A little more than a century ago, on December 28, 1903, one of the most important mathematicians of modern times was born in Budapest, Hungary. John von Neumann is known today as the father of the electronic computer, the founder of game theory, and the pioneer of artificial intelligence. He was also one of the developers of the atom bomb. Von Neumann distinguished himself in traditional areas like pure mathematics and the mathematical foundations of physics, modern topics like computer science, and postmodern topics like neural nets and “cellular automata.” (The latter were to be rediscovered a few decades later by another genius, Stephen Wolfram; see Chapter 18.)

Jancsi, as he was affectionately called by his family, was the son of well-to-do Jewish parents. His father, a banker, had acquired the aristocratic title of von—to be put in front of the rather pedestrian-sounding Neumann—by purchasing it. As was custom among the well-to-do in Budapest, the young boy was brought up by German and French governesses. Already as a child he exhibited signs of genius. He was able to converse in Ancient Greek and could recite by heart whole pages from the telephone directory. It did not take long for Jancsi’s teachers at the Protestant high school of Budapest to become aware of his mathematical talents, and they furthered him as best they could. (By the way, von Neumann was not the only outstanding intellect to attend this remarkable school: Eugene Wigner, recipient of the 1963 Nobel Prize for Physics, was a student in the class above von Neumann’s, and John Harsanyi, Nobel Prize winner for economics in 1994, also was a graduate, as was Theodor Herzl, the ideological founder of the State of Israel.)

To nobody’s surprise, von Neumann was eager to study

mathematics after graduating from high school. But his father thought mathematics was a profession with little prospects and preferred for his son to embark on a business career. Jancsi demurred and, in the end, a compromise was reached, which saw the young von Neumann studying chemistry in Berlin. At least, according to his father, chemistry was a subject that was practical and could provide an income. However, the student simultaneously registered with the faculty of mathematics at the University of Budapest. Needless to say, the strict “numerus clausus,” aimed at preventing Jewish students from attending the university, in no way hindered von Neumann. He also never experienced any anti-Semitism at the university since he did not attend lectures. He only traveled to Budapest to sit for exams.

In 1923 von Neumann changed universities and moved from Berlin to Zurich, where he enrolled at the prestigious Eidgenössische Technische Hochschule (ETH). Besides attending the compulsory chemistry lectures, he participated in the seminars on mathematics offered by the ETH. By 1926 he had gained not only the title of diplomierter Chemiker ETH but also a doctorate in mathematics from the University of Budapest. The topic of his thesis was set theory, a field that broke new ground and proved seminal for the development of mathematics.

Shortly afterwards the young Herr Doktor—at about that point in time already known in his circles as a genius—arrived in the German town of Göttingen. The town’s university contained what was then hailed as the world’s leading center of mathematics. Its outstanding representative, David Hilbert, the world’s most eminent mathematician of his time, received him graciously. The stay was followed by lecture series in Berlin and Hamburg.

Just before scientists of Jewish origin were banned from European universities, von Neumann traveled to the United States at the invitation of Princeton University. That was in the early 1930s, and quantum mechanics had just been developed by Max Planck, Werner Heisenberg, and others. Von Neumann was able to give the theory what until that time it had lacked—a firm and rigorous mathemati-

cal footing. This remarkable achievement earned him an appointment to the Institute for Advanced Study, where he became, together with Albert Einstein, one of the six founding professors. From then until his death, the institute was a true home to the mathematician, who had in the meantime become an American citizen and had changed his name from Jancsi to Johnnie.

Not only was von Neumann interested in the foundations of pure mathematics, he was fascinated by the application of mathematics to other areas. At a time when Europe was swept up by war and when the natural sciences and their application to warfare became increasingly important, his work on hydrodynamics, ballistics, and shock waves aroused the interest of the military. It did not take long for von Neumann to become an adviser to the American army, and from there it was but a small step to his appointment, in 1943, to the Manhattan Project in Los Alamos, New Mexico. Together with a group of Hungarian emigrés, including Eugene Wigner, Edward Teller, and Leo Szilard, he became involved in the development of the atom bomb. (Soon this handful of Hungarian scientists were being referred to by their colleagues as the “people from Mars”: With their superhuman intelligence and the incomprehensible language they used among themselves, it was rumored that they must have arrived on earth from a different planet!) In Los Alamos von Neumann came up with the decisive calculations that would enable scientists to develop the plutonium bomb.

In the labs of Los Alamos mathematicians had to solve many tedious, routine calculations. To speed things up, they developed numerical techniques that were carried out manually by dozens of human number crunchers. But the need for something faster became more and more pressing. It so happened that von Neumann was familiar not only with the ideas of Alan Turing, an up-and-coming mathematical talent from Britain who at the time was working on his doctoral thesis at Princeton, but also with those of the engineer John Eckert and his physicist colleague John Mauchly. The former pioneered the ideas of a modern computer; the latter two were in the process of con-

structing the first American electronic computing device in Philadelphia. Building on their preparatory work, von Neumann went on to develop the ideas that would henceforth be known as “computer architecture.” To this day “von Neumann architecture” controls the data flow in every desktop PC. It was von Neumann who recognized that programs could be stored in the computer and called up whenever needed, much the same way as data. Until then the experts had thought it would be necessary to wire programs as a piece of the hardware, the method that had been used in mechanical adding machines.

One day during a discussion with Oskar Morgenstern, an economist who had emigrated from Vienna to Princeton, the two men hit on ideas that would henceforth be known as game theory. Von Neumann and his Viennese friend proved the so-called mini-max theorem, which postulates that for board games it makes no difference whether one maximizes gains or minimizes losses. Game theory, which is applied also in the business world and in international politics, has since developed into a separate scientific branch located somewhere between mathematics and economics. (One of its greatest proponents was John Nash, Nobel Prize winner for economics in 1994—together with John Harsanys and Richard Selten—and the central figure in the movie A Beautiful Mind.)

Toward the end of his life von Neumann became interested in the brain. In publications on analogies between the human brain and computers that appeared posthumously, he put forth the opinion that the brain functions in both binary and analog modes. Furthermore, he wrote, it makes use not so much of the von Neumann architecture used in PCs but, rather, methods of parallel processing that are used by today’s supercomputers. He thereby anticipated the theory of neural networks, which play an important role in today’s artificial intelligence research.

Von Neumann had a keen sense of fun. Together with Marietta, his first wife, and, after his divorce, with his second wife Klari—both of whom hailed from Budapest—he attempted to import to America the cabaret atmosphere that he had gotten to know and enjoy as a student

in Berlin. The parties thrown by the von Neumanns in Princeton, which lasted long into the night, became legendary.

Von Neumann was honored during his lifetime with numerous scientific prizes and titles. But his final months were very difficult. At age 52 he learned that he had cancer. He could not cope with the inevitable. The scientist with the restless mind was confined to a wheelchair during the day and suffered panic attacks at night. A year later, on February 8, 1957, Johnnie von Neumann succumbed to his illness at Walter Reed Hospital in Washington, D.C.