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I am sorry if I am posting this question here; I thought that since I am looking for historical evidences of successful people in mathematics, so may not this question be an opinion-based one. And also not duplicate as it is not about getting PhD at later age or the like.

I am 30 years old; I have studied physics to masters degree, even though I liked physics but I left it mostly because I didn't find any strong talent to do a great thing in physics and I thought that I can achieve it in mathematics. It's been a few months that I have started mathematics from scratch and I am spending average 14 hours a day learning maths. Though I have found mathematics more fascinating than any other things but my strong stimulus to go ahead especially as a self-learner is hope to do a ground-breaking research and be successful in that.

My questions are:

1- Will my mind be biologically too old to do comparable to what Fields medalists or other brilliant people have done or maybe more (like Perelman's work)?

2- Would you let me know even one person in history who started or turned to maths at their 30s or late 20s, but did famous works?

Some notes:

  • My question is not about getting a PhD in late ages or be successful in finding an academic position (including research), although soon or late I have to get a PhD in math as well, especially because of being in math community and other advantages. BTW, works that are not considered breakthrough or even writing books in math for students are as invaluable as e.g. Perelman's work, I believe. Please consider that my questions are not about comparisons.

  • There were some people in history who got their academic degrees at old ages but they were 'in' mathematics from theirs youth or even childhood; so examples of these people aren't relevant since by starting math now I mean that I am 30, and I am just starting undergraduate books in maths.

  • Physics is not math or even close! For example, I learnt differential forms in general relativity texts but it was just about 10 pages in 430-page physics text. And now I see that almost everything in a simple topology text is new for me.

Thanks to everyone for reading and taking the time for the great responses. Really appreciate it!

MKR
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    Harish-Chandra switched from physics to mathematics at about age 25, and went on to produce some of the most important representation theory of the 20th century. There's not a significant biological difference between 25 and 30, but there might well be a significant biological difference between Harish-Chandra and everyone else. – Stephen Jun 22 '15 at 14:23
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    I don't mean to discourage you, but you should not expect to be able to produce Fields medalist quality work at any age. It's a good thing to aspire to but not a good thing to expect. – Matt Samuel Jun 22 '15 at 14:35
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    Karl Weierstrass originally studied law, but then pursued mathematics, and ended up making significant contributions to analysis at a relatively late age. Also, Paul Erdős, while a child prodigy, did continue to do exceptional work up until his death at age 83. –  Jun 22 '15 at 15:32
  • It is difficult to enter or return to math later in life for many reasons: the lack of any other experience being useful in the subject (cf. industry experience being useful in computer science, for example), the decline in the required creativity as one gets older, the assumption that the above is true even if it isn't, and so on. At the very least, math isn't really done outside academia, and you'll have trouble getting an academic position in math as a post-doc in your early 40s. – anomaly Jun 22 '15 at 15:36
  • @Stephen - Thank you very much for your example and the rest of your comment. Very helpful! –  Jun 22 '15 at 15:49
  • You might have a look at this post: Too old to start math. (You will find several other links there.) – Martin Sleziak Jun 22 '15 at 16:21
  • @MartinSleziak - I read all of it before I posted this. Thank you. –  Jun 22 '15 at 16:23
  • @anomaly: Is that true "trouble getting an academic position in math as a post-doc in your early 40s"? Here are a list of opposite opinions. But if you're really sure that age matters, your supporting reason(s) would be very helpful for me and I really appreciate your further comment(s) on this matter. PS - actually, I was supposed to leave academia for a long time as I thought age isn't an issue. Many thanks. – MKR Jun 23 '15 at 13:45
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    @MKR: Mathematics is unusual in that respect. Certainly no PhD program is going to summarily reject you for being too old, but there is an assumption in the field that you've done your best, most creative work by your mid-30s. It's not universal, but there are far fewer middle-aged postdocs in math than in, say, computer science. – anomaly Jun 23 '15 at 13:53

2 Answers2

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Must humans never get to do work that would get them a Fields medal, independently of the age at which they started doing math (or anything else)

Using Fields medals as a parameter of anything is simply absurd. Just don't.

Mariano Suárez-Álvarez
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    This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. – Mankind Jun 22 '15 at 17:02
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    Yes, I did read it. You asked «Will my mind be biologically too old to do something like what Fields medalists have done» and I am telling you that that is an absurd question. I am answering that (most of) your question is unanswerable. No one knows «how old» is too old for a Fields medal, and there is absolutely no evidence that there is even correlation with age. – Mariano Suárez-Álvarez Jun 22 '15 at 17:02
  • Voting to close would be more logical then... –  Jun 22 '15 at 17:05
  • Well, I disagree. Moreover, I cannot vote to close for my vote is binding. – Mariano Suárez-Álvarez Jun 22 '15 at 17:05
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    I don't think it is too difficult to see that what I wrote is an answer. I request you stop making these comments, which are quite off-topic. – Mariano Suárez-Álvarez Jun 22 '15 at 17:08
  • I very much agree with this answer. However we do acctually know "how old" is "too old": it's 40 years. – Winther Jun 22 '15 at 17:55
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    @Winther the question is not how old is too old to be able to get a medal but how old is too old to do something like what would get you a medal. One can certainly do something worth a Fields medal and not get a Fields medal, even when you are well under 40. – Mariano Suárez-Álvarez Jun 22 '15 at 19:15
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    @Mariano Suárez-Alvarez♦: the last comment is contrary to the provided answer, mate! – MKR Jun 23 '15 at 03:59
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    @MKR, huh? My answer very clearly states that most humans never get to do work at the level of a Fields medal (which is obviously true) and that has absolutely nothing to do with the content of my last comment, which states three facts: that the OP's question is not about how old is too old to get a Fields medal, that the question is about how old is too old to do work at the level of a Fields medal, and that one can certainly do work at the level of a Fields medal after 40 (and these three are rather indisputable, too) I suggest you read more carefully, "mate". – Mariano Suárez-Álvarez Jun 23 '15 at 12:55
  • @Mankind I thought Mariano's answer was fine. – zhw. Aug 06 '16 at 18:03
  • Why is absurd? why does it exist then? –  Oct 05 '18 at 04:32
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$1-$ Read here and its linked posts if you're looking for an analytic answer!

$2-$ Alexandre-Théophile Vandermonde started to study mathematics at 35, and began to publish in this field the same year. Eugène Ehrhart started publishing in mathematics in his 40s, and finished his PhD thesis at the age of 60. Marjorie Rice, an amateur mathematician with no formal education in mathematics beyond high school, did not begin studying tessellations until December 1975; as she was born in 1923, this means she was either 51 or 52 when she began, depending on her birthday. She developed her own system of notation and used it to discover three new types of tessellating pentagons and over sixty distinct tessellations by pentagons by 1977. Caspar Wessel published his only mathematics paper at the age of 54. Roger Apéry proved Apéry's theorem at the age of 63. ...

MKR
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