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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?

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    $\begingroup$ 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
    Feb 28 at 9:43
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    $\begingroup$ 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
    Feb 28 at 9:44
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    $\begingroup$ This post is also tangentially related: Too old for advanced mathematics? And maybe you can find some related posts also on Academia. $\endgroup$ Feb 28 at 9:46
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    $\begingroup$ Lefschetz started his PhD at age 33. So no age is too late. $\endgroup$
    – Kapil
    Mar 1 at 12:03
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    $\begingroup$ @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. $\endgroup$ Mar 2 at 11:08

8 Answers 8

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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.

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    $\begingroup$ @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
    Feb 28 at 19:28
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    $\begingroup$ 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. $\endgroup$ Mar 1 at 8:34
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    $\begingroup$ 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
    Mar 1 at 14:31
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    $\begingroup$ 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. $\endgroup$ Mar 2 at 4:42
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    $\begingroup$ @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
    Mar 2 at 10:04
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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.

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    $\begingroup$ 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. $\endgroup$ Feb 28 at 18:31
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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.

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    $\begingroup$ 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. $\endgroup$
    – Matt F.
    Mar 1 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. $\endgroup$ Mar 1 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. $\endgroup$
    – Matt F.
    Mar 1 at 18:09
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    $\begingroup$ @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. $\endgroup$ Mar 1 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. $\endgroup$
    – Matt F.
    Mar 2 at 16:38
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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.

BUT

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.

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  • $\begingroup$ Do your parents support this career? Is it not easy to overcome some anxiety of peer pressure in this process? $\endgroup$
    – Alex
    Mar 1 at 14:16
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    $\begingroup$ 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
    Mar 1 at 14:39
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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.))

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  • $\begingroup$ 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
    Mar 1 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
    Mar 1 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. $\endgroup$
    – Matt F.
    Mar 1 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
    Mar 1 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
    Mar 1 at 19:53
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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.

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  • $\begingroup$ how come? if i may ask $\endgroup$
    – tomos
    Mar 2 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. $\endgroup$ Mar 2 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
    Mar 2 at 19:01
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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

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    $\begingroup$ Which field are you working in? $\endgroup$
    – Alex
    Mar 1 at 12:18
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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.

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  • $\begingroup$ 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). $\endgroup$
    – Matt F.
    Mar 1 at 18:47
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    $\begingroup$ 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. $\endgroup$ Mar 1 at 20:41

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