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 of von Neumann’s “conversion.” On the other hand, I don’t see it as a great sin.  If it brought him peace at the time of his death, it was worth it. As far as I am concerned, dogma, whether it be Catholic or Protestant, is worthless.

Von Neumann was born Neumann János Lajos to a wealthy, acculturated and non-observant Jewish family. His Hebrew name was Yonah. Von Neumann was born in Budapest, then in the kingdom of Hungary, part of the Austro-Hungarian Empire. His father, Neumann Miksa (English: Max Neumann) was a banker, who held a doctorate in law. He had moved to Budapest from Pécs at the end of the 1880s. In 1913, his father was elevated to the nobility for his service to the Austro-Hungarian Empire by Emperor Franz Joseph. The Neumann family thus acquired the hereditary appellation Margittai, meaning from Marghita (even though the family had no connection with the town). János became Margittai Neumann János (John Neumann of Marghita), which he later changed to the German Johann von Neumann.

Von Neumann was a child prodigy. As a 6 year old, he could divide two 8-digit numbers in his head, and, reputedly, could converse in ancient Greek. Formal schooling did not start in Hungary until the age of 10. Instead, governesses taught von Neumann, his brothers and his cousins. His father believed that knowledge of languages other than Hungarian was essential, so the children were tutored in English, French, German and Italian. By the age of 8, von Neumann was familiar with differential and integral calculus, but he was particularly interested in history, reading his way through Wilhelm Oncken’s 46-volume Allgemeine Geschichte in Einzeldarstellungen.

Von Neumann entered the Lutheran Fasori Evangelikus Gimnázium in 1911. This was one of the best schools in Budapest, part of a specialized education system designed for the elite. The school system produced a generation noted for intellectual achievement, that included Theodore von Kármán (b. 1881), George de Hevesy (b. 1885), Leó Szilárd (b. 1898), Dennis Gabor (b. 1900), Eugene Wigner (b. 1902), Edward Teller (b. 1908), and Paul Erdős (b. 1913). Collectively, they were sometimes known as Martians. Wigner was a year ahead of von Neumann at the Lutheran School. When asked why the Hungary of his generation had produced so many geniuses, Wigner, who won the Nobel Prize in Physics in 1963, replied that von Neumann was the only genius.

Although his father insisted von Neumann attend school at the grade level appropriate to his age, he agreed to hire private tutors to give him advanced instruction in those areas in which he had displayed an aptitude. 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. By the age of 19, von Neumann had published two major mathematical papers, the second of which gave the modern definition of ordinal numbers, which superseded Georg Cantor’s definition. Von Neumann entered Pázmány Péter University in Budapest, as a Ph.D. candidate in mathematics in 1923, even though his father tried to steer him towards chemical engineering as a more profitable career. For his doctoral thesis, he chose to produce an axiomatization of Cantor’s set theory. He passed his final examinations for his Ph.D. in 1926 and then went to the University of Göttingen on a grant from the Rockefeller Foundation to study mathematics under David Hilbert. He completed his habilitation on December 13, 1927, and he started his lectures as a privatdozent at the University of Berlin in 1928, being the youngest person (24 years old) ever elected privatdozent in its history in any subject. By the end of 1927, von Neumann had published 12 major papers in mathematics, and by the end of 1929, 32 papers, at a rate of nearly one major paper per month. In 1929, he briefly became a privatdozent at the University of Hamburg, where the prospects of becoming a tenured lecturer were better, but in October of that year a better offer presented itself when he was invited to Princeton University in Princeton, New Jersey. In 1933, he was offered a lifetime professorship on the faculty of the Institute for Advanced Study in Princeton, which is separate from the university, and had been founded 3 years earlier. He remained a mathematics professor there until his death.

Von Neumann’s personal values are pretty much an open book. He liked to eat and drink, and his second wife, Klara, said that “he could count everything except calories”. He enjoyed Yiddish and crude humor (especially limericks). He was a non-smoker. At Princeton he received complaints for regularly playing extremely loud German march music on his gramophone, which distracted those in neighboring offices, including Albert Einstein, from their work. Von Neumann did some of his best work in noisy, chaotic environments, and once admonished his wife for preparing a quiet study for him to work in. He never used it, preferring the couple’s living room with its television playing loudly. Despite being a notoriously bad driver, he nonetheless enjoyed driving—frequently while reading a book—occasioning numerous arrests, as well as accidents. When Cuthbert Hurd hired him as a consultant to IBM, Hurd often quietly paid the fines for his traffic tickets. Von Neumann once said,

I was proceeding down the road. The trees on the right were passing me in orderly fashion at 60 miles per hour. Suddenly one of them stepped in my path.

The paradox that intrigues me concerns his work on the Manhattan project. He was called in, for several weeks at a time, to help solve the problem of getting the fissionable material in a nuclear bomb to explode. Without von Neumann’s equations on implosion it is unlikely that the Manhattan project would have been successful, certainly not at the rate that it was. Without getting too technical the problem is fairly easy to state simplistically. To get fissionable material to set off an explosive chain reaction it has to be of a certain shape, mass, and density. Von Neumann worked on the concept of an explosive lens that, via conventional explosives, would cause the fissionable material to implode, forcing it into a compact spherical shape that would trigger a nuclear explosion.  As best as I can tell, von Neumann saw this as a technical problem, and was not particularly concerned about the lives that would be lost should the bomb be detonated. Indeed, he was present at several experimental explosions set off in the New Mexico desert, and it seems likely that his exposure to radioactive material is what caused the cancer that killed him.

After the war he became what many see as the prototype for Dr Strangelove in that he advocated stockpiling nuclear weapons in the arms race to create what he called Mutually Assured Destruction (MAD) between the Soviet Union and the United States. His reasoning was that MAD, through stockpiling weapons, would guarantee that they would not be used, rather than the opposite. No rational leader would initiate a first strike if the result would be not just the destruction of the other party, but one’s own destruction also. This reasoning is based, in part, on game theory (which he created), and assumes that the participants in the “game” are rational. That might have been true in von Neumann’s time, but I’m not sure about now. Not least, there are many more countries stockpiling nuclear weapons these days, so the “game” has become considerably more complex.

In 1955, von Neumann was diagnosed with what was either bone or pancreatic cancer. He was not able to accept the proximity of his own death very well, and he invited a Roman Catholic priest, Father Anselm Strittmatter, O.S.B., to visit him for consultation. Von Neumann reportedly said, “So long as there is the possibility of eternal damnation for nonbelievers it is more logical to be a believer at the end,” essentially saying that Pascal had a point. Father Strittmatter administered the last rites to him. On his deathbed, Von Neumann entertained his brother by reciting, by heart and word-for-word, the first few lines of each page of Goethe’s Faust. He died at age 53 on February 8, 1957, at the Walter Reed Army Medical Center in Washington, D.C., under military security lest he reveal military secrets while heavily medicated.

Von Neumann’s wife noted: “He likes sweets and rich dishes, preferably with a good nourishing sauce, based on cream.  He loves Mexican food.  When he was stationed at Los Alamos… he would drive 120 miles to dine at a favorite Mexican restaurant.” This gives you a lot of options to celebrate the man, but I’ll go with pollo a la crema, a classic Mexican dish. You’ll need crema Mexicana, but if you cannot find it, use a mix of half and half heavy cream and sour cream. Crema Mexicana is a cultured cream with a sour, tangy taste, used in sauces.

Pollo a la Crema


1 tbsp olive oil
2 boneless chicken breasts, cut into strips
1 onion, peeled and sliced
½ cup fresh mushrooms, sliced
½ cup green pepper, seeded and cut into strips
½ tbsp Spanish paprika
½ cup rich chicken stock
1 cup crema Mexicana


Heat the olive oil in large skillet over medium heat. Sauté the chicken strips, peppers and onion until the chicken is cooked on the outside and the onions and peppers are soft. Add the cream, mushrooms, paprika and chicken stock. Bring to a boil, uncovered, and simmer for about 5 minutes, or the chicken is tender. Do not overcook. The sauce may be a little thin, but it should be creamy.

Serve hot immediately with refried beans, rice, and flour tortillas.

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