Dec 282017

Today is the birthday (1903) of John von Neumann (born, Neumann János Lajos) legendary mathematician who could well lay claim to being the greatest mathematician of all time, if I were given to superlatives. He made major contributions to a number of fields, including pure mathematics (foundations of mathematics, functional analysis, ergodic theory, representation theory, operator algebras, geometry, topology, and numerical analysis), physics (quantum mechanics, hydrodynamics, and quantum statistical mechanics), economics (game theory), computing (Von Neumann architecture, linear programming, self-replicating machines, stochastic computing), and statistics. Quite a mouthful. Next to von Neumann, the iconic genius, Einstein, who had an office down the hall from von Neumann at Princeton for many years, was second rate. Yet von Neumann tends to be forgotten in the popular mind these days, except perhaps indirectly when people refer to a “zero-sum game” which was a small part of the game theory he invented.

Writing something both interesting and useful – as well as being brief –  about von Neumann is a real challenge. I won’t say too much about his mathematical genius except to say that he was the rare person, indeed, who could see mathematical problems in their totality almost instantly, and could solve them almost as fast, because, unlike most other mathematical geniuses, he usually did not have to wade through calculations to find a solution, but could see the big picture with paths leading in and out intuitively. Such a mathematical mind does not come along very often.

Georg Pólya wrote that von Neumann was,

The only student of mine I was ever intimidated by. He was so quick. There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the class. I came to a certain theorem, and I said it is not proved and it may be difficult. Von Neumann didn’t say anything but after five minutes he raised his hand. When I called on him he went to the blackboard and proceeded to write down the proof. After that I was afraid of von Neumann.

I’m not sure whether I would include von Neumann on my list of people (alive or dead) I would like to have dinner with.  By all accounts he had a decent sense of humor, and was a good storyteller, but he could also be crudely insensitive, and tell off-color jokes without concern that he might offend.  His interest in women was strictly sexual, and the secretaries at Los Alamos had to put cardboard modesty screens on the front of their desks because he would quite blatantly ogle their legs when he was in the room even though he was a married man. I would go as far as to say that despite being an exceptionally intelligent man, he had little grasp of certain fundamental principles of living. In fact, he acknowledged as much on many occasions.  This famous quote may be the most telling:

If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.

An interesting quote to parse on many levels. There is no doubt that van Neumann found mathematics simple, even mathematical problems that stumped great minds. By comparison, he thought that life was much more complex, and, by implication, cannot be reduced to mathematical models. At one point he said:

There probably is a God. Many things are easier to explain if there is than if there isn’t.

Von Neumann took Pascal’s wager when he was near death and embraced Catholicism, while being overtly agnostic all his life (even though he was baptized in 1930 after his father’s death and before he married, for convenience only). Pascal argued that if death is the end, then you lose nothing by being a Christian. But if death leads to heaven or hell, it would be much better to die a Christian than not. Either way you win. The small trick here, which von Neumann apparently did not allow for, is that you have to be a believer, not just a Christian according to the letter of the law. Naturally he chose Catholicism for his church, presumably knowing that the Catholic church (overtly) places higher value on correct action over correct belief. This stance led to the Protestant Reformation, so, as an ordained Calvinist minister, you know what I think