Magyar News, 2000. szeptember-2001. augusztus (11. évfolyam, 1-12. szám)
2001-07-01 / 11-12. szám
that the high school curriculum soon stopped to offer him anything of interest and his parents hired a private teacher for him: Mihály ( Michael) Fekete, an adjunct professor of mathematics at Budapest University, who became later a well known mathematician (eventually the President of the Hebrew University of Jerusalem). Neumann was 16 years old, when he published his first paper, with Fekete as co-author. When he graduated from high school at 18 and college enrollment was to follow, Neumann's choice was obvious: he wanted to study mathematics. To his father, the practical business man, the choice was not so obvious at all: being a mathematician, meant an income that could only support a modest life style and Miksa Neumann wanted more than that for his son. At this point one might ask: why was this rich man concerned with the financial future of his family? One can only speculate about his motives. The year was 1921 ; three years after the collapse of the Austro- Hungarian Monarchy at the end of the First World War, followed by two revolutions and a counter revolution. For a while, the Neumann family fled to Vienna. The value of the currency ( the "korona' - "crown") shrank to 1/14,000th of its pre-war value: an unprecedented rate of inflation in history (up till then). Though Miksa Neumann apparently managed to stay a rich man but many people of means became paupers. It was obvious to him that the only stable value one can rely upon in a changing world, is a marketable skill that one can carry in his head. He laid down the rule: Janos should get a "practical" degree in a profession of his choice - he can’t study mathematics. Janos satisfied his father's wishes in an amazing manner. He enrolled as a chemistry student in Berlin, but he also enrolled as a mathematics student at the university in Budapest. He spent his time in Berlin, except that at the end of each school year, he returned to Budapest to take the examinations - without ever attending a lecture. After two years in Berlin, he went to Zurich and in two years, graduated as a chemical engineer in 1926 from the famous Federal Institute of Technology (ETH). He also interacted there with two widely known mathematicians and took over the classes of one when the professor went abroad for a short while. Also in 1926, he took his Ph.D. in mathematics in Budapest. Neumann became a student of somebody else only one more time: in 1926/27 , he studied in Gottingen under David Hilbert, the leading mathematician of the 20th century. But by then, he was a celebrity: at mathematical conferences, this young man in his 20-s was pointed out as a genius. In 1929, John Von Neumann was invited to Princeton and his peregrinations ended; first he was a visiting professor at the University, then he was appointed professor there, but soon (1933) he moved to the Institute for Ad-vanced Study where he stayed till his death. During his Princeton years he was overwhelmed with acknowledgments, both by his scientific peers and by society at large (two Presidential Awards, amongst many other honors). Obvious that we are dealing here with a man of extraordinary accomplishments. But what was the exact nature of those accomplishments? And here comes the difficulty. John Von Neumann's accomplishments were mostly (though not exclusively) attained in the field of mathematics. Reviewing the more than 120 publications which contain the results of his unfortunately short life span (he died of cancer at age 53) we can find only very occasionally a title which is meaningful to the non-mathematician. The reason that compelled the mathematicians to develop their own language is the fact that modem mathematics deals with concepts that are absent from ordinary life. Therefore, if we want to get an idea about the significance of Von Neumann’s work, we have to accept the judgment of his peers: at age 30, he was one of the original six mathematicians / physicists appointed to the Institute for Advanced Study in Princeton; Albert Einstein was also amongst the six. The appointment was an acknowledgment of the fact that Von Neumann proposed revolutionary new basic concepts in several areas of mathematics. In addition to the esoteric areas of mathematics, the breadth of Von Neumann's genius extended to topics which are more accessible to the layman. When Isaac Newton established the basic laws of physics, the mathematics of his time were not adequate to perform calculations necessary to him. Therefore, Newton developed new areas of mathematics ( differential and integral calculus). Newtonian physics - and the associated mathematics- reigned for about 300 years but around the turn of the 20th century, it was found that at very small dimensions (the atomic level) Newtonian physics has to be modified. The new chapter of physics is called quantum theory. Small wonder that quantum physics needed additional effort in mathematics to be able to follow events at the subatomic level with calculations. In 1927, the 26 year old John Von Neumann provided to his physicist colleagues a service similar to what Newton did for himself. Another activity of Von Neumann with an appeal to the non-mathematician is his foundation of the mathematical theory of games. He later expanded his game theory to explain the economic behavior of people and this work resulted in a classic book: "Theory of games and economic behavior” (co-authored with the economist Oscar Morgenstern). But the accomplishment of the most interest to the contemporary general public, is his participation in the Manhattan project. Von Neumann immediately recognized that the amount of calculations necessary for such an undertaking will result in a bottleneck: there were simply not enough mathematicians to support the physicists and the engineers. The solution: an electronic calculator. The first computer was built at the University of Pennsylvania with the active participation of John Von Neumann. His wife was the first programmer. During the calculations preparing the atomic bomb, Von Neumann participated in investigations that lead to the hydrogen bomb. Considering all the accomplishments of Von Neumann, the question may be asked: how can he be rated on some kind of a scale for intellectual greatness? Is there any such scale at all? When Alfred Nobel established the prize named after him, he bypassed the necessity to deal with the measurement of the intellect of the individual : the Nobel Prize goes to the accomplishment, rather than to the accomplisher(s). Though, after a while, the Nobel Committee started to honor , sometimes, the collective lifetime accomplishment of an individual rather than a particular piece of work, clearly in contradiction to the intent of the founder, who even specified that the accomplishments of the past year should be considered).Also, there is no Nobel prize jor mathematics. So, if we want to find a "measurement" for the greatness of Von Neumann, we have to look for some appropriate criterion. Perhaps, the following definition might be helpful: a great intellect will leave the field of his activity in a shape different from the way he found it at the beginning of his career. It is clear that this was the case with John Von Neumann. We can safely say, that had John performed his accomplishments in the society where nobility was a reward for outstanding intellectual performance, he would have become a nobleman in his own right. Page 5 The ENIAC took up a room with many people working with it. Compare it to a lap-top computer that is the size of a big book.
