What should everyone know about John von Neumann?

He was likely one of the most brilliant human beings who ever lived. Just a few facts from Wikipedia:

János, nicknamed “Jancsi” (Johnny), was an extraordinary child prodigyin the areas of language, memorization, and mathematics. As a 6 year old, he could divide two 8-digit numbers in his head.[14] By the age of 8, he was familiar with differential and integral calculus.[15]

At the age of 15, he began to study advanced calculus under the renowned analyst Gábor Szegő. On their first meeting, Szegő was so astounded with the boy’s mathematical talent that he was brought to tears.[16]

How Math Can Defeat Bullies

Impressed by this extraordinarily bad ERA, I mentioned it diffidently to my teacher during a class discussion of sports. He looked pained and annoyed and sarcastically asked me to explain the fact to my class. Being quite shy, I did so with a quavering voice, a shaking hand, and a reddened face. (A strikeout in self-confidence.) When I finished, he almost bellowed that I was confused and wrong and that I should sit down.

An overweight coach and gym teacher with a bulbous nose, he asserted that ERA’s could never be higher than 27, the number of outs in a complete game.

For good measure he cackled derisively.

.. Later that season, the Milwaukee Journal published the averages of all the Braves players. Since this pitcher hadn’t pitched again, his ERA was 135, as I had calculated. I remember thinking then of mathematics as a kind of omnipotent protector. I was small and quiet and he was large and loud. But I was right and I could show him. This thought and the sense of power it instilled in me was exciting. So, still smarting from my earlier humiliation, I brought in the newspaper and showed it to him. He gave me a threatening look and again told me to sit down. His idea of good education apparently was to make sure everyone remained seated. I did sit down but this time with a slight smile on my face.

We both knew I was right and he was wrong.

Oddly, this particular teacher did give me a potent reason to study mathematics that I think is underrated: show kids that with it and logic, a few facts, and a bit of psychology you can prevail over blowhards no matter your age or size.

.. It seemed obvious to me that an atom couldn’t think, and so I “thought” that this proved that humans couldn’t think either.

The Pursuit of Beauty: Yitang Zhang solves a pure-math mystery

The filmmaker George Csicsery has made a documentary about Zhang, called “Counting from Infinity,” for the Mathematical Sciences Research Institute, in Berkeley, California. In it, Peter Sarnak, a member of the Institute for Advanced Study, says that one day he ran into Zhang and said hello, and Zhang said hello, then Zhang said that it was the first word he’d spoken to anyone in ten days. Sarnak thought that was excessive, even for a mathematician, and he invited Zhang to have lunch once a week.

.. “You expect a guy like that to want to show off or explain how smart he is,” Yang said. “He gave beautiful lectures, where he wasn’t trying to show off at all.”

.. Until Zhang was promoted to professor, last year, as a consequence of his proof, his appointment had been tenuous. “I was chair of the math department, and I had to go to him from time to time and remind him this was not a permanent position,” Eric Grinberg said.

.. In “The Psychology of Invention in the Mathematical Field,” published in 1945, Jacques Hadamard quotes a mathematician who says, “It often seems to me, especially when I am alone, that I find myself in another world. Ideas of numbers seem to live. Suddenly, questions of any kind rise before my eyes with their answers.” In the back yard, Zhang had a similar experience. “I see numbers, equations, and something even—it’s hard to say what it is,” Zhang said. “Something very special. Maybe numbers, maybe equations—a mystery, maybe a vision. I knew that, even though there were many details to fill in, we should have a proof. Then I went back to the house.”

.. Zhang wasn’t interested in finding the smallest number defining the gap. This was work that he regarded as a mere technical problem, a type of manual labor—“ambulance chasing” is what a prominent mathematician called it.

.. Is there a talent a mathematician should have?”

“Concentration,” Zhang said.

.. Zhang’s preference for undertaking only ambitious problems is rare. The pursuit of tenure requires an academic to publish frequently, which often means refining one’s work within a field, a task that Zhang has no inclination for. He does not appear to be competitive with other mathematicians, or resentful about having been simply a teacher for years while everyone else was a professor. No one who knows him thinks that he is suited to a tenure-track position. “I think what he did was brilliant,” Deane Yang told me. “If you become a good calculus teacher, a school can become very dependent on you. You’re cheap and reliable, and there’s no reason to fire you. After you’ve done that a couple of years, you can do it on autopilot; you have a lot of free time to think, so long as you’re willing to live modestly. There are people who try to work nontenure jobs, of course, but usually they’re nuts and have very dysfunctional personalities and lives, and are unpleasant to deal with, because they feel disrespected. Clearly, Zhang never felt that.”