Do mathematicians and physicists peak early? I have heard it said that most of the great mathematicians did their best work before the age of 25. Thereafter, many of these men continued to make solid contributions, but not at the level of their earlier brilliance. Likewise for physicists-the late Richard Feynman was heading a major Manhattan Project research group at the age of 23.
Is there something peculiar about mathematics/physics that favor younger brains? Or does the “conservatism” set in-as humans age, they become resistant to new ideas?
In any case, I’m still working on my “big idea”-no time frame for fruition, so far!
What a timely question:
Yesterday’s xkcd.
Earlier, at least, than spelling brians! 
I remember reading of one eccentric elderly math genius (IIRC, he did not have a home or even a constant income, but basically was the world’s houseguest) who was considered somewhat of an exception for the fact that he continued to contribute meanngfully at an advanced age.
Exactly what I came in to post, dammit…I’m late to the party all day so far!
I wonder if it a “flash of insight” kind of thing. To some extent education railroads people into doing things as they have always been done. A young person may not “know” better when contemplating something his elders would think is crazy and so pursues it.
Sadly such brilliant insights seem generally limited to one per person per lifetime. Although at that level they may well spend a substantial portion of their lifetime refining just that one insight. They are still contributing in meaningful ways but nothing groundbreaking or new seems to come from them after that one flash.
Then we wait for the next one.
You speak of Paul Erdos.
Is Wizar are newly coined word for maths genius?
Well, it’s clearly a typo, but I doubt the original instance was ares.
(That xkcd strip depresses me greatly, or mirrors my existing concerns, at any rate; I so often feel just like the stick on the right)
There’s certainly a stereotype of the old, uselss mathematician. It’s often implied that the older math professors don’t do any research, but rather just attach their names to papers written by their graduate students. I even heard Orson Scott Card mention this stereotype during a graduation day speech while I was in college.
The only issue I have with it is that it’s not true. In fact, it’s the opposite of the truth. Graduate students in math generally attach their names to papers written by their professors, not the other way around. (I say this as a former graduate student in math.)
There’s also Mark Feinberg (no wiki entry that I can find) who contributed an article to The Fibonacci Quarterly in 1963 when he was 14, and died in a motorcycle accident four years later. Feinberg named and described so-called “Tribonacci numbers” (a sequence in which each member is the sum of the three previous members).
That seems like a fairly obvious and simple sequence; did he prove some surprising properties of it or anything? I mean, it’s a little impressive for a 14 year old, perhaps, but it’s nowhere near the level of accomplishment of Galois.
Prolly not. So what?
I’m sorry people. but listing various and sundry people who did “X” when they were young isn’t very helpful to the discussion. Aside from which, in math there are numerous counterexamples.
The following link may be of use.
Nothing; I was just curious if there was more to it, since you seemed to remember his name and story to an extent I found surprising. No hostility intended.
I got his info from Mathematical Circus by Martin Gardner, a copy of which I’ve had in easy reach for some 20 years and is this moment sitting in my lap like a hardcover cat.
Sylvia Nasar discusses this phenomenon in A Beautiful Mind.
In general it’s true that mathematicians tend to do their best work at an earlier point in their life than other academicians. It’s not consistently true though. For instance, there’s de Branges, who proved an important theorem at 52:
If anyone ever goes through his supposed proof of the Riemann hypothesis, fixes the problems in it, and discovers that it actually does prove what it claims to prove, that would mean that de Branges has proved an important theorem at 72.
In any case, so what? I’ve read that medievalists tend to do their best work from about 45 to 60. That’s because it takes so long to learn all the material and the methods that one can’t do one’s best work until later in life. I would think that’s true of most academic fields. I would imagine that that’s true of most careers in general.
It’s becoming less and less true that mathematicians do their best work when they’re young. The problem is that it now takes longer and longer for mathematicians to learn enough about their field to reach the important problems. Galois was able to do great work at 20 because it wasn’t as necessary then to learn huge amounts of background to understand the cutting-edge problems.
This article makes much the same point: