Three mathematicians

There are many outstanding individuals, who have done for humanity much more than Olympic gold winners and many entertainment celebrities, but the wider public does not know their names. I have written already about Bartini. Today, I would like to honor three mathematicians.

I learned about them accidentally and was impressed by their lives and achievements. The common theme among them is giant productivity and amazing humility – both are features of true genius. Not to take a lot of your time, I will mention only a few facts that impressed me the most and provide links, so you would be able to read more, if you like.

In 1958, Alexander Grothendieck (French, aged 30) announced a massive program to rewrite the foundations of geometry and conducted a seminar that met 10 hours a day, 5 days a week, for over a decade. Every day he talked and the seminar participants took notes, went home, filled in details, expanded on his ideas, wrote final drafts, and returned the next day for more. Jean Dieudonne, a mathematician of quite considerable prominence in his own right, subjugated himself entirely to the project and was at his desk every morning at 5AM so that he could do three hours of editing before Grothendieck arrived and started talking again at 8:00. The resulting volumes filled almost 10,000 pages and rocked the mathematical world.

In 1966 he was awarded Fields Medal, often described as the “Nobel Prize of Mathematics.”

In 1988 he declined the Crafoord Prize with an open letter to the media. He wrote that established mathematicians like himself had no need for additional financial support and criticized what he saw as the declining ethics of the scientific community, characterized by outright scientific theft that, according to him, had become commonplace and tolerated.

In 1996, Grigori Perelman (Russian, aged 30) turned down the prestigious prize of the European Mathematical Society.

In August 2006, Grigori Perelman (aged 40) was awarded the Fields Medal for “his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow.” Perelman declined to accept the award or to appear at the congress, stating: “I’m not interested in money or fame.”

On 18 March 2010, it was announced that he had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. The Millennium Prize Problems are seven problems in mathematics that were stated by the Clay Mathematics Institute in 2000. A correct solution to any of the problems results in a US $1M prize being awarded by the institute. The only solved problem is the Poincaré conjecture, solved by Grigori Perelman in 2003.

On 1 July 2010, he turned down the prize, saying that he considered the award unfair and that his contribution to solving the Poincaré conjecture was no greater than that of Richard Hamilton, the mathematician who pioneered Ricci flow with the aim of attacking the conjecture. He also turned down the prestigious prize of the European Mathematical Society.

In 1985, Shinichi Mochizuki (Japanese, aged 16) entered Princeton University as an undergraduate and graduated salutatorian in 1988. He then received a Ph.D. under the supervision of Gerd Faltings at age 23. In 1992, he joined the Research Institute for Mathematical Sciences in Kyoto University and was promoted to professor in 2002.

On the morning of 30 August 2012, Shinichi Mochizuki (Japanese, aged 43) quietly posted four papers on his website. The papers were huge — more than 500 pages in all — packed densely with symbols, and the culmination of more than a decade of solitary work.

In them, Mochizuki solved the abc conjecture, a 27-year-old problem in number theory that no other mathematician had even come close to solving. It is one of the most astounding achievements of mathematics this century and completely revolutionizes the study of equations with whole numbers.

To complete the proof, Mochizuki had invented a new branch of his discipline, one that is astonishingly abstract even by the standards of pure maths. “Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space,” number theorist Jordan Ellenberg, of the University of Wisconsin–Madison, wrote on his blog a few days after the paper appeared.

Mochizuki has estimated that it would take a maths graduate student about 10 years to be able to understand his work, and one of his collaborators, number theorist Ivan Fesenko of the University of Nottingham (UK) believes that it would take even an expert in arithmetic geometry some 500 hours. So far, only ten mathematicians say that they have been able to read the entire proof.

The great physicist Richard Feynman related his doubts about accepting Nobel Prize award:

“I don’t see that it makes any point that someone in the Swedish academy just decides that this work is noble enough to receive a prize — I’ve already gotten the prize. The prize is the pleasure of finding a thing out, the kick in the discovery, the observation that other people use it — those are the real things. The honors are unreal to me. I don’t believe in honors.”

He accepted the prize, but to the end of his life maintained that it took away from his life more than has brought in.