Mathematicians who were late learners?-list

  • It is well-known that many great mathematicians were prodigies.

    Were there any great mathematicians who started off later in life?

    Am I the only one bothered by "well-known" and "great"? Unqualified by context, these are unreliable terms at best.

    So is "prodigy." But I think the intent of the question is clear.

    My only response is a strong desire to go in and add [citation needed] to the first sentence.

    Is it time for this one to die? I am not sure it would survive if it was started today.

    "... many great ..." sounds like an oxymoron. Actually, this is a huge World, and there is no contradiction in the quoted phrase.

    Am I the only one bothered by "mathematician" and "many"? Unqualified, etc..

    I'm 26, currently in my last semester undergrad. studying Physics and Mathematics. You have no idea how encouraging this thread is.

    This question helped me despite having been deemed "unlikely to help any future visitors."

    I want to absolutely thank you for this thread. I am 18 now and I feel that I do not know enough mathematics to make anything out of myself in the future. This thread gives me hope that if I work hard enough, I'll make it. Thanks.

    So amusing the self-assuredness of the claim 'unlikely to help any future visitors' :). Looking for something completely different, this popped up 2nd on the search results. As someone for whom too much had got in the way of studying math post grad but now finally what I need to do move toward a PhD having just turned 40, this thread, which presented itself inexplicably (my search string was literally 'abc report'!!), has hugely helped me and am very grateful to all the contributors. I've saved a copy of it lest it be lost, and I know I'll be coming back to it in years to come. Thank you.

    They say that Leibniz only started learning mathematics when he was 24, but I'm not sure if this is true. He probably only started dedicating himself fully to it when he was 24, but most of had some prior exposure to it throughout his education and prior studies.

    I want to add one more person to the list. Although she's an engineer, her story is really inspiring. That is no other than Barbara Oakly (

  • Joan Birman went back to grad school in math in her forties, and is now one of the top researchers in knot theory.

  • Karl Theodor Wilhelm Weierstrass (Weierstraß) Follow this link


    Andrew, all-caps is considered impolite on the internet; it's equivalent to yelling.

    I disagree. All-caps is equivalent to speaking more loudly. Depending on the context, just like in personal conversation, this can range from yelling to genuine excitement (to a variety of other things). In this case, it's clearly an all-caps of excitement, which in personal conversation would not be construed as impolite.

    I consider them to be more gauche than impolite. I see it more of issue of something losing its original impact due to overuse during certain periods of internet development. It's the discussion forum analogue of the dancing baby animated gif.

    SIGH.I can't win in here.........

    In these comments, limited as they are, there is * and ** and then all caps.

    (@Andrew: that was a loud sigh :-)

    Was just reading Sadri Hassani's book! Weierstraß was a "champion beer drinker" and a first rate fencer. Almost 40 when he published his first paper.

    Your statements about the equivalence of all-caps and yelling are unproven, and while the proof of the statement in one direction is well known and trivial, the other direction remains an open problem.

  • She didn't get started late, but I do know that Alice Roth wrote an important thesis in 1938, took 35 years off from research, and then did very beautiful and influential work in complex approximation starting at age 66.

    WOW. A great example and a tragic reminder of the pathetic status of women in Western Culture for most of human history.

    @TheMathemagician Not only "western" culture. If you want to really be depressed, read about historical treatment of women in the East.

  • According to this Notices article, Raoul Bott was undistinguished in high school, but displayed impressive talent once he reached graduate school (though his thesis was actually in electrical engineering, rather than mathematics).

    I used to play hockey with (sometimes against) one of his former grad students -- who was a student of Bott's back when Bott was an electrical engineer. One game our teams got into a bench-clearing brawl. We skated up to each other and started talking about Morse functions on manifolds. The person I'm referring to is Dave Delchamps, at Cornell.

  • I don't think that Stephen Smale really distinguished himself until after graduate school.

    Somewhere there's a wonderful letter of recommendation written for Smale by one of his professors at Princeton. The letter basically says (in the first sentence) that Smale didn't seem very good until his final year, when he solved several open problems. The writer then suggests his improvement might be due to his having gotten married that year. The remainder of the letter is a digression about Smale's wife. (Does anyone know where this letter appears? I can't think where I might have seen it. My best guess was Stalling's webpage, but it's not there.)

    Smale basically corroborates Ben's answer in his interview for More Mathematical People.

    @dan: Smale's PhD is from Michigan -- perhaps you were thinking of the letter from Ray Wilder that appears at the bottom of the page here, and mostly on the top of the next page:;lpg=PA37&ots=PbP5jaTaQM&dq=stephen%20smale%20wife%20letter&pg=PA37#v=onepage&q&f=false The book is "Stephen Smale: the mathematician who broke the dimension barrier" vy Steve Batterson

    The letter from Wilder is also available on the 4th page of this pdf file from the Notices

  • Eugene Ehrhart (of Ehrhart polynomial fame) was born in 1906, taught in various French lycees (high schools), began his work on geometry in the 1950's, did his best work in the 1960's, and received a Ph.D. in 1966. See

    Awesome,Richard-thanks! And thanks for finding the time in your really busy schedule to post here.

  • Well, there's Witten. He got his degree in history, then attempted to be a political journalist and get a grad degree in econ before looking into physics and math, but got the Fields Medal.

    I am not sure that simply the fact that his first degrees were not in Physics or Mathematics is enough to deduce that he was a late learner. His father, Louis Witten, is a well-known relativist. Perhaps he was "home-schooled" :)

    Exactly.This thread,to me,is supposed to be about people who were at an age the rest of the world has given up on them and go on to have strong careers.

    economics is too hard.

  • Here, Rob Kirby describes some of his experiences as an undergraduate at Chicago, and how he "snuck into graduate school".

    As an undergraduate, I'd been far more interested in chess, poker, and almost any sport, than in the game of mathematics. I had little chance of getting into a good graduate school. However, I failed German and didn't get a B.S. in four years, so in my fifth year I took most of the graduate courses on which the Masters Exam (really a Ph.D. prelim) was based. With a B.S. I asked to be admitted to graduate school so as to take the Exam. They cautiously said yes if I got grades closer to B than C in the fall quarter. I got a B and a C (measure theory from Halmos and algebraic topology from Dyer) and a Pass, and no one told me to leave.

    The Masters Exam could have four outcomes: you could pass with financial aid, pass without aid but with encouragement, pass with advice to pursue studies elsewhere, and fail. I got the third pass, but really liked Chicago and turned up the next year (1960) anyway.

    Great story,Kevin. Don't know if Kirby qualifies in terms of age,but sure shows grades don't mean squat when determining the potential of someone to be a mathematician!

    So at the time the University of Chicago had a test you could take that guaranteed you admission to grad school?

  • Sophus Lie didn't become interested in mathematics until after university, and before then didn't seem to have shown significant aptitude for it.

  • Somebody who probably fits the bill here is Albrecht Fröhlich who after fleeing Nazi Germany as a teenager, eventually attended university only when he was about 30. He later went on to jointly organize the Brighton conference which put class field theory on the mathematical map, essentially create a new branch of number theory and produce his most important work well into his fifties.

    There's a biographical memoir here.

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Content dated before 6/26/2020 9:53 AM