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Education Science

Is Math a Young Man's Game? 276

Bamafan77 writes "Slate has an interesting article on the relationship between the productivity of mathematicians and age. The conventional belief is that most significant mathematical leaps are all made before the age of 30. However, the author gives pretty compelling reasons for why this once may have been true, but is definitely not the rule now. Two of his more interesting pieces of evidence include Grigori Perelman's (probable) proof of the Poincare Conjecture at 40 and Andrew Wile's proof of Fermat's Last Theorem at 41."
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Is Math a Young Man's Game?

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  • Not too young (Score:5, Insightful)

    by Uber Banker ( 655221 ) on Saturday May 17, 2003 @08:22AM (#5979395)
    I think 40 is probably the peak between the tradeoff between knowledge accumulation and physical decline. But stand for a psychologist or neurologist to correct me.

    A bit like athletes maybe... experience vs. physiology results in a trade off.

    • Re:Not too young (Score:3, Insightful)

      by Uber Banker ( 655221 )
      Perhaps the increase in knowledge base necessary not to keep reinventing the wheel increases the experience in your equation... thereby pushing up the age of tradeoff?

    • Mathematics like computer programming I think is more easily tackled by young brains. There is a caveat though, in that as the complexity of the problem increases, the refinement of approach matters more than the brilliant math or coding tactics. So application architects with many years experience are much more valuable than a recent graduate (even though the recent graduate may be able to code faster). I think the same holds true for extremely complex mathematical problems-- sometimes it is the approac
  • by Anonymous Coward on Saturday May 17, 2003 @08:22AM (#5979397)
    I completely agree that math is a young man's game.

    I'm so old, I lost count. Damn wippersnappers and their meaningless symbols.
    • The conventional belief is that most significant mathematical leaps are all made before the age of 30.

      That sounds about right. According to another study, mathematicians reach their prime just before discovering sex, after which it is all downhill. It will give the old codgers some solace to know that they can expect a brief comeback after their wives stop having sex with them.
    • A young man's game? (Score:3, Interesting)

      by BrokenHalo ( 565198 )
      Ok, I'm a man, and I'm getting oldish (40) but it seems to me that the most brilliant of all the mathematics students (undergrad and post-) at "my" university are mostly female. And not necessarily under 40, either.
  • by Anonymous Coward on Saturday May 17, 2003 @08:26AM (#5979409)
    When you get married and have some kids it is real hard do get any work done..

    "Okay Dear I'll mow the lawn now"

    I also suspect the growing complexity of screensavers as a factor..
    • by Davak ( 526912 ) on Saturday May 17, 2003 @09:08AM (#5979511) Homepage
      Sorry, I don't have any mod points... but I'll blast away my Karma bonus... I agree.

      Thinking, exploration, calculation, research, experimentation--all of these take a great deal of time. Relationships with friends, your SO, and eventually kids require a great deal of this time to keep healthy and strong.

      If you want smart kids/pets, that takes time as well.

      No, I am not saying that one can't be productive or creative once older; however, it just becomes more difficult. Those that do it successfully usually do it though their profession. That is... you can do it though your job if they give you the freedom to do so.

      I don't think all of this is so bad... most of us would rather have healthy relationships than awards/accomplishments as we get older.


  • by morganjharvey ( 638479 ) on Saturday May 17, 2003 @08:30AM (#5979415)
    Two of his more interesting pieces of evidence include Grigori Perelman's (probable) proof of the Poincare Conjecture at 40 and Andrew Wile's proof of Fermat's Last Theorem at 41.
    Yes, but at the tender age of 22, I can not only add my bar tab together, but also figure an appropriate tip.
    Young people can't do hard math my ass.
    • Yes, but at the tender age of 22, I can not only add my bar tab together, but also figure an appropriate tip. Young people can't do hard math my ass.

      A single example is not a proof. You can use a single counterexample to disprove a statement:

      1. For all members of the group "young people," none can do hard math.
      2. I am in the group "young people" and can do hard math.
      3. The proposition is disproved; there exist members of the group "young people" who can do hard math.

      Note, however, that (3) does not prove tha

  • by cperciva ( 102828 ) on Saturday May 17, 2003 @08:31AM (#5979417) Homepage
    A century ago, mathematics was primarily a new field. New fields are characterized by inventiveness and a lack of prerequisite knowledge -- there isn't a lot of background to learn, and if you look at problems "the right way" you can get results very quickly. Most of mathematics is no longer a new field; in most areas, one must spend years studying before one can do anything new, and even then it's likely to be the result of long hard work rather than a quick new insight.

    Computer science is moving in the same direction, but is many years behind. Thirty years ago, computer science was a new field; there were few if any courses teaching necessary background material; and someone with the right insight could find very important work very easily. Now, we're starting to see movement away from that -- there is a body of important work to build upon, and anyone who hasn't studied that work will have "new insights" which simply reinvent already existing work.

    Mathematics is no longer a young man's game, and this is probably the last generation when computer science has been a young man's game. Next generation, the young will find a new field to excel in -- perhaps genomics?
    • by spyderbyte23 ( 96108 ) on Saturday May 17, 2003 @08:47AM (#5979455) Homepage
      A century ago, mathematics was primarily a new field.
      More precisely, there were many new fields within mathematics to explore. However, there was already quite a large body of existing knowledge. It's just that it was about as much as a sophomore engineering student knows(give or take).

      Now, as the article says, you are a graduate student -- and probably not a new graduate student -- before you're even looking at other people's cutting-edge work, let alone doing your own.

      • More precisely, there were many new fields within mathematics to explore. However, there was already quite a large body of existing knowledge. It's just that it was about as much as a sophomore engineering student knows(give or take).

        No way, dude. The original poster who said "A century ago, mathematics was primarily a new field" was way off base, and the follow up isn't any closer. Sophmore engineering students are pretty amazing, I know -- check out those concrete canoes! -- but their math curriculu

    • by Omkar ( 618823 ) on Saturday May 17, 2003 @08:53AM (#5979468) Homepage Journal
      Hmm, so the Greeks, Euler, Descartes, and thousands of other mathematicians don't count? Math is one of the oldest fields I can think of.
      • by Brian_Ellenberger ( 308720 ) on Saturday May 17, 2003 @10:06AM (#5979732)
        Hmm, so the Greeks, Euler, Descartes, and thousands of other mathematicians don't count? Math is one of the oldest fields I can think of.

        And yet, someone could learn and understand all of their most important discoveries before they graduate with a B.S. in Math. From what I've read of Andrew Wiles final resolution of Fermat's Last Theorem, it would take years of specialized study to understand.

        • Yes, we can learn the already discovered algorithms by the time we have a Math BS, but by then we are around 22. Our current system does not allow the best to advance at their own pace.

          I was reinventing Calculus by 8th grade. I was about to win second place in an international math contest. (I was beaten by a 9th grade Canadian.) I usually ignored whatever was being taught in Math class, since I could literally get an A without waking up.

          I was attempting to find the area under a curve defined by a form
          • This sort of thing really annoys me. I was in a similiar situation with computer science - The first time I saw a PC, I tried to rewrite windows to work on my spectrum, heh.

            My dream goal is to set up something like the school in x-men. Not the mutant part, but the school for the gifted.
            I know that sounds so ridiculous, but I think it would be beneficial, and would help a lot.

            I was so yearning for people to teach and help me when I was young, and I was lucky that I had a great headmaster at school who pu
          • ``French calculus''? I think you mean Leibniz' work, but Leibniz was German. Not french.
        • I think the original poster meant that generic RIGOROUS mathematics is a new field. Geometry has always tended to be rigorous, but many mathematical "discoveries" in the middle ages were conjectures, not proofs. Proofs were not popular until the 1800s in France, if I remember correctly. Now, mathematics is largely a creative sport, so the lack of rigorous proofs isn't necessarily a bad thing, because lots of important mathematical ideas aren't based on anything other than observation; the ideas behind ca
      • Greeks made some discoveries in geometry. But very little in other fields. They lacked our number system, so number theory was quite the pain. With the roman number system, this was even worse. On top of that, most of the mathematical knowledge of the greeks came from the pythagoreans, but they wouldn't let anyone in on their discoveries. So their knowledge died with them.

        In the middle ages people weren't very interestes in mathematics

        Then we finally get descartes, Euler, Fermat end those dudes, who
        • In the middle ages people weren't very interestes in mathematics

          You neglect the contributions of the Arabic and Indian mathematicians at your peril. There's a reason they call them "Arabic numerals," and the word "algebra" comes from the Latin mistransliteration of the Arabic mathematician who first wrote a dicourse on it.

      • Prostitution. That's older.
    • I might have picked a different example for a new field -- IMO, doing serious research work in genomics will require a very large body of context. Very substantial knowledge of both organic chemistry and cellular biology would seem to be mandatory, plus the rapidly growing body of knowledge about genomics itself. IIRC, human scientific knowledge is currently doubling roughly every ten years. The amount of time needed to learn enough to reach the "leading edge" where research is done is getting longer and
      • I was looking forward to a hypothetical future where working out the structure of a folded protein is easy, given the nucleotide sequence, but constructing a sequence which will result in a given structure is harder. I can imagine that the "programmers" who would construct such sequences would be very much like early assembly language programmers.
      • As a 34-year-old computational biology grad student, I've put a lot of thought into this. <g>

        Definitely, computational biology (of which genomics is a subset) is a field which requires experience in a number of other fields, and that takes time. I spent eight years in the Air Force as a medic; and medicine is applied biology, so when I started taking bio classes, I had a much better feel for the way living things work than most of my classmates.

        And I also did a lot broader work as an undergrad tha
  • by Anonymous Coward on Saturday May 17, 2003 @08:32AM (#5979421)
    0 to 5: Curious phase
    5 to 15: Productive phase
    15 to 40: Reproductive phase (some like to begin early and post longer :-)
    40 to 60: Consumer phase
    60 to ...: Irrelevant phase (atleast that's how it's treated by others)
  • ...that young mathematician are forced to spend 10 years or so learning old and flawed terminology and concepts.
    After that brainwashing people aren't simply able to do anything outstanding anymore. There are some accidential great scores, but they are very rare.
    I think we should change our mathematics education to tackle with this problem. And we should indeed already start in school were the first and the most foul foundations are laid. Instead of teaching children basic counting, set theory and algebra
    • Very impressive, no doubt you will gain the +5 insightful mod you're trolling for.

      In the meantime, WTF is a Lie group? WTF is an algebraic varity? Non-holomorphic sounds very impressive, but WTF is it?

      You might be right; I've observed that certain Asian groups do seem to have a handle on maths that many Western brains don't, and I doubt it's entirely due to genetics. But if you actually want to change things, as opposed to sounding clever, people have to understand what you're on about. I don't, and

      • A Lie group is a set that has a multiplication operation defined on it (giving it a group structure) and has a topology defined on it (giving it a manifold structure) in such a way that multiplication is a continuous operation (so if y is close to x, then z*y is close to z*x for all z). For example, the unit circle in the complex plain, with the usual multiplication operation is a Lie group, with the topology being just the induced topology from the metric on the complex numbers (so two points on the circl
    • by bj8rn ( 583532 ) on Saturday May 17, 2003 @08:58AM (#5979482)
      You'll say now: "That's not possible nobody can visualized 4 dimensional spaces."

      An architect, a physicist and a mathematician were asked whether they could imagine a 4-dimensional space.
      The architect said: "That's impossible! I can't draw that!"
      The physicist said: "Well, that can be done, if we say that time is the fourth dimension..."
      The mathematician said: "Let us imagine an n-dimensional space. Now, let n equal four..."

      • For great insights into the mind of a world class mathematician, please read A mathematician's apology [] by G. H. Hardy. Hardy was one of the top mathematician's of his era (1877-1947). Hardy is perhaps most famous for his discovery of Ramanujan [] and "A mathematician's apology" has a great Foreword by C. P. Snow documenting some of the details of the Hardy-Ramanujan collaboration.

        Here are some nuggets from "A mathematician's apology". (Hope the copyright police are busy elsewhere.)

        "No mathematician s
    • Dude can you please post that again in english?
      Since I wanted to know if you were trolling or if you were seriously trying to contribute something I looked at your posting history.Most of the posts were either classified as trolls or modded up as funny (though the posts seemed very similar to what you said in the post above).
      Since I still have not figured out what you are trying to accomplish I have no other choice but to ask you to repost that in a Language atleast some of us can understand.
      • He is trolling, but doing an exceptionally good job of it. The "bait the fanatics, while everyone else laughs in their beer" variety.

        Notice further down, where we start to see misspellings in the post come to light, and enough general inconsistencies. In fact, the parent's point simply has no legitimate claims (obivious to anyone who is even close to understanding the math involved), but everything is just close enough to be misinterpretted (comically) by charletan mathmeticians. A most excellent troll

    • Mensa member, beware of the high IQ
      Pretentious Mensa member, beware of the masturbation. For those of you in the first few rows, safety goggles have been provided.
    • On a serious note, I am an advocate of teaching The Calculus right after arithmatic. Algebra is almost a complete waste of time as is demonstrated when compairing many algebra problems and the number of steps taught to solve, vs. the "answer one line later" of The Calculus.

      Algebra can be relegated to classes dealing with spreadsheets and accounting.

      The counter "arguement" I have gotten from Mathematics teachers at all levels boils down to "the proper appreciation of [calc/algebra] will not be gained by t
      • Well, sorry teach, I do not recall anything from algebra that was ESSENTIAL for Calc.


        Can you demonstrate exactly how you'd go about calculating a limit without knowledge of algebraic manipulations? How about deriving/proving one of the rules for taking derivatives? What about any but the simplest of symbolic integration?

        The only thing I can think of that you *can* do in calc without at least some knowledge of algebraic manipulation is taking simple derivatives. And even then, you'd be doing it without understanding why the rules work, and you'd be unable to do many of the calculations that make derivatives interesting.

        There is plenty of more advanced algebra that is taught prior to calculus that teaches complex, laborious methods that are replaced by much simpler, cleaner ones when you learn calc, and you can argue that those could be bypassed. Personally, I found it valuable to learn the non-calc techniques first, both for what I learned for the process and for the appreciate it gave me of the ideas in calculus.

    • "That's not possible nobody can visualized 4 dimensional spaces."
      But this is only because your basic mathematical education fucked up your brain.

      I think you'll find that the problems that most people have with visualising spaces with more than three spatial dimensions is that our evolution has equipped us with excellent tools with visualising three-dimensional spaces, and in general found no need to help us visualise spaces with more dimensions. This should not really be surprising.

      In short, the problem
    • Ummmmmmmm (Score:3, Insightful)

      by Sycraft-fu ( 314770 )
      "But this is only because your basic mathematical education fucked up your brain."

      No, actually, it is because of our world and our perceptual makeup. We live and interact in 3 normal dimensions (time is special form a perceputal point of view). When you look at something in the real world, you see three dimensions. Be it an inherant thing, a learned thing, or some combination of the two, you are equiped to deal with 3-dimensional perception.

      Whenever you deal in higher space, you are limited by that in ter
    • The problem is not with modern mathematics, rather with modern mathematicians. Here's where the train comes off the rails:

      "Indeed most "Joe Adverage" problems can be reduced to Lie/algebraic geometry problems."

      No, most Joe Average problems are how to calculate 15% of a tab and how to bottom-line the monthlies on that house you're looking at and none of them reduce to abstract mathematical principles. It's great that there are a generation of brilliant new chinese mathematicians. It has nothing to do with
  • Andrew Wile (Score:5, Interesting)

    by Andrast ( 670757 ) on Saturday May 17, 2003 @08:42AM (#5979441)
    Also worked on the proof for Fermat's theorem for 7 years in secret(which in the mathematics community is a rather odd thing to do). He was dreaming of solving it while he was still a child. There is quite a good book on the subject for anyone with any level of knowledge called fermats last theorem. I'd give you a link but i'm tired..
    • Re:Andrew Wile (Score:3, Informative)

      by spaic ( 473208 )
      Check it out over at Simon Singh's [] website. Fermat's Last Theorem is great reading, not to mention The Code Book if you fancy cryptography, technology or just drama.

    • by Paul87 ( 201172 ) on Saturday May 17, 2003 @09:40AM (#5979628)
      I have discovered a truly remarkable link for that book which this margin is too small to contain.
    • The Book is "Fermat's Enigma" by Simon Singh. I highly recommend it. Singh has a talent for writing about deeply analytical subjects. He also wrote "The Code Book" about the history of cryptography, and he's written a Nova episode or two.

      I wish he'd written more books; an Amazon search turns up little else than these two.

  • by mactov ( 131709 ) on Saturday May 17, 2003 @08:46AM (#5979451) Homepage
    Definitely this is the women-not-invited dept., as billed, but it reminds me of a conversation I had with a 98 year old woman in 1982. I was 28, had a toddler and an infant, and was very much afraid that motherhood would be the end of any other kind of creative work for me. (The exhaustion factor alone was daunting.)

    Miss Mae said to me, in a Miss-Daisy sort of Southern accent, "Honey, women are not like men -- we get better with age. After all, you can't think straight until your parts settle. I promise, when you are 45, you'll know what you want to do with yourself, and it won't have anything to do with diapers."

    She was right about women, or about me, at any rate. I'm 48 and in my first year of professional school while the "baby" is at his first year of college. (What this has to do with my "parts" I am less sure.)

    What I notice is that my younger colleagues are quick and bright, but that what I lack in speed I make up in context. And all of us are passionate about what we are doing, but the flavor is a little different depending on age. When we are working well together, the combination of gifts is truly wonderful. Perhaps instead of framing the "game" (of math or of anything else) as a contest, we ought to be looking at ways to make progress that makes use of both the experience of age and the quickness of youth.
    • Definitely this is the women-not-invited dept., as billed, but it reminds me of a conversation I had with a 98 year old woman in 1982. I was 28, had a toddler and an infant, and was very much afraid that motherhood would be the end of any other kind of creative work for me. (The exhaustion factor alone was daunting.)

      Hey, would somebody mod this up? I love women, they are so mysterious. I would love an intelligent discussion of the differences between men and women's intellectual development.


  • Career path (Score:4, Insightful)

    by Anonymous Coward on Saturday May 17, 2003 @08:50AM (#5979466)
    Let's not forget that most pure mathematicians are University faculty members, and that the longer you're on faculty, the more committees you sit on and the more non-research responsibilities you end up stuck with.
  • The real question is whether or not great discoveries in a field come from someone being young and having therefore enough mental clarity or from an amount of exposure to a field, resulting a certain level of understanding.
  • Life expectancy (Score:5, Interesting)

    by glgraca ( 105308 ) on Saturday May 17, 2003 @08:59AM (#5979486)
    Could it be because not so long ago
    people usually didnt live
    beyond 40?
    • Could it be because not so long ago people usually didnt live beyond 40?


      The lifespan of a reasonably well-off individual hasn't been that short since the middle ages. Many of the youthful math geniuses of centuries ago died young because of various causes, but many of them also lived into their 70s and 80s.

      Also, the fact that "average" lifespan was short during much of history does not mean that there weren't plenty of individuals who lived to a ripe old age.

  • Young MAN'S? (Score:3, Insightful)

    by backlonthethird ( 470424 ) on Saturday May 17, 2003 @09:01AM (#5979491)
    What about young women?

    I know, I know: math, like so many of the things discussed here on /., is primarily an activity of men.

    But it seems to me that we would be much better served if we talked about how to get more women in the field, not how we could keep old men in it. I mean, aren't there enough old men around anyway?

    (spoken by a future old guy - hopefully)
    • But it seems to me that we would be much better served if we talked about how to get more women in the field

      It depends on the reasons that women aren't going into the field. If it is because of some "old boy's club" keeping them down, then that is wrong. If it is because women in general, for whatever reason, don't necessarily want to go down that path then no one should push them on it. Just make it equal for the women who want to be mathematicians.

      Women don't generally go to Star Trek conventio

      • The dynamics of school are changing, and changing rapidly. In this article [] in Business Week, it now looks like it's the boys that are at a disadvantage at school.

        I find this to be horribly unfortunate. Why is it that for one sex to excel, the other pays a price? This isn't right.

  • by Saint Stephen ( 19450 ) on Saturday May 17, 2003 @09:04AM (#5979499) Homepage Journal
    It's simple: Young mathemetician's aren't getting laid -- so they work like hell on on their maths. Since male sex drive peaks at 18, the less sex drive you have, the less driven you are to find another way to spend the time.

    Or maybe they got married and their wife nags at them to death and ruins their concentration.
    • Or maybe they got married and their wife nags at them to death and ruins their concentration.

      Speaking from experience, there, matey? *wink* *wink* *nudge* *nudge*
      Depending on what the nagging is all about, it might not be a bad thing, you know.
      With mathematicians working "like hell on on their maths", they may be
      nagging about being neglected in the bedroom -- I wouldn't mind being nagged about that...
      not at all...
    • I don't know about you, but my sex drive hasn't peaked yet. Then again, I'm an engineer...
  • by e**(i pi)-1 ( 462311 ) on Saturday May 17, 2003 @09:04AM (#5979501) Homepage Journal
    When visiting mathtutor [] one can see that even 200 years ago, many important discoveries were done in the later stages of the Mathematicians career. Stories like the ones about Abel or Galois distort the picture.

    More and more discoveries of younger mathematicians are achieved through collaboration or by standing on the shoulders of people with more experience (who tend also to be more generous with sharing their ideas without expecting credit).

    Mathematical knowledge continues to accumulate in a fast pace and only few of this knowledge has been absorbed in books. Chances grow that a young mathematician will discover something already known or to be a special case of a much more general result. Fortunately, there are better and better online databases [] but it also needs more and more time to dig through that material.

    The most productive age for a mathematician will grow also in the future. The same will happen in physics or computer science (as a previous post has pointed out already).
  • by Call Me Black Cloud ( 616282 ) on Saturday May 17, 2003 @09:07AM (#5979508)
    I can't believe that statement! I'll have you know that at 38 I'm just was I going to say? Hey, today's Saturday! The buffet has the early bird special today for dinner at 4pm! I'd better get the oil changed in my Oldsmobile first...

    The truth is I don't feel any older than I did at 25 (still like the same age women as a matter of fact), I'm in better shape than I was then, and if coding skills are any indication I'm sharper than my 20-ish coworkers. So there!

    Now if you'll excuse me I have to knock back my Ensure before I chase the kids off my lawn.
  • by fiiz ( 263633 ) on Saturday May 17, 2003 @09:09AM (#5979515) Homepage
    It can definitely be said that some mathematicians produced work at an early age. As the article said, many died early, some continued to produce work throughout their lives. And the body of maths has increased so much that it's much more work getting an good overview of a field.
    Note also that before the 19th century, scientific research didn't have the same place in society: it has grown quite a lot.

    But regardless of the mathematician's age, what has to be taken into account is the relationship between groundbreaking work, and sturdy, low-profile, everyday work that is achieved by the mathematics community as a whole.

    Without that, the breakthrough cannot happen: it loses its value, as it has no ground to stand on.

    This is of course relevant physics and astrophysics as well: if you didn't have people studying and cataloguing stellar spectra, you couldn't develop theories about distances, and, more crucially, n-dimensional cosmological models. Now remember, stellar spectra themselves are boring as hell, so are atomic spectra (the spectra that prompted quantum mechanics, etc.)

    There are a lot of romantic ideas in the non-scientific public about science: I meet them every day. Sometimes they are just funny, but other times you wonder about the image that society has of your work. Of course I am by no means degrading the value of scientific breakthroughs and original thinking: any deep thought is a process that I consider to be mysterious in essence.
  • by sonoronos ( 610381 ) on Saturday May 17, 2003 @09:39AM (#5979622)
    It took Andrew Wiles seven years to write a rigorous proof for Fermat's Last 'Theorem'. If he had started when he was 23 instead of 34, he would have proved it while he was 30, instead of 41.

    The real problem, of course, is that it wasn't until Andrew learned about the Taniyama-Shimura conjecture that he figured out the method for proving Fermat's Last Theorem. He then waited for 2 years before starting.

    Who I think is a better example of mathematician burnout is Yutaka Taniyama himself. He started his career at 28 - way old for a mathematician - and killed himself at age 31. A year after his mathematical prime. Coincidence? Maybe. But you never know...

    • The real problem, of course, is that it wasn't until Andrew learned about the Taniyama-Shimura conjecture that he figured out the method for proving Fermat's Last Theorem. He then waited for 2 years before starting.

      Actually it wasn't learning about the Taniyama-Shimura conjecture that was necessary, it was learning that Ken Ribet had proven that Fermat's Last Theorem was a consequence of the Taniyama-Shimura conjecture. Prove the latter and you prove the former. That didn't happen until 1986

    • >killed himself at age 31. A year after his
      >mathematical prime.

      30 is not prime.

  • by stomv ( 80392 ) on Saturday May 17, 2003 @09:42AM (#5979636) Homepage
    A counterexample:

    Paul Erdös. Read about him in this [] book.

    The man did math until he died of old age, at a pace of about 18 hours per day. He cared not for material things, as he lived out of a suitcase. He cared not for life's physical pleasures, as he (almost!) never even had a girlfriend, or boyfriend for that matter. He had his doctor perscribe speed to him, so he could work more hours on mathematics.

    An amazing read about a guy who I am amazed by, but also whose qualities I am glad I don't have.

    No, back to studying linear & nonlinear programming, stochastic processes, dynamic programming, and queueing theory for my qualifier on Monday.
  • The article [] is written, of course, from the viewpoint of the Theorem itself.

    A highlight:

    Did Yarosh, Cauchy or Kummer--or even Euler, for that matter--care that I was French? Or that I was born in 1637 in Castres? Okay, Euler might have. At first, he seemed different from the others. He'd spend every waking moment thinking about me. Oh, how that made me feel! But understand me? No. In the end, he was just like the rest, interested only in what I could do for his career.

  • OK, I've got karma to burn so mod me down, but...

    The abbreviation "math" really grates on me (outside the US it's called "maths"). It's not mathematic, it's mathematics.

    Don't get me started on sulfur either...

    • That's funny-- I always find it odd when the British and Indian folks call math "maths." It's an interesting cultural difference. And I disagree with your abbreviation argument-- "math" is a prefix of "mathematics" while "maths" is not. In fact, pluralizing "math" makes it seem like you concede that there does exist a "mathematic" singular, which you abbreviate to "math," and then pluralize again to mimic the original word.
  • by AxelTorvalds ( 544851 ) on Saturday May 17, 2003 @10:08AM (#5979739)
    Paul Erdos did important work up in to his 80s.

    A lot of very tallented mathematicians go down a dark road in their 20s, trying to prove the impossible, giving up prime years to fail at something and a few actually do prove something important and then are spent. Godel was nuts to start with and the work he did in his 20s pushed over the top.

  • not a lot of people ever achieve anything after the age of 30... but then again; not a lot of people ever achieve anything before that either!
  • by MisterMook ( 634297 ) on Saturday May 17, 2003 @10:33AM (#5979845) Homepage
    Of course the real reason that scientists might make more discoveries at advanced age than in past times is simple. Viagra. What's more inspiring than getting some tail?
  • by CastrTroy ( 595695 ) on Saturday May 17, 2003 @11:03AM (#5979983) Homepage
    Andrew Wiles' proof of the famous x^n + y^n = z^n equation having no proofs wasn't really just a breakthrough at the age of 41. He'd caught interest on this equation at the tender age of 10, and had been working on the thing his entire career. This was probably the dedication required to solve such a proof. Most people would have given up in the time it took him.

    Anyway, read Fermat's Enigma, It's a great book, even though it's about math, it is surprisingly interesting
  • by lildogie ( 54998 ) on Saturday May 17, 2003 @11:09AM (#5980007)
    I think that the proposition that mathematical breakthroughs are predominantly made in youth, whether true or not, relates not to the vigour of youth, but to the settling in of dogma.

    I've seen this proposition about physicists in more than one lay venue. It was made clear that most breakthroughs in physics were made by minds that had the flexibility to "think outside the box." The gist of the "youth" paradigm is that the more years dedicated to a subject, the more that the thought patterns get set in their ways, precluding the intuitive leaps that change the intellectual landscape.

    That being said, Wiles didn't just make some brilliant leaps. He worked damn hard on the details. It may have been more than 10% inspiration for him to prove Taniyama-Shimura (the real achievement for which Fermat was a by-product). Still, from what I've read about his accomplishment, his work was definitely more than half perspiration.
  • Is Math a Young Man's Game?

    Well, if virgins are men, then yes.
  • I read about a study some time back about how much more productive, in terms of publishing, Professors in Academia are until they get tenure.

    I've worked in and around Academic departments and I can tell you that you can sure see it. The Assistant Professors are busting their butts, late nights and weekends on their research and that immediately changes the day they get tenure.

    Some tenured Professors work hard on their research, those that really love the field. People who really love their field are wha

  • I think the mathematician productivity rule applies to musicians too. A lot of Western classical musicians have been most prolific in their early years. Of course, it's not that they stop writing good music after a certain age.

    Notable counterexamples are Haydn of the Classical period, who started writing his best symphonies after 50. Also, there's Beethoven, who wrote the 9th Symphony when fairly old and stone deaf.

    A quote attributed to Marvin Minsky: "Ever notice that mathematicians tend to be good at

  • by Imperator ( 17614 ) <slashdot2@omersh ... minus pi> on Saturday May 17, 2003 @12:25PM (#5980376)

    When a mathematician is in grad school or fresh out of it, she wants to publish as much as humanly possible, because having a 15 page CV helps one get tenure at a good university. So just about any thought she has that adds a tiny bit to the sum knowledge of humanity, she'll send to a journal. This is not to say she's not doing good work, just that she's publishing early and often. But that's what the tenure granting committees look for, so what else should she do?

    But when she gets older, she can settle down and try to tackle harder and more time-consuming problems--that's one of the reasons for the tenure system, after all. So she may not look as productive, but she's contributing her time to mathematics in just as important a way as she did when she was younger. Also, her experience will allow her to supervise research more effectively, and she'll find that her time is well spent supervising a number of graduate students, giving them advice and help in their research.

    On another note, remember that the vast majority of professional mathematicians will never solve a famous problem. And yes, every young mathematician tries to solve the Riemann hypothesis, but as he grows older he learns to spend less time on problems on which he's unlikely to make progress. There are exceptions to this, like Andrew Wiles. (And personally, if I had been on his post-tenure review committees during those 7 years, I'd have wanted to know what he was doing to justify a salary: mathematicians very rarely keep their work secret like that.) But while a mathematician in his 20s may be encouraged to try long-unsolved problems, he tends to grow out of it unless he's brilliant enough to have success with it.

  • Senility (Score:3, Funny)

    by Charles Dodgeson ( 248492 ) <> on Saturday May 17, 2003 @12:39PM (#5980429) Homepage Journal
    As Paul Erdos (active until his 80s) used to like to say:
    The first sign of senility is when you forget your theorems. The second sign is when you forget to zip up. The third sign is when you forget to zip down.
  • Isn't this idea an insult to all the doctors who have nearly doubled the human lifespan in the past century?
  • The other week I took an IQ test. I got the same IQ as my father. However he got 6 fewer questions out of 60 than me. How come? Well, he's older naturally. It seems that the brain slows by about 10% as you get older, (and interestingly below the age of 21 you're slower too). The IQ test score accounts for that age difference, and we ended up with the same score.

    But, 10% isn't that bad.

    So, I don't think it's biological. I think it's more to do with stuff like spare time, having a drive to do something, lo

  • The changes of travel made me forget my mathematical work. Having reached Countances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry.

    There's an ongoing discussion about how "smart" computers have to be before they will be indistinguishable from

  • A notable exception. (Score:3, Informative)

    by Tyler Durden ( 136036 ) on Saturday May 17, 2003 @03:39PM (#5981242)
    One mathematician whose ability didn't decline at all in his older years was Paul Erdos. He was making important contributions right up until his death at age 83. The only person who created more proofs than him was Euler. But if one included mathematical proofs which others made because of Erdos' help, he'd beat him.

    You can learn more about it from this [] book.

"Never face facts; if you do, you'll never get up in the morning." -- Marlo Thomas