From: Matt Jensen (firstname.lastname@example.org)
Date: Tue Jan 02 2001 - 17:14:44 PST
There was a good article last month in the Chronicle of Higher Education:
"Are mathematicians past their prime at 35?" Unfortunately, they charge
for access, so the cheaper route is to buy just that article, at...
If I recall correctly, the average age of first significant work is around
38, and the average age of last significant work is in the late 40s.
It's ironic that some mathematicians, who aim for precision in their work,
can throw out generalities about math and age with words like "nobody" and
"never". There are undoubtedly smooth curves describing populations of
mathematicians, even if they are skewed. A good example of >35yo success
is Andrew Wiles, who's basic solution to Fermat's Last Theorem came when
he was 40 , the final answer coming when he was 41 1/2. He said "It
was the most important moment of my working life." True, 41 1/2 is not as
impressive as 61 1/2 would be, but it's significant in that Wiles had been
working on Fermat's theorem for most of his working life, so it runs
counter to the idea that a mathematician needs to an area new to him (as
young mathematicians inevitably do) in order to produce great work.
BTW, I was looking for another reference on this topic, and stumbled on a
report about "anzan", an ancient Japanese technique for impressive mental
calculations. Schoolchildren practice it, and then compete in events.
e.g., "Tsuchiya, for example, takes only a few moments to solve a problem
like 992.587318 divided by 5,647.723" Very interesting stuff.
On Tue, 2 Jan 2001, Stephen D. Williams wrote:
> '30', as evidenced by the mathematical '25', is probably relative to a field. > Few doctors have the experience to innovate drastically at 30. Of course, in > the medical field innovating is tough in any case. Ice skating and gymnastics > place that number far lower, although it may be the coaches who are innovating > sometimes through others. > > Not to mention exceptions to this everywhere. > > Certainly the distractions and responsibilities of a family between late 20's > and early 40's makes a big difference to large numbers. The latter makes risk > taking seem selfish to most. > > sdw > > Dave Long wrote: > > > > > The "Thirty Hypothesis" is the belief that one's useful life ends at > > > 30. This rule was first proposed by Rohit as the "Mathematician's rule > > > of 25," which states that anything that was ever useful in mathematics > > > was discovered and/or proved by a person by the time s/he was 25. > > > > Aristotle (Rhetoric) says young men would rather do noble > > deeds than useful ones, but old men would rather do useful > > than noble. By his definitions then, this hypothesis > > should read "one's noble life ends at 30", for I believe > > the reason that the young people make all the discoveries > > is the older ones are too busy exploiting what has already > > been discovered. > > > > Kaufmann (The Origins of Order) points out that on rugged > > fitness landscapes, those which have a large number of > > local optima, adaptation shows two phases. In the first > > phase, the initial point is poorly adapted and variants > > in its vicinity are only slightly fitter, but variants > > at a long jump away can be very much fitter. Once a fit > > segment of the space has been discovered, however, the > > variants at a distance are usually less fit, whereas the > > variants found locally may be slightly fitter, and so > > adaptation climbs a local hill in the second phase. > > > > Young mathematicians and engineers are in their first > > phase, so they make the long jumps, the "discoveries". > > Older ones have a sense of gradients in the landscapes > > of their fields, as well perhaps as a sense of their > > own fortes and foibles, and so limit themselves to the > > main chance with the goal of doing useful work. > > > > -Dave > > > >  "They are too fond of themselves; this is one form > > that small mindedness takes. Because of this, they > > guide their lives too much by considerations of what > > is useful and too little by what is noble -- for the > > useful is what is good for oneself, and the noble > > what is good absolutely." > > > >  "The race is not always to the swift, nor the battle > > to the strong, but that's the way to bet." > > -- > email@example.com firstname.lastname@example.org swilliams@Jabber.com > Stephen D. Williams Insta, Inc./Jabber.Com, Inc./CCI http://sdw.st > 43392 Wayside Cir,Ashburn,VA 20147-4622 703-724-0118W 703-995-0407Fax Dec2000 >
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