Ultimate Mathematician

引用巴拿赫Banach的名言,体现举一反三的境界:

A mathematician is a person who can find analogies between theorems;

A better mathematician is one who can see analogies between proofs

and

The best mathematician can notice analogies between theories.

One can imagine that the ultimate mathematician is one who can see analogies between analogies.

Father and son Mathematicians

Mathematics, unlike Medicine, is hardly inherited, as in “Like father like son” running in the family.

There are some exceptions in the history, the most outstanding Mathematician family is Bernoulli.

http://en.m.wikipedia.org/wiki/Bernoulli_family

2. 祖冲之和儿子祖暅之
Zu Chongzhi (424 – 500 CE) and son computed the first
\pi = \frac{355}{113}
or
3.1415926 < \pi < 3.1415927

http://en.m.wikipedia.org/wiki/Zu_Chongzhi

3. Emil Artin and son Michael Artin: both great algebraists.

Old Mathematicians Live Young

J.J. Sylvester, who coined the term Matrix, pointed out that Leibniz, Newton, Euler, Lagrange, Laplace, Gauss, Plato, Archimedes, and Pythagoras all were productive until their 70s or 80s.

“The mathematician lives long and lives young,” he wrote.

“The wings of the soul do not early drop off, nor do its pores become clogged with the earthly particles blown from the dusty highways of vulgar life.”

Sylvester himself was his 82nd year, in 1896, when he “found a new enthusiasm and blazed up again over the theory of compound partitions and Goldbach’s conjecture.”

Another mathematician Harold S. M. Coxeter (9/2/1907 – 31/3/2003) attributed his longevity to love of mathematics.