John von Neumann (1903

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John von Neumann (1903
John von Neumann (1903

John von Neumann (1903–1957): Father of computers

He was born as Neumann János in Budapest, as John von Neumann he died in Washington D. C. – he was one of the greatest mathematical geniuses of the 20th century.


His father was a we althy Jewish banker who bought the title "Baron von" in 1913 but did not use it; however, the son later attached importance to the "from". Raised multilingually, János Neumann is said to have conversed in ancient Greek at the age of six; it is reported that he could divide eight-digit numbers in his head and after a quick glance at a page in the phone book knew names and phone numbers by heart. At the age of eight, he studied differential calculus, but also regularly read a history encyclopedia.

Already at the age of 17, i.e. still during his school days at the German-speaking Lutheran high school, he published his first article in a mathematical journal. However, his father does not want him to study mathematics, since one cannot acquire we alth with it; he finally agrees with him to study chemistry - in Berlin, because after the end of World War I the anti-Jewish mood in Budapest had become threatening. János Neumann commutes between the universities in Berlin, Budapest and Zurich. Simultaneously with his degree in chemistry in Zurich, he passed the examination in mathematics in Budapest with honors, although he cannot attend the lectures systematically.

George Pólya (1887–1985), who had studied law, languages, literature, mathematics, physics and philosophy in Budapest and was temporarily his university teacher of mathematics in Zurich, later admits that János Neumann was his only student, of which he himself was "afraid"; there has hardly been a lecture in which he as a lecturer has formulated a problem for which his "student" could not have presented a solution at the end of the lecture.

Due to the work of Georg Cantor (1845-1918), a new area of mathematics had developed at the end of the 19th century, the (later viewed as "naive") set theory. In 1901, Bertrand Russell (1872-1970) discovered a contradiction that arises if arbitrary sets are allowed to be defined: Is there a set of all sets that does not contain itself? In his doctoral thesis in 1925, von Neumann succeeded in creating a consistent, axiomatic construction of set theory.

He received a Rockefeller scholarship from David Hilbert (1862-1943) in Göttingen and worked as the youngest private lecturer at the universities in Berlin and Hamburg. From 1930, parallel to his activities in Europe, he began working as a guest lecturer at Princeton University; his reputation as a mathematical genius spread worldwide. In 1933, along with Albert Einstein (1879–1955), he was one of the first five professors to be appointed to the newly created Institute for Advanced Study in Princeton. In 1937 he became an American citizen.

1926 he deals with the seemingly contradictory theories of the atomic physicists Werner Heisenberg (1901-1976) and Erwin Schrödinger (1887-1961) and tries to write a mathematical theory that includes both approaches: "Mathematical foundations of quantum mechanics " was published in 1932. This work provided new impetus for functional analysis, a field of mathematics that generally deals with the properties of the function space ("von Neumann algebra"). In 1936 he wrote a contribution to a new "logic" of quantum mechanics: photons cannot pass through polarization filters that are perpendicular to one another; according to "classical" logic it shouldn't matter if you add a third filter. If the third filter is placed diagonally in front of or behind the two filters in the path of the photons, then nothing actually changes, but it does if it is placed in between.

Von Neumann is considered the founder of mathematical game theory; In 1928 he published a contribution to the "minimax theorem". This mathematical theorem is about the strategy of minimizing the maximum loss of the players involved in a zero-sum game (that is, the sum of the win and loss of all players is equal to zero). In 1937 he generalized this to questions of the balance between supply and demand and in 1944 together with Oskar Morgenstern (1902-1977) he wrote the standard work of economics, "Theory of Games and Economic Behaviour", which shows, among other things, that collective bargaining, have strategic company decisions and international conflicts described using mathematical models.

1936 Alan Turing (1912–1954) attends the Princeton Institute for his doctorate; in his famous work "On Computable Numbers with an Application to the Decision Problem" he deals with the computability of a mathematical problem (so-called Turing machine). His presence at Princeton stimulated von Neumann to get more involved in building automatic calculators.

He analyzes the existing computer concepts and develops them further in his famous work "First draft on a Report on the EDVAC" (Electronic Discrete Variable Automatic Computer). What is important is his realization that the programs should not be hardwired, but should be saved in the same way as data. Since then one speaks of the von Neumann architecture of the computers; According to her, a computer consists of an arithmetic unit, a control unit, the input and output devices and a shared storage unit for instructions and data (which was only changed in the most recent PC generations). He is interested in biological information processes and investigates neural networks (analogy of computer and brain).

From 1937 on von Neumann de alt with questions of mathematics in military applications, for example with the effectiveness of bombs as a function of the explosion height, and wrote a thesis on "shock waves". The most important application of this work comes in 1945 with the atomic bombing of Hiroshima and Nagasaki. He is a key contributor to the Manhattan Project (making the first atomic bomb) as well as the team that developed the first hydrogen bomb.

In this context, he develops simulation methods (Monte Carlo method) and designs a method for generating pseudo-random numbers, the "middle square method": You start with a 4-digit number, the square of which results in an 8-digit number from which then the middle 4 digits are taken, and so on. von Neumann does not accept criticism of the poor quality of the numbers generated in this way; you would notice if the simulation was not useful. Also: "Anyone who considers arithmetical methods of producing random numbers is, of course, in a state of sin."

In his lectures as a mathematics professor, he is said to have often been erratic in the proof and chaotic in the blackboard; he doesn't care much about this, as he provocatively expresses the opinion: "In mathematics you don't understand things, you just get used to them." and "If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

At the end of 1956 he was diagnosed with pancreatic and bone cancer, consequences of his presence in the nuclear tests in the Pacific and his work in the Los Alamos laboratories. When John von Neumann died, he had written 150 scientific papers, 60 each in pure and applied mathematics and 20 in physics.

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