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Is Math a Young Man's Game?
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."
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..
Why me?
" is there anything really brain demanding or innovating you can do after 30?"
Demanding: Writing the GPL, starting FSF, the Hurd, travelling the world over, believing in yourself despite others jeering you - RMS age 50.
Innovating: Buying an OS from someone, putting it onto someone else's h/w, building up a monopoly, driving out others (using suspect means), releasing newer and newer OSes that do essentially the same things, generate obscene profits, etc. etc. - William Gates, Age 45 (?)
Life begins after 30, methinks.
If you keep throwing chairs, one day you'll break windows....
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.
-- Support Ometz le-Serev.
Could it be because not so long ago
people usually didnt live
beyond 40?
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).
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.
Davak
In a nutshell the grandmother can provide additional food resources to the weaned children of her child or her childrens mates (to increase their fertility) since she no longer has to provide those resources to her direct children and can produce excess to what she consumes.
Thus there is an evolutionary advantage to women surviving following their fertile years, and this advantage likely continues in different ways now.
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As far as age and mathematics go, though, I'd have to agree that the effects of age are, if not disappearing, then at least being shifted back a number of years. Not long ago, I had the fascinating realization that after 3 years of college, I know more mathematics than Euclid, Diophantus, al-Kwahrizmi, Fermat, Newton, Leibniz, Euler, Hamilton, and Abel. This is not because I'm some sort of mathematics genius (I'm not even a math major), but rather because there is simply more mathematics to learn now, and I merely came later than those guys. For centuries, the situation was such that almost all of the human race's mathematics knowledge could exist in few enough books to carry in your hands- namely, Euclid's Elements and Diophantus's Arithmetica, eventually followed by a few others like Fibbonacci's Liber Abacci. In the 17th-19th centuries, mathematics used these simple foundations to create an incredible wave of new mathematics. (Just take a look at Fermat's annotated copy of the Arithemetica.) Now the number of books written on some specialized part of mathematics like Lie algebras or K-theory could fill a library.
Also, mathematics works a bit differently than the natural sciences- it's harder to create a general survey course in mathematics. Just look at the way these subjects are taught- you generally take high school science courses in physics, chemistry, and biology, but math courses in algebra, geometry, and calculus. The specialization has to start much sooner because eachthing builds off of the previous. In my high school chemistry courses, I remember covering some basic p-chem, some orgo, etc, and in my physics courses there was mechanics, E&M, optics, etc.. I of course returned to all of these in excrutiating detail in my college course, but the simple point is that you couldn't do a similar thing with math. In physical sciences, you can give a broad overview of a subject, and then later reurn in depth, because there isn't such an elaborate hierarchy connecting all of the fields. Conversely, mathematics works more like a pipeline, shuttling students from simpler subjects (basic arithmetic, simple Euclidean geometry) to harder ones (integral calculus, diff eq, set theory). The pipe opens up at the top- areas of specialization become apparent, and a frontier is reached where knowledge in one field is not necessary for knowledge in another.
In fact, there are so many fields and subdisciplines now that it has become incredibly difficult to become a polymath (in the quite literal sense of the term) in the vein of Euler or Gauss or Riemann. The idea of a single person making revolutionary discoveries in both, say, topology and number theory is steadily becoming more remote. If this were to happen, it would have to be someone who spent a long time mastering several disciplines, i.e., an old person. It's a sublime paradox- in the past, incredible leaps of insight that would connect disparate theorems and fields of math could only be made by the young mathematicians with the creativity and the daring to do so (or, if you're cynical, the neuronal plasticity), but now such individuals will still be in grad school learning the ropes.
Look at Andrew Wiles- it took him years to learn enough a
"FDA staff reviewers expressed concern about the number of patients who were left out of the study because they died."