from whatever field you worked in before coming back to academia. Knowledge of project management, accounting, communication, writing, public speaking, software programming, publishing, writing grant proposals, networking, team management…the list goes on and on of skills you might have learned in the workplace that applies to your PhD. Remember: a PhD is not a marathon, it’s a triathlon, that involves different skills at different times. So your skills in the workplace really help!

Resilience in the face of failure. You are going to fail…a lot. And, if you have worked in a variety of different environments, you’ve probably built up different ways of coping with failure. And you will also be familiar with rejection, which is also a critical part of academia. Peer review is a tough process at all stages of learning, and, if you’ve had a few years of working in harsh environments, this will help you pick yourself up again and keep going forward.

You know yourself. You have a separate identity outside the confines of academia. For me, I knew I had been successful in other spheres and so I did not feel as much of a let down when I submitted my dissertation. I knew a life outside the PhD endeavour and so, I didn’t have any missing identity problems of submission that I have seen other people who have never been outside of academia struggle with. Having a separate life and identity can be a real benefit.

There’s no FOMO (Fear of Missing Out) . I had spent 15 years working and travelling around the world, doing various things. I never envied anyone else’s experiences while I was writing my dissertation, because I had similar experiences already. There was no “what might have been” longing within me to distract myself.

You know what you want. I’ve found that most “later in life” PhDs are really clear as to their intentions and motivations. This makes it easier to focus your time and attention to complete your dissertation.

The Challenges

You need to park your ego. Now that you are a PhD student, you are no different in the eyes of the academy to your 23 year old peer. Your experiences and previous job titles no longer matter. You’ll have to leave your ego at the door and really humble yourself to learn from your supervisors, as well as the potentially younger and less experienced students around you. Learning can be a painful process, especially when you feel you have achieved so much in another field. This was a real struggle for me but honestly, it was also very liberating to leave my past behind and just embrace being a student again. Listen to your supervisors and your fellow students; you don’t know it all in academia (no one does).

Some doors are now closed to you. It is true, once you get that PhD, you can be perceived as being “over qualified” and there for, unhirable for many jobs out there. Be prepared for these doors to close and not re-open. There are really exciting new doors that are now available to you but these might be different than you were expecting. But before you start, make sure you are quite happy for those doors to be closed permanently.

Sacrificing your high earning years is tough. If you are doing a PhD later in life, you might be sacrificing earning potential for those years. This can have long ranging impacts on your ability to afford a home or your retirement plans. So be aware of the financial hit that you are about to take.

You may be older than your advisors/supervisors. It is true; you might have more experience and maturity than the supervisors on your committee. But here is the thing: they have more experience than you in academia. No matter where you are at in your PhD process, respect the pathway of those ahead of you, even if they are younger in age. Even if you disagree with your supervisors or advisors, do your best to always remain respectful in those disagreements. Remember: 90 percent of your happiness during a PhD will be based on your relationships with your committee, so do your best to be a great student.    

You will feel really uncomfortable. I felt (and still feel) pretty stupid most of the time in research; it makes me feel deeply uncomfortable at times. If you were a highly competent professional in your last career, you might not remember when the last time it was that you felt utterly out of your depth…and stupid. So be prepared to feel stupid, it will happen. The best thing you can do is admit to this feeling and pushing forward until you no longer feel uncomfortable.

You’ll be a bit rusty. If you’ve been out of school for more than four years or so, your research brain may be a bit rusty. The advantages of doing a PhD right away is that your brain has been primed to work in the research environment and you’ve developed habits based on this. Academia changes rapidly; methods, informed by technology, can force you to learn new things. It may take time to come back up to speed and you may feel behind before you even begin. This is okay, keep going!

For me, doing a dissertation was one of the best decisions I have ever made. It challenged me and I certainly struggled. But I do not regret the decision I made to pursue a PhD. Hopefully the above will give you an understanding of what you are in for if you decide to do one later in life. It can be a rewarding pathway, especially if you know what to expect before going in. Accept the journey you’ve put yourself on and bow your head to the experience. If done properly, the PhD can be a transformative time in your life.

Dr. Sara K. McBride is a Mendenhall Fellow at the U.S.G.S in Menlo Park. Sara has 20 years of experience as a professional communicator and disaster responder, having recently shifted careers into social science research.  She has a Bachelor’s Degree in Arts in Law and Justice from Central Washington University, a Master’s in Public Administration from the University of Hawai’i at Manoa, and her Ph.D. from Massey University in English and Media Studies. Sara McBride is an employee of the U.S. Geological Survey but the above views do not represent the USGS’s position and is not an official statement from the organization. This post was not sponsored.

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How challenging experiences led me to pursue a PhD in Mathematics by Shanise Walker

As a student graduating high school, I was convinced of one thing: I was going to be a high school mathematics teacher. Everything I had done in high school and the inspiration and encouragement I received from teachers, family, and friends helped me feel reassured that my decision was the right one. As a high school student, I excelled in every subject, but doing mathematics was a passion. My love for mathematics led me to tutoring both middle school and high school students in mathematics, participating in mathematics competitions, and learning about other areas of mathematics outside of the curriculum. I had even earned the highest achievement award every year for mathematics in my grade level, so being a high school mathematics teacher seemed like the perfect choice for me.

As an undergraduate student, I immediately declared that I wanted to be a mathematics education major. Although I would have to be accepted into the program, I was sure of my choice in major. Completing the requirements to get into the program were easy because I was eager to be a math teacher. For the first few years of undergrad, things were going well. I added the mathematics major to my degree program and became a double major in mathematics and mathematics education. I was accepted into the mathematics education program and was set on my goals; everything was going well.

Fast forward to the spring semester of junior year, something changed. While taking a math education course focused on technology in the classroom, I found myself in a situation that I could not explain and one that could not be explained to me at the time. One of the first assignments in the course was to write an argumentative essay on technology in the classroom and its benefits or hindrances. When I wrote my essay, I focused my attention on the hindrances and how too much technology could lead students to rely heavily on devices and not enough on understanding the concepts. In the end, I received a low score on this assignment and when I inquired about the low score, the teaching assistant responded, “It’s just wrong.” This was just the beginning of a long battle of receiving low grades because “it’s just wrong.” Those words haunted me, so I stopped inquiring and just accepted the grades. I received lower grades than my peers, even on assignments where we had the same answers. I really disliked going to that class, but I knew I needed to finish the course because it was a requirement for my mathematics education degree. The real test came during the group final project. The project consisted of a group paper and a class demonstration on teaching a math topic to students. For the group paper, my group scored near perfect, but on the class demonstration, I scored significantly lower than my classmates. My group members and I did not understand it since I had written over half of the group paper and the project idea was one that I had brought to the group. I spent countless hours working on this project only to get near perfect or perfect grades on the group graded portion of the project but a low grade on my individual portion.

After receiving the group project grade, I had had enough. I decided to meet with the instructor of the course about my grades and my displeasure with the course. During our meeting, I asked the instructor to explain to me why my grades were much lower than classmates, especially on assignments where we had the same answers. It was then that I learned that this was not about my work, but about who I am. The professor outright admitted that the teaching assistant had given me lower scores because I was Black. The professor was already aware of the situation and had been for semesters before I became a student in his course. It had happened to other Black students who had taken the course before me. I was given assurance that while my grades were low, my final grade would not be. When I left that meeting, I cried. I was angry. While I knew that the particular teaching assistant would not be a grader for any other courses I would take in the major, I felt that I no longer had a place of belonging in that major. Despite feeling like I didn’t belong, I still had a passion for teaching high school mathematics, so I was determined to complete the degree.

The determination to continue with my mathematics education degree would change while I was a participant in an 8-week summer REU mathematics program. When I arrived at the REU program, I had no knowledge of how to conduct mathematics research and I was also unsure of what exactly I would be researching. However, with good mentorship from my research mentor and a postdoctoral student (now a tenured faculty member), I found myself interested in mathematics beyond teaching it. I was interested in solving math problems and I found that sense of community during the REU program that was lacking in my home department. Within the first few weeks of the REU program, I had decided that I wanted to get a PhD in mathematics–a thought I had not had before. My research mentor gave me advice on preparing and applying to graduate school. I took the advice and applied for PhD mathematics programs.

When I returned to my university the fall after the REU program, I was still pursuing a double major in mathematics and mathematics education. I knew that I had only one semester of coursework before I would be student teaching, but there was some unrest in me in continuing my mathematics education degree. I had just come from spending an entire summer doing math research, and I had this motivation in me to pursue a PhD. A week before classes started, I dropped my remaining mathematics education courses. After dropping the courses, I found myself in the position of being able to graduate at the end of the semester since I needed only one mathematics course and one elective course in a certain area to graduate. However, I decided I wanted to stay the entire senior year, so I enrolled in two mathematics courses and other electives.

While I dropped my mathematics education courses, I did not immediately drop my mathematics education major because I was still a bit torn about the idea of perhaps not being able to teach high school mathematics. However, before the fall semester ended, I went for it. I dropped the major and pursued my newfound interest of getting a PhD in mathematics. I started on a research project with a faculty member in the mathematics department and began submitting applications for graduate school. I submitted a number of applications for PhD in mathematics programs before the Thanksgiving break, so everything was going well.

In the spring of my senior year, I had another incident that solidified my pursuit of a mathematics PhD. I attended a graduate school fair at my institution to learn about other graduate programs at other institutions. While doing so, I stumbled upon a master’s program in mathematics education and thought to myself: “Well, maybe I could get my teaching certification while in this program because after all, I still had a passion to teach high school mathematics.” The program was at an institution close to my hometown, so that also meant that I would be able to spend more time with my family. The deadline to apply to the master’s program had not yet passed, so I thought to myself I would give it a shot. I spoke with the program’s representative, and we discussed the program and my GRE scores. She told me that I would likely get into the program with probationary status due to my GRE composite score. When I told her I had already been accepted into PhD programs in mathematics, there was a bit of shock on her face (and I am sure on mine as well). What I knew to be true was that my GRE Verbal Reasoning score was not as high, but I had done well on the GRE Mathematics portion. The composite score missed the mark for their institution to be granted full admission, so with this information in mind, I did not apply to the program. I continued with my plan to get a PhD in mathematics and finally decided that teaching high school mathematics was not the best fit for me. The following fall, I went off to graduate school, pursuing a mathematics PhD program at the same institution I had done the REU. Six years later, I completed the program and earned a PhD in mathematics.

Now, as I write about this experience almost ten years later, for the first time I ask myself, “How can eight weeks change the whole course of your life?” This is exactly what the REU program did for me. It changed the course of my life. It gave me a mathematical experience that I had not encountered before. It provided me with the mentorship I needed to succeed and gave me a sense of belonging in the mathematics community that I had not felt before. It also provided me with motivation to pursue something different–a doctoral degree. For this, I am grateful.

Two years ago, I had an opportunity to fulfill my passion of teaching high school mathematics. I taught calculus to a group of underrepresented minority students at a STEM summer program for high school students. This experience was just as joyful as I thought it would be, and I will always cherish it.

1 Response to How challenging experiences led me to pursue a PhD in Mathematics by Shanise Walker

Hi, I’m really inspired by your passion ,persistence and clarity to stick on to take up mathematics at research level. Currently I’m doing my ph. D program in management in India. But having graduated in bachelor’s degree in maths, I now have ardent desire to continue my masters and then proceed to do ph. d in maths. Though it’s 30 years since I lost touch, your life story is still furthering my passion. Thanks and a nice flow of narrative. Regards, Soundra

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Ph.D. Program

Degree requirements.

In outline, to earn the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.

• Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics
• Pass the six-hour written Preliminary Examination covering calculus, real analysis, complex analysis, linear algebra, and abstract algebra; students must pass the prelim before the start of their second year in the program (within three semesters of starting the program)
• Pass a three-hour, oral Qualifying Examination emphasizing, but not exclusively restricted to, the area of specialization. The Qualifying Examination must be attempted within two years of entering the program
• Complete a seminar, giving a talk of at least one-hour duration
• Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee
• Meet the University residence requirement of two years or four semesters

Detailed Regulations

The detailed regulations of the Ph.D. program are the following:

Course Requirements

During the first year of the Ph.D. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses offered by the Department of Mathematics. Exceptions can be granted by the Vice-Chair for Graduate Studies.

Preliminary Examination

The Preliminary Examination consists of 6 hours (total) of written work given over a two-day period (3 hours/day). Exam questions are given in calculus, real analysis, complex analysis, linear algebra, and abstract algebra. The Preliminary Examination is offered twice a year during the first week of the fall and spring semesters.

Qualifying Examination

To arrange the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Advisor (Dissertation Chair), someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective advisor, the student forms an examination committee of 4 members.  All committee members can be faculty in the Mathematics Department and the chair must be in the Mathematics Department. The QE chair and Dissertation Chair cannot be the same person; therefore, t he Math member least likely to serve as the dissertation advisor should be selected as chair of the qualifying exam committee . The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval, it is to be circulated to all faculty members of the appropriate research sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one section of the department. Sample syllabi can be reviewed online or in 910 Evans Hall. The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program. For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student.

Department of Mathematics

Mathematics phd program.

The Ph.D. program in the Department of Mathematics provides students with in-depth knowledge and rigorous training in all the subject areas of mathematics. A core feature is the first-year program, which helps bring students to the forefront of modern mathematics. Students work closely with faculty and each other and participate fully in both research and student-run seminars.

Questions? Email [email protected]

• The firm deadline for applications for Autumn 2025, is December 5, 2024.
• The (general and advanced) GRE tests are no longer accepted. Please do not submit these scores.

To apply for admissions and financial aid, or for additional information on admissions requirements for the Ph.D. program in pure mathematics, please go to the appropriate Harvard Kenneth C. Griffin Graduate School of Arts and Sciences website listed below. All other inquiries may be directed to the Graduate Program Administrator of the Mathematics Department.

• Harvard Kenneth C. Griffin Graduate School of Arts and Sciences (Harvard Griffin GSAS)
• Mathematics Graduate Studies
• Financial Support

Graduate Program Administrator

The Department of Mathematics does not discriminate against applicants or students on the basis of race, color, national origin, ancestry or any other protected classification.

Preparing the Application The statement of purpose for graduate applications is carefully weighted by the admissions committee. The applicant’s statement should convince the committee that they are able to communicate effectively and with a deep understanding of mathematics. It is not intended to be a biographical sketch or a reflection on one’s decision to enter the field.

Three letters of recommendation are required. Letter writers should be faculty or others qualified to evaluate the applicant’s potential for graduate study in mathematics. The letters must be submitted online and by the application deadline.

Applicants should include any research papers, publications, and other original works they would like to have evaluated by the admissions committee.

The department requests that applicants submit GRE Mathematics Subject Test scores if practical. Applicants should check on the ETS website for test dates in their area to ensure the scores will be submitted before the application deadline. An official score report should be sent to Harvard Kenneth C. Griffin Graduate School of Arts and Sciences using code 3451.

While the admissions committee reviews all applications submitted before the deadline, missing math subject test scores provide one less data point available to evaluate the application. Depending on the strength of the application, the missing subject test scores may put the application at a disadvantage.

Applicants who are non-native English speakers and who do not hold an undergraduate degree from an institution at which English is the primary language of instruction must submit scores from the Internet Based Test (IBT) of the Test of English as a Foreign Language (TOEFL) or the International English Language Testing System (IELTS) Academic test.

Harvard Griffin GSAS requires applicants to upload an electronic copy of undergraduate transcripts. Hard copies of official transcripts are not required at the time of application.

Ph.D. Program in Pure Mathematics The department does not grant a terminal Master’s degree, but the Master’s can be obtained “on the way” to the Ph.D. by fulfilling certain course and language exam requirements.

In general, there is no transfer status application to the Harvard Kenneth C. Griffin Graduate School of Arts and Sciences or to the Department of Mathematics. No formal credit is given for an MSc or MA earned elsewhere. All applicants are considered to be applying as first-year graduate students. The only difference Master’s study may make is to better prepare students for the Qualifying Exam.

All graduate students are admitted to begin their studies in the fall term. The department plans on an entering class of about twelve students. Since the admissions committee receives a few hundred applications, the competition is keen.

Funding Graduate Study Applicants are urged to apply for all funding available to them. If no outside funding is available to the applicant, financial aid in the form of scholarships, research assistantships, and teaching fellowships is available. In general, students who do not have outside support will get scholarship support in their first year, but students are required to act as a teaching fellow for one-half course (i.e. for a one-term course) in their second through fifth years.

The department strongly recommends applicants to seek out and apply for all sources of financing available to them for graduate study. Recommended sources for funding US graduate students are NSF Graduate Fellowships and NDSEG Fellowships . Applicants from the UK are urged to also apply for the Kennedy fellowships and applicants from UK, New Zealand, Canada and Australia for Knox fellowships . International students may apply for the Fullbright IIE or any home country fellowships available for study abroad.

Harvard John A. Paulson School of Engineering and Applied Sciences The Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) offers programs for both the Master’s degree and the Ph.D. degree in Applied Mathematics. Please visit the SEAS website for more information on degrees in applied mathematics at www.seas.harvard.edu

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Grad life: to stay in academia or not, that is the question.

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Should I stay in academia or not after I graduate?

It’s a question that most PhD students find themselves asking at some point in their graduate careers. Some have unequivocal answers from the beginning, while others struggle with the decision even towards the end of their studies. Some just don’t want to think about it until close to their graduation or after they have had three shots of tequila on a Friday night.

Traditionally, postdoctoral positions leading to tenured track professorships would be the expected career path for PhD students. At the same time, the process it takes to get tenure is not easy, to say the least. In this article, we shall explore the vices and virtues of academia and see what prompts someone to lean towards one way over the other.

1. Passion and Freedom: The Light Side of Academia

Being an academic can feel like being an explorer and an entrepreneur with added job security. You are at the frontier of your field, navigating an uncharted territory of knowledge and pushing beyond the current limits of understanding. You often have the freedom to pursue a whole range of different projects that pique your interest.

“Working as a tenured professor essentially makes you your own boss,” said Gilbert Strang, Professor of Mathematics at MIT, “it’s great to get up in the morning and decide what you want to do for the day.”

Having been an MIT faculty since 1960s, Professor Strang is a prominent researcher and an active educator in the field of mathematical analysis, linear algebra, and partial differential equations. Recently he has moved on to machine learning.

“Machine learning has been exploding for the past few years and I simply decided to create a new course and a book,” said Professor Strang, “It’s a privilege to have the chance to pursue whatever looks exciting.”

Professor Madeleine Odin can’t agree more.

"The freedom to choose what you want to work on and who (sic) you collaborate with is one of the nicest things about academia," said Professor Odin, "at the Koch Institute where I did my postdoc, it was a great experience interacting with scientists and engineers from different fields.”

Madeleine was awarded a prestigious K99/R00 Pathway to Independence grant by the National Cancer Institute which led her to becoming an assistant professor at Tufts University. The projects funded under the grant are based on her past research, but incorporating new ideas, collaboration and strategies to tackle cancer.

2. Hyper-competitiveness and under-payment: The Dark Side of Academia

Given that you have the passion for your field, academia can be such a heaven- but only after you get tenure. Before that, it is also unstable and underpaid.

Let’s do some math here: after obtaining a PhD, you usually have to pursue one to two postdoctoral positions, each of which pays around 40K a year and can last somewhere between two to five years. After a series of postdoc positions, you would apply for assistant professorship (AP), which gives you around five years to demonstrate research capability and obtain tenure before the appointment expires. Summing up, you would have to go through nine years (four years of postdoc + five years of AP) of job insecurity and low salary after graduate school. Assuming you graduate at the age of 28, you would be close to 40 when finally getting a stable job.

The above calculation is way too optimistic. It does not take into account the hyper-competitiveness of the academic job market. During the interview, Professor Gil Strang spoke about the number of very strong PhDs on the academic job market, “I wish the success of so many good graduate schools did not lead to this problem.” At MIT, for instance, every AP position often receives  400 applications , leading to an acceptance rate which is  30 times lower  than the Early Action admission rate of the undergraduate program. The hyper-competitiveness entails that you would have to adapt a fairly nomadic life, relocating to where the jobs are. As documented in an  NYTimes article , a brilliant biologist by the name of Emmanuelle Charpentier rotated through nine research institutions across five countries for 25 years, before finally finding a permanent position at the Max-Planck Institute.

3. The Catch-22 of Academia

It looks like we are facing a catch-22 problem: being an academic can be one of the most passionate and stable jobs, but getting there typically requires you to face great job insecurity in one of the most saturated job markets. Ultimately, as graduate students, we have to balance our scholarly dreams with realistic concerns. At the same time, non-academic options do exist, which you can find more information about  here .  

Grad Life blog posts  offer insights from current MIT graduate students on Slice of MIT.

This post originally appeared on the  MIT Graduate Admissions student blogs . 

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Gustie erin coleman wins two prestigious scholarships the physics and mathematics and computer science double major is well on her way to a career in astrophysics research. posted on july 10th, 2024 by luc hatlestad.

Erin Coleman '25 has spent the past two summers conducting research at UC Davis and Caltech.

Gustie Erin Coleman ’25 has landed two highly competitive academic awards that will help her continue her plans to eventually pursue a PhD in astrophysics.

The Physics and Mathematics and Computer Science double major earned a Barry M. Goldwater Scholarship in March, the seventh Gustie to earn this scholarship in the past six years. The award was established by the United States Congress in 1986 and is given to exceptional sophomores and juniors who plan to pursue research careers in the natural sciences, mathematics, and engineering.

A short time after learning of the Goldwater award, Coleman became one of 11 students at Lutheran colleges in the U.S. to win a Rossing Physics Scholarship, the second time she’s earned that honor. It is bestowed by the Thomas D. Rossing Fund for Physics Education, which created the awards in partnership with the Foundation of the Evangelical Lutheran Church in America (ELCA). Dr. Rossing was an accomplished physics scholar who wanted to support academically exceptional physics majors.

Coleman said both scholarships will help her pay for her final year at Gustavus, and they’re especially timely given that her younger sister is about to start her own college journey. “It will be tough for my parents to help pay tuition for both of us, so this was very welcome news,” she said.

Coleman has been building her research skills since she arrived on the Hill. It started with a First-Year Research Experience (FYRE) with the Physics Department’s Darsa Donelan . Then, in summer 2023, Coleman earned a National Science Foundation Research Experience for Undergraduates (NSF REU) at UC Davis to conduct research in which she made novel discoveries, based on mathematical modeling, of a galaxy’s gas flow. She’s now spending summer 2024 conducting research on gravitational waves at Caltech . “I’ve been super interested in space since I was little, and the FYRE work really cemented my interest in research,” said Coleman, who also finds time to play in the Gustavus Symphony Orchestra and the Women’s Nordic Ski Club, among other co-curricular activities. “FYRE gives our students a really unusual opportunity to do research at a high level, and I think it definitely made my applications for subsequent summer research opportunities a lot more competitive.”

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How realistic it is to change to a different field of mathematics after PhD?

Once I was told that in mathematics, after one gets a PhD, it is very hard to change one's field of specialization (within maths). Is this true? What are the reasons? How common are counterexamples?

In your answers please also specify what country are you talking about, if you believe it matters.

• mathematics
• changing-fields

• 1 You need someone who is prepared to invest some of his time and reputation into helping you into that new field. If you have a common goal (i.e. funded project) and/or something to give in return ... –  Karl Commented Dec 10, 2016 at 8:43
• It depends on what field you wish to change to. Could you kindly state or list out the field(s) you have in mind? –  Ébe Isaac Commented Dec 10, 2016 at 11:33
• 1 @ÉbeIsaac: I do not want to be too specific. Let me tell you one example from the past which is quite exceptional however. A. Grothendieck started in functional analysis and then switched to abstract algebraic geometry which is very different field. Are there analogous examples today? –  user65712 Commented Dec 10, 2016 at 11:58
• 8 Oh. So by changing specialization, you mean changing fields within Math, not across other fields in STEM, right? –  Ébe Isaac Commented Dec 10, 2016 at 12:02
• @ÉbeIsaac: yes. –  user65712 Commented Dec 10, 2016 at 12:19

6 Answers 6

I think it's quite misleading to hold up examples of very talented mathematicians or mathematicians from the distant past. The answer depends heavily on the field you want to switch into, hold closely related it is to the field you wrote your dissertation in, and how talented and hard-working you are.

In the most classical, long-established subfields of mathematics, there is a large amount of background one needs to learn to be able to do significant, original research. To take the worst example I know, a graduate student who wants to work in the general area of the Langlands program needs about 18 months to 2 years of dedicated study after their second year graduate courses to get to the point where they can tackle some problem of interest to the research community, and this is with an advisor to guide their study and steer them away from pitfalls that would result from having an incomplete knowledge of the field. (In particular, this means the graduate student likely still has some blind spots in their knowledge that would greatly slow down their research if they didn't have an advisor.)

A graduate student doesn't only have the advantage of an advisor; he or she also has a good deal more time. Most postdocs and almost all professors have more teaching responsibilities than graduate students, and professors also have service responsibilities which increase as one gets older. Furthermore, one also has to do enough research to write somewhere between one and two reasonably significant papers a year (depending on subfield) in order to be competitive for jobs that allow time for research and eventually to earn tenure in such a job. If one wants to switch into a new field, then one presumably has to do this research in their old field while learning the new field.

If someone in representation theory or algebraic geometry or other parts of number theory wants to switch to working on Langlands, then he or she needs to learn the material in one second year graduate course (because they already studied the other two or three that a complete beginner needs) and another 18 months of specialized study. It's true that some patterns of thought will be familiar, even if the specific ideas are different, so one is going to learn somewhat faster when one learns their second field, but moving into a new field still requires at least a year of dedicated study unless someone is an unusually fast learner or extraordinarily hard working. Most people don't have the time and energy to fit an extra year of work above their other duties within any reasonable timeframe. Fifty years ago, one could have given up a couple years of paper-writing to accomplish the switch, but someone trying that today would never get another job that allows significant time for research in today's far more competitive job market.

Most areas of research don't require as much background as Langlands, but unless one is moving into an essentially brand new field requiring minimal background, switching fields requires a substantial amount of time that one simply rarely has after obtaining a PhD.

Lack of an advisor can be an issue, but it is less likely to be one than lack of time. Many fields do have a significant amount of "folklore" that is well-known to experts but not clearly stated in print anywhere. These are usually ideas that are too advanced and specialized to appear in a graduate textbook, but at the same time too easy to be the subject of a research paper. At some point this folklore is used to establish more significant results in a paper, but since "everyone" knows it, it might not be explained very clearly or be easily found by someone who needs it for some other purpose. However, most fields have experts who are quite friendly and willing to explain the necessary folklore to new entrants to the field, and, at worst, one does things in a clumsy way in his or her first papers in a new field and has some folklore pointed out by a referee. If one appears talented and capable, then it is not so hard to get some help. Researchers in countries not connected to the international mathematical community (such as in Africa) generally face much more significant problems with having access to experts than people trying to switch fields.

Is it possible? Yes, but it's very hard.

• 3 Very good answer. I will only add that some transitions are easier than others, and this is not transitive! For example, moving from theoretical PDE to applied PDE is anecdotally much more common than the other direction. –  user37208 Commented Dec 11, 2016 at 3:29
• 1 Good answer. Just curious, what do you consider to be "second year graduate courses"? –  Alex Mathers Commented Dec 11, 2016 at 4:21
• 2 "classical, long-established subfields of mathematics" is a big caveat. In applied math, can be simpler to move between subfields, especially if there is some overlap in methods - e.g. maybe mechanics vs biology, but still numerical PDEs at the core. A bigger fraction of the needed knowledge in applied math is "domain knowledge" where a good advisor can guide a technically adept postdoc through the first project, and where the postdoc can then pick up the domain knowledge on the fly. –  AJK Commented Dec 11, 2016 at 4:43
• 1 @AlexMathers - in this case, it would be Algebraic Geometry, Algebraic Number Theory, Representation Theory, and Complex and Harmonic Analysis, all at a level assuming first year graduate courses covering a wide spectrum of Analysis, Algebra, and Geometry. –  Alexander Woo Commented Dec 11, 2016 at 13:31

Plenty of people change fields, and it is probably easier in math than in other disciplines, since we don't need any equipment. And for most people, the transition is very natural rather than forced.

Assuming that you were interested in the topic of your PhD thesis, when your interest changes gradually, so will the problems that you're interested in. But since many problems in modern mathematics actually require some training to even understand, the problems you're interested in are probably going to be in topics adjacent to your PhD thesis. And in this way, you can shift to various problems.

If you think that you're interested in a topic that is completely unrelated to your PhD thesis, be wary, because it should be really hard to judge whether a problem is interesting or not. It's very unusual to be interested in a problem without knowing any of the current techniques of the field, and you should remember that many of the cranks also approach problems this way. This being said, if you're able to find a mentor in this new field who is willing to work with you on a problem, then you might be able to overcome this difficulty.

There are many doctorates who have done their PhD in one specialization and moved their work to another. Receiving a PhD in a domain of specialization doesn't mean that they are confined to it. Mathematics is no different in this aspect.

Some of the Math professors I know did change fields and worked quite successfully. Mathematicians who work on widely applicable fields, such as statistics, computational mathematical modelling, linear and non-linear optimization methods, are considered to be versatile. They change fields and can even move across to nearly any other fields in STEM to apply their expertise.

If you are specific about counterexamples, here are a few:

• Jean-Michel Morel : PhD in partial differential equations; became a specialist in image processing
• Michael Atiyah : PhD in algebraic geometry, then moved on to index theory in differential geometry, then to Guage theory, a part of field theory
• C.T.C. Wall : PhD in cobordism theory in algebraic topology; a co-founder of the surgery theory in geometric topology
• Robert Langlands : PhD focussed on the analytical theory of semigroups, but is now known for representation theory and automorphic forms
• Ben J. Green : PhD in combinatorics, but also an expert in number theory
• Terence Tao : PhD in harmonics analysis, but is also known for partial differential equations, compressed sensing and analytic number theory, and several types of combinatorics

So, how realistic is it to switch fields in Mathematics?

It is very realistic. Most of the famous mathematicians (as in the list above) have done it and and there are evidence stating so many typical mathematicians current generation continue to do so successfully.

• 26 It seems to me that a variant of your argument can be used to show that it is very realistic to receive a Fields Medal. –  Carsten S Commented Dec 10, 2016 at 15:56
• 1 @CarstenS. :-) I see that my list is pretty confined to famous mathematicians. They were the first to appear on a shallow search. I just wanted to prove that it is possible . Besides, I found many people who did change fields but thought of giving a more verifiable set of examples. –  Ébe Isaac Commented Dec 10, 2016 at 15:59
• 9 No, Carsten is completely right, saying "it's possible because these Fields medalists did it" is the lowest possible quality answer you can give to a question like this. "Many famous mathematicians have ... and here is plenty of evidence typical mathematicians successfully switch as well" would be better –  user18072 Commented Dec 10, 2016 at 20:10
• @djechlin Thank you for the suggestion; I've made the necessary edit. –  Ébe Isaac Commented Dec 11, 2016 at 3:16
• 2 IMO it's a poor answer unless you actually supply this evidence. And honestly speaking, I don't really believe you as-is. Many questions are raised for what such a "typical student" looks like and how they accomplish this. –  user18072 Commented Dec 11, 2016 at 3:37

[EDIT] Just saw the comment on changing within maths. So yes, new discoveries are often made by linking apparently foreing, or weakly connected, areas. Think for instance about the proof of the Fermat conjecture by Andrew Wiles. I'l add other examples later.

The specialization you invest on in a PhD IS NOT you. A (well-chosen) PhD is a unique chance in life to focus on a topic for 3+ years, and what you learn can be deployed in many other domains.

On a general side, mathematics has become a tool for selection. And doing great in maths does not mean you cannot do something else. Mathematics stories abound about great mathematicians who hesitated between two paths before a PhD, for instance with Greek or Latin, when those where selection tools (a century ago). Mathematics is a (if not THE) common language of science.

On the local side, it also depends which the side of mathematics you are on, and your power of conviction with respect to the new field you want to play on. Optimization, functional analysis, combinatorics, logics, arithmetics, even topology can lead to a number of topics: data analysis, bioinformatics, economics.

I am a not a fully trained mathematician with electrical engineering background. My personal path was on pure arithmetics (Diophantine equations) and applied data compression. I switched to harmonic analysis (wavelets). I now apply what I learned (I mean the methodology) in data processing: chemistry, biotechnologies, engine management, even real-time simulation. Most of what I use comes from my shallow math background

Mathematical reasoning is a great tool.

I usually tell people something which is almost opposite (usually in the context of having an advisor who is inexpert in what the student wants to research): you can change your research area after you get your PhD, and this is fairly common.

Here are some points to keep in mind:

it's very common to work on other types of problems after you finish your PhD

often problems you work on (and this is true of most good problems) are related to other areas, so you may be naturally led to other areas from your present work. also most areas are closely connected to many other areas.

some fields are easier to get into than others (both in an absolute sense, and also depending where you are now)

you haven't specified what you consider to be "fields" (they could be defined quite broadly or narrowly)

many problems lie at the intersection of many fields, so possibly you could do something very similar and be considered in a different field. a lot of people in area say they do representation theory, some say they do number theory, and some aren't sure.

at certain stages of your career, you have less time (say in a given semester) to spend learning new mathematics. but also at certain stages of your career you have less pressure to produce theorems.

moving to different places/talking to different people can lead naturally to working on different problems

it's possible to dabble in different fields, or work in multiple fields at once

In my experience, most mathematicians enjoy learning new things and will end up working on different things throughout their career. Certainly the majority do not make a huge field shift (e.g., PDEs to geometric representation theory), but I think many (possibly a majority) of us shift quite a bit from our thesis to the point where it feels like we're doing a different kind of mathematics. Often this is gradual, but could be sudden, and we may float back and forth between different areas. I think most of the faculty at my department (at least among those whose research I'm fairly familiar with) have at least done some work out of their "comfort zones" (e.g., algebraic number theory to analytic number theory, Riemannian geometry to combinatorial probability, etc.)

In summary, I think it's not unrealistic to change fields, particularly if that's what you want to do. Personally, I have been a number theorist since grad school, but in the 12 years since my PhD have enjoyed (and continue to) working on other things in combinatorics, harmonic analysis, representation theory, hyperbolic geometry, finite group theory, etc as well--I just choose to stay a number theorist because I want to. Just be aware that (1) some areas may be hard for you to "break into," particularly without a mentor/collaborator, and (2) it may take some time to learn the appropriate things to transition.

An opening note, I am an undergraduate student, working towards becoming a research mathematician, so perhaps I am not qualified and experience enough to answer this question, but here goes

I do believe most research mathematicians have multiple areas interests among a few particular fields. Furthermore there often aren't well-defined boundaries between different fields of mathematics, if there were, well mathematics wouldn't be where it is today.

Obtaining a PhD is more an entrance to the world of mathematical research I would say than defining the type of mathematician you want to be. Though more often than not the topics PhD students would pick for their thesis would be closely related to the areas of mathematics they find interesting.

It doesn't mean that because you obtained a PhD in say Algebraic Topology, you are destined to be a Topologist for the rest of your life.

An example I can give, is that to study Algebraic Geometry (let alone write a thesis on it), one needs to have a good understanding of Analysis, Abstract Algebra, Commutative Algebra, Algebraic Topology and a bit of Differential Geometry. So I don't see why a mathematician who obtained a PhD in Algebraic Geometry couldn't also do research in Algebraic Topology, Differential Geometry or even in Algebraic Number Theory.

Different fields of mathematics are not as separated as you may think, apart from research in some of the foundational stuff I would say (Logic, Category Theory etc.)

• It sounds like you have more of a "field" view of mathematics research and less of a "problem" or "specialty" view. But I feel this would more accurately describe the experience of obtaining a Ph.D. and doing subsequent research. "Interdisciplinary" and "specialized" are not mutually exclusive. –  user18072 Commented Dec 11, 2016 at 3:40

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Educational resources and simple solutions for your research journey

What Next After PhD? Decoding Your Life After a PhD

Acquiring a doctoral degree is undoubtedly a momentous occasion worthy of celebrations—students can relax, unwind, and let go of the many stresses associated with the past few years of hard work. But soon, these celebrations are followed by questions on the steps needed to grow professionally after a PhD. In this post, I hope to guide you toward finding an answer to the question “What comes after a PhD?”

So what does life after a PhD look like? It is inevitable that your PhD will leave you with an array of skills that are transferable across different sectors. These could be technical skills that are domain-specific and, more importantly, broad skills such as project management, data analysis, and effective communication. Often, it takes a while after a PhD for students to acknowledge that they are indeed equipped with these skills. Hence, it is a good idea to create a portfolio, mapping different skills to the projects and tasks that were undertaken during and after your PhD.

Choosing the next step in your career and life after PhD would then trickle down to your personal preferences and leveraging your skills tactfully. If you’ve felt stuck with the question of what to do after a PhD, here are some career options to consider:

• Postdoctoral fellowship. After a PhD, if you are keen to continue doing research, you can pursue a postdoctoral fellowship in an academic institution and then work toward securing a tenure-track professorship. And while this path surely has its perks, especially if you want to set up your own research lab, it may be helpful to know that this is not the only worthwhile career path in life after a PhD.
• Industry research. If you are not keen on research in academia after a PhD, you can opt to join the industry directly or after a few years of academic or industrial postdoctoral fellowship. If you choose this life after a PhD, you may need to invest additional time and energy in understanding the differences in work ethic and culture between industry and academia. However, orientation to these aspects is usually part of the training that you might receive as a new employee. Upon entering the industry, you can expand your portfolio by exploring sales and marketing, product development, and business development options.
• Publication support. If you envision your life after PhD to be closely associated with research, but not directly involved in it, you can opt for careers in publication support, and work with publishers/journals or organizations specializing in scholarly communications.
• Science journalism and social outreach. If after a PhD, you are keen to explore your communication skills and contribute to filling the gap between science and society, you can opt for a career in science journalism/communication and can look for organizations that are involved in science outreach and social engagement.

If you have wondered about your career after a PhD, by now it may be clear that what comes after PhD is not a question you should stress about as there is no dearth of career options. However, here are a few additional points to consider helping you shape your life after PhD and to ensure that your career choice aligns well with your personal preferences.

• Financial aspirations. Financial perks vary drastically across the above-mentioned career options, and it is important to understand your personal financial goals before deciding what to do after PhD. Choosing an option that will help you grow both professionally and financially will keep you happier in the long run.
• Working in a team vs. working solo. As a PhD student, you may be used to working on your own and taking complete ownership of your projects and ideas. You may not always have this option in your life after PhD. It is important to acknowledge your preference regarding the change that might occur in an organization where you are expected to engage in teamwork and share credit for your ideas.
• Fixed work hours vs. flexible work hours . The doctoral journey is filled with unpredictability and you might have started getting used to the flexible work hours. However, after a PhD if you are planning to work in an organization where fixed work hours are a norm, then you might want to relook at your preferences and reconsider what to do after a PhD.
• Hierarchical vs. non-hierarchical work environment. This can be an important point to consider when assessing where you can thrive the most in your life after a PhD. A structured work environment, like an established company with a defined hierarchy may provide you security, stability, and opportunities for a steady rise up the career ladder. On the other hand, working in a non-hierarchical or non-structured environment like a start-up may require you to perform a variety of roles simultaneously, give you the flexibility and chance to explore new domains and acquire new skills regularly, and could be rewarding in its own way after a PhD.

Through this article, we hope you found an answer to the common conundrum of what’s next after a PhD. Ultimately, for a happy and satisfying life after PhD, adopting a growth mindset will take you far in your career, no matter which direction you choose.

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‘Pursue your dreams’: woman proud of mother, 53, graduating from top China university

• Woman comes to represent increasingly common trend of people getting degrees later in life

A mother in China has become an inspiration for her ability to balance work and study to earn a graduate degree from a prestigious university.

When the woman, 53, graduated from Fudan University in Shanghai, her 23-year-old daughter, identified as Xu, made sure to attend the ceremony.

Xu told the mainland media outlet Dami video that, in 2021, her mother had applied for the school’s Masters of Business Administration programme.

The mother, who was not named, spent two hours every evening studying for her courses.

Xu said: “My mum was very happy during her studies. My dad and I would usually help with household chores for her.”

The woman also held a full-time job while attending the programme, and successfully balanced her work and academic life with unconditional support from her family.

The mother’s certification means the entire family has earned graduate degrees. Xu attended the Chinese University of Hong Kong, and her father graduated from the South China University of Technology in Guangzhou in southern China.

When her mother successfully graduated from Fudan University, Xu said: “I’m very proud of my mum! Now, our family’s education levels are all the same.”

Having achieved success in both her career and education, the mother has inspired many young people on mainland social media.

One online observer said they forwarded this story to their parents, telling them: “Even as parents, you have the right to pursue your dreams.”

Another commented: “Parents are the best role models for children.”

In Chinese tradition, parents often see their children’s success as extensions of their own lives and achievements.

They often say wang zi cheng long to their children, which means “they hope their children will become dragons in the future”. This phrase conveys the parental aspiration for their children to become accomplished individuals with successful careers.

But now, more and more young people send similar expectations and blessings to their parents.

One netizen shared his father’s story on Douyin, saying: “My dad got his PhD degree at the age of 59. Over the years of his studies, when my dad would become anxious, my mum and I took him travelling and did everything to make him happy.

“I couldn’t be happier when I saw my dad fulfil his dreams. I was happier watching him than achieving my own success.”

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We’re So Back

The “get-your-ex-back” industry is booming. it really shouldn’t be..

Benny Lichtenwalner got married young. The father of four—who spoke to me from his Kansas City home in a salt-and-pepper beard and a pair of translucent, milky-white eyeglasses, and with the tiny outline of a heart inked at the tip of his right cheekbone—was raised in a devoutly Catholic family. His parents encouraged him to settle down with his first wife fresh out of high school, and perhaps unsurprisingly, Lichtenwalner was already divorced by his mid-30s. That was when he met the woman of his dreams. “She’s the polar opposite from my wife. She’s the fun tattoo girl, while my wife was rigid,” said Lichtenwalner. “And then she just crushes me. She breaks up with me out of nowhere. Cheats on me. The whole thing.”

The heartbreak brought Lichtenwalner to his knees, and he resolved to try anything to win the “fun tattoo girl” back. So he turned to the internet and sought the advice of so-called get-your-ex-back coaches—YouTubers, authors, and podcasters who have made their careers in the large and mostly uncertified world of breakup rehabilitation. These coaches offer their clients a proprietary set of psychological and rhetorical strategies that, they claim, will cause a former lover to return to the grasp of their dumped partner, restoring the relationship.

Lichtenwalner was particularly fond of Coach Corey Wayne, one of the original innovators in the field, whose marquee self-help video, viewed more than 1.6 million times, is titled “ 7 Principles to Get an Ex Back .” Lichtenwalner followed Wayne’s advice to the letter, and sure enough, “fun tattoo girl” orbited back into his life. Naturally, two months later, the pair had broken up all over again, but Lichtenwalner became obsessed with the process of romance restoration. In 2018, he decided to get into the business himself.

“I walked the path of a lot of this stuff, and I realized I could help other people,” said Lichtenwalner, who is now 43, and is remarried. “I got on TikTok, and started putting out all these videos, and I realized that the ones about getting your ex back tend to do well. So I switched up my whole brand to be focused on that.”

Today, Lichtenwalner, who goes by “Coachbennydating” on TikTok, has over 280,000 followers. He offers free advice on his page, where he distills general-use relationship axioms into bite-size, social media–friendly clips. In one recent video, Lichtenwalner— recording shirtless from a white-sand beach —outlines the “No. 1 one skill” needed to reattract an ex: The “emotional discipline” to refrain from overindulgences like double texting. But for a more curated experience, Lichtenwalner offers one-on-one coaching sessions, via a 45-minute Zoom call, at $350 a pop, where he promises to craft a more personalized recovery plan for a client’s romantic disaster. If those clients desire even more access to Coach Benny, patrons can shell out $499 for his personal phone number, allowing them to send two “500-character inquiries” about the current status of their breakup per day. This approach has been lucrative. Lichtenwalner claims to be making “multiple six figures” from his coaching.

“No more feeling lost,” reads Coach Benny’s website, outlining the texting plan. “Take control of your relationship and navigate any challenges that come your way.”

Breakups are a foundational part of life. They happen all the time. A couple might be unable to find equitable ground on a variety of existential questions—parenthood, faith, lifestyle—and call it quits. Or two people can slowly grow distant from each other, without either party being the sole author of the discontent, until they mercifully concede that the love has flickered out. Sometimes, a relationship can detonate in spectacles of pure id—ravenous infidelity, screaming arguments, sobbing in bar bathrooms, 200 texts per hour—eventually leaving both ends of the partnership feeling raw, extreme, and ideally, free . The point here is that relationships often come to an end for a good reason, but coaches like Lichtenwalner believe that with the correct approach, anyone who’s been recently dumped can devise a way to mend even the grisliest wounds.

But can anyone truly optimize their way back into the good graces of an ex? Breakups are an amalgam of soft, emotional truths. Can they really be cracked like a math problem with the help of good coaching? Lichtenwalner’s clients, who are all invariably stinging from the hallucinatory pain of a life-defining heartache, would certainly like to believe so.

“It’s at that price because that’s what people pay,” said Lichtenwalner, when asked if he possessed any hesitation about charging such a hefty cost for his services. “My schedule is packed back-to-back all week. Think of the worst breakup you’ve had. Would you try to solve it for the price of a PlayStation? I think if their ex said, ‘Hey, give me a PlayStation and we’ll be back together,’ they’d do it. I can sleep at night just fine. Because I love that I’m helping people.”

It is difficult to know how many get-your-ex-back coaches are working on the internet. There are a handful of big names in the sector, all of whom command sizable followings on social media and loom over the smaller players. Brad Browning, who advertises himself as the “Ex Back Geek,” has over 600,000 subscribers on YouTube , while Dan Bacon, with 431,000 subscribers, promotes a $297 Get Your Ex Back Super System, which includes a video detailing how to achieve “Ultimate Makeup Sex.” The majority of get-your-ex-back mentors tend to be men, though there are some women in the field, and the coaches themselves claim to work with clients of all genders. (Lichtenwalner said that his demographics skew slightly toward women. “Most women want a man’s perspective on things because they’re talking mostly to their friends about their relationship,” he said.)

In general, life coaching—in which dubiously certified experts offer for-profit consultations on the touchy-feely facets of ill-defined “self-improvement”—is in the midst of a legitimate boom period. The New York Times reported that there has been a 54 percent increase in the number of professional coaches between 2019 and 2022 . It’s a fair assumption that other, more specific avenues of mentorship might have seen similar growth.

The prices for get-your-ex-back coaching are notoriously expensive across the board. Lichtenwalner’s premiums are actually a tick cheaper compared with some of the other relationship coaches on social media. Lee Wilson, a 44-year-old from Tennessee, runs MyExBackCoach.com. A session with him comes in at $579 for a 70-minute call. “Coach Lee,” as he’s better known on the internet, tells me he got his start in this field at a Christian marriage counseling nonprofit, where he was tasked with the rehabilitation of couples who were considering a divorce. Around that time he also developed, and then sold, a dating site in the early 2000s, and he figured a leap toward a more secular brand of relationship advice was within his expertise. So, Wilson made his way to YouTube. He uploaded a video called “What Your Ex Is Thinking During No Contact” in 2018 , where he imagines the satisfying second guesses that might be running through the head of a former partner in the aftermath of a dumping. It racked up more than 2 million views, and shortly afterward, Wilson started offering his own courses.

“[An ex] will reach out with something casual like, ‘Just wanted to see how you were doing,’ ” he said, in that video, outlining how someone can slyly direct a separation toward reconstitution. “Tell them that you’re having a great week. … That’s how they can feel the same loss that you felt when they broke up with you.”

Wilson believes that every breakup is unique, and each is buoyed by a distinct flavor of conjugal strife. But he’s also confident that there are a few objective maxims that, when learned and deployed, can help a wide swath of people get their exes back. Chief among these is the principle of “no contact,” which is also endorsed by Lichtenwalner, and practically every other relationship coach on the internet. Essentially, in cases where an ex claims that their feelings have faded, Wilson encourages his clients to systematically shut off all streams of communication with them, while simultaneously directing their time in singlehood toward personal enrichment—trusting that a boost in their own self-esteem will eventually remind a former partner of the goodness they’ve abandoned.

“They see that you’re not going to chase them down, which prevents them from running further away,” explained Wilson. “And when they do start doubting their decision to break up with you, it’s easier for them to reach out, because they haven’t attempted to escape you.”

Versions of this basic doctrine are plastered all over Wilson’s YouTube channel, essentially repeating the same idea in slightly different ways. There are videos titled, “Stages of No Contact for Your Ex,” “Mistakes You Must Not Make During No Contact,” and “Psychology of No Contact on the Dumper.” Occasionally he delves into stranger and more conspiratorial territory, while still hitting the basic notes. Earlier this month, Lee published his take on how to win back a “brainwashed ex,” a condition he blames, in part, on peer pressure put on a former partner by their single friends who “make an effort to destroy a relationship.” Taken together, the catalog reads like an attempt to squeeze down the vast cerebral mysteries of a breakup into a parsable formula—to simplify kaleidoscopic pain with black-and-white sensibility.

The problem with this is that “no contact” is not exactly exclusive information. The method has its own Reddit community , its own Quora threads , and its own Forbes explainers , and I think I speak for pretty much everyone who’s ever been dumped when I say that a label-free variation of “go no contact” is the standard advice meted out by friends and family whenever we must recover from heartbreak. It raises the question: What exactly are people paying for, when they shell out nearly $600 to Coach Lee?

“I put so much energy into the calls. I usually go over the allotted time,” said Wilson. “I bring a lot to the table as far as helping someone to really see clearly when they’re in a situation where it’s very difficult to see anything but the pain. And that’s a vulnerable place to be. They think $570 is a cheap price to pay to alleviate the pain and win a person back. They want to win. They don’t want to lose. I’ve had people say things about the price, and my opinion is, ‘Well, I’m not making you do it.’ “

Both Wilson and Lichtenwalner are adamant that the time they spend with their clients over the phone is thoughtful, well-considered, and empathetic. They’re also steadfast that the best coaching they do is when they can speak directly to a client, one-on-one, and analyze their predicament from all angles. (“Sometimes I’ll tell them that getting their ex back isn’t worth the effort,” said Wilson. “That I think they’re better off trying to move on because of the situation.”) But Kelli Harding, a professor of psychiatry at Columbia University, questions whether a single-minded devotion to the rejuvenation of a lapsed relationship is the most effective way to heal from heartache. And she has concerns about the mental state a prospective client might be in when they charge their credit card a large sum for some coaching.

“A breakup can feel like your survival is at risk,” she told me. “It really is on that biological, physiological level. And if you suddenly have someone promising you a way out, it can be tempting to lay down the cash. Being in a situation where you feel under threat, there’s definitely some risk of … I’m cautious to use the word exploitation. But you’re definitely in a vulnerable period.”

Harding’s fear lines up with the experience of Jay Pimentel, a 27-year-old from Maui, who hired the services of Coach Lee last year to heal from what he describes as a torrid, three-month-long “situationship.”

“I ended up following every breakup coach imaginable on TikTok and watching every single video that could help me in my situation,” said Pimentel, recalling the fallout of his breakup. “I felt so desperate.”

Pimentel organized a free 15-minute consultation with Wilson, who recommended that he purchase his “emergency breakup kit.” It’s a service on his website that promises to contain an “ex-return formula,” brimming with videos and self-help guides, to “reignite the spark again” in their former lover. The large red button, leading to the payment portal, is marked with the words, “WIN HER BACK!” Pimentel said it cost him $60. He made the purchase, dove into the material, and pretty soon afterward, began to feel like he’d just been scammed.

“The general thrust is just, ‘Go no contact and work on yourself,’ which is already posted on all of their videos for free, and is just a mature response in general. But it’s not worth a $60 price tag,” said Pimentel.

Pimentel ended up using the no contact method to no avail. “It ended up being just an old tall tale,” he said, of its ineffectiveness. Pimentel has since moved on. He’s healed from the breakup and is enjoying a renewed sense of growth and self-knowledge—which is the silver lining of all heartache. But he continues to harbor ill will for all the dating coaches who inculcated a false sense of hope in him.

“These coaches prey on people desperately wanting to get their partner back, say that you ‘need’ to pay for their services, and that they will ‘make a plan’ for you,” said Pimentel. “But in reality we can’t control others. We can only control ourselves.”

Honestly, Pimentel was lucky to only spend $60. Another former get-your-ex-back client, who is 28 and asked to be kept anonymous, spent a total of $1,400 on a dating coach when he was 20 and languishing in the psychic destruction of his first major breakup.

“I didn’t get her back. No amount of coaching would have helped anyways, in hindsight,” he said. “I was pretty much willing to pay anything to invest in my happiness. Which, again, was pretty impulsive and felt kind of predatory, since relationship coaches know people are not thinking straight and rationally.”

For what it’s worth, Wilson reiterated to me that he never promises his clients that the advice he offers will be effective. “The other person is their own person, they have free will, and I’m not a mind reader,” he said. Lichtenwalner, meanwhile, argued that while he is confident that the coaching is sound, practical, and battle-tested, he has little faith that his clients will wield it correctly.

“The advice that I have to give is so emotionally disciplined that I do know that a lot of people aren’t going to be able to implement it,” he said. “I have to disconnect from the results in many cases.”

This all gets us back to the central question in the get-your-ex-back industry: Can a breakup be truly mended with the designs of a carefully orchestrated psyops campaign? It makes you consider how profiteers have sold the reassurance of calculable logic within the mercurial chaos of romance for ages. Lichtenwalner and Wilson both bring to mind the pickup artists of the mid-2000s, who advertised a similar set of pseudo-anthropological nightclub theories ( negging , approach anxiety , and so on) that, the pickup artists said, would increase the number of women a man could seduce during a night out. Naturally, Lichtenwalner tells me he is familiar with pickup artist dictums and regards his get-your-ex-back turn to be a nicer, more wholesome interpretation of those same dating schemes.

“The pickup artists were operating from a manipulative perspective. Everyone got a bad taste in their mouth from the cheesy pickup artists. But a good pickup artist is just somebody that learned charisma,” said Lichtenwalner. “There’s a tasteful way to have a charismatic effect on people, and that’s important for the guy who’s lost his wife, and his kids, and the empire they have together.”

It is nice to believe that human behavior could be so predictable, in the same way it is nice to believe that, one day, your ex will miraculously shed all of the points of tension that tore them away from you in the first place, leaving the two of you fully renewed. Unfortunately, just like a breakup itself, sometimes you need to live through the pain in order to accept the truth.

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Econ PhD... too late for me?