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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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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...
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.
Support a few technologists in Washington.
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 finally got the math ball rolling. But it didn't get REALLY interesting until in the twentieth century.
In that light, mathematics, at least modern mathematics could be considered young in the beginning of this century.
And that's the same math that's getting old now.
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."
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.
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 formula. It seemed appropriate to do the work in math class. One day, my eight grade math teacher asked what I was doing. I showed him my current theory. He told me that there was already a proof that it was impossible, so I moved it from active work to the "known impossible, but cannot stop trying" category that includes a simple formula for discovering factorials.
If he had mentioned the word "calculus", I would have researched what was already done and continued with new discoveries. Or he could have encouraged me to repeat the discovery. Instead, he told me it was PROVEN IMPOSSIBLE.
Personal note: This was an important event in my life, because a few years later they tried to teach Pre-Calculus. I immediately absorbed the entire book, and then taught myself Calculus. But I could have done that a few years earlier. And it was the first time that I had proof an authority figure lied to me. The realization that adults have no clue even in their specialty was a major part of my maturing. Now I question facts even when the person giving them is the "top authority".
If our education system helped students that showed an aptitude for math to advance at their own rate, they would probably be finding better algorithms for known problems, with the possibility of discovering something new, as a teenager. Tiger Woods specialized in golf starting at age 3. Most Ice skaters, gymnasts, and dancers start before they are 6. Why should mathematicians need to wait until college before specializing?
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Off-topic details: I was reinventing Newtonian Calculus. Newton invented a system about the same time the current system was discovered by the French. Both systems were used for a time, but further advances (Differentials) were only possible using the French version, so Newtonian Calculus was dropped. So it was unlikely my redicovery would help advance today's knowledge, since it was on a dead branch.
I spend my life entertaining my brain.