Israel Gelfand, the student of Kolmogorov (the Russian equivalent of
Gauss), created in 1964 the famous VZMSh, a national Math Correspondence School.
He wrote: “4 important traits which are common to Math, Music, and
other arts and sciences:
4th Crazy ideas.
The Russian mathematicians also built special Math-Physics schools:
Moscow School #7, #2, #57 (one of the best high school in the world, http://www.sch57.msk.ru) Leningrad Schools #30, #38, #239 (Perelman studied here)
Rukshin at 15 was a troubled russian kid with drink and violence, then a miracle happened: He fell in love with Math and turned all his creative, aggressive, and competitive energies toward it.
He tried to compete in Math olympiads, but outmatched by peers. Still he believed he knew how to win; he just could not do it himself.
He formed a team of schoolchildren a year younger than he and trained them.
At 19 he became an IMO coach who produced Perelman (Gold IMO & Fields/Clay Poincare Conjecture). In the decades since, his students took 70 IMO, include > 40 Golds.
Rukshin’s thoughts on IMO:
1. IMO is more like a sport. It has its coaches, clubs, practice sessions, competitions.
2. Natural ability is necessary but NOT sufficient for success: The talented kid needs to have the right coach, the right team, the right kind of family support, and, most important, the WILL to win.
3. At the beginning, it is nearly impossible to tell the difference between future (Math) stars and those who will be good (at IMO) but never great (Mathematician).
Andrei Nikolaevich Kolmogorov (1903-1987)
Russian great mathematician with unique teaching style:
1. He didn’t lecture, just ask questions, waiting for remarkable answer.
2. He introduced literature, music, hikes, excursions, expeditions.
3. He didn’t mind if students didn’t become mathematicians, as long as they had broad outlook and unsatisfied curiosity.