# John von Neumann

## The birth of a genius-

On December 28, 1903, in Budapest, Hungary, married couple Miksa and Kann Margit Neumann gave birth to their first baby boy János von Neumann .

## Child years-

As a child "Jancsi" (a childhood nickname) could exchange jokes in classical Greek with his father, memorize phone books, and had extraordinary mental calculation abilities. When he was eight, von Neumann entered the Lutheran Gymnasium, quickly impressing his math teacher. Von Neumann's father made him pursue a career in engineering.

## After college-

Finishing college with a chemical engineering degree from ETH Zürich in Switzerland, he also received a doctorate in mathematics from Pázmány Péter University when he was 22. He went off to teach at the University of Berlin. In 1930, he was requested to teach at Princeton University, he took the offer, taught along side Albert Einstein, and stayed there until retirement.
*"John von Neumann from Berlin wrote a letter to his professor Lipót Fejér in Budapest (1929)"*

## Game Theory

The science of strategy. It attempts to determine mathematically and logically the actions that “players” should take to secure the best outcomes for themselves in a wide selection of “games.” More typical are games with the potential for either mutual gain (positive sum) or mutual harm (negative sum), as well as some conflict. All in all, without the success of one, there is no success of the other.

## Quantam Theory

Quantum theory is the theoretical basis of modern physics that explains the nature and behavior of matter and energy on the atomic and subatomic level. In 1932, in Mathematical Foundations of Quantum Mechanics, John von Neumann explained that two fundamentally different processes are going on in quantum mechanics, not at the same time. Process 1 of the quantum theory is a “non-causal process”, in which the measured electron winds up randomly in one of the possible physical states (eigenstates) of the measuring apparatus plus electron. The probability for each eigenstate is given by the square of the coefficients (cn) of the increase of the original system state (wave function ψ) in an endless set of wave functions (φ) that represent the eigenfunctions of the measuring apparatus plus electron. According to von Neumann, the particle simply shows up somewhere as a result of a measurement.

Ex. cn = < φn | ψ >

## Set Theory

The contributions that von Neumann devoted to the Set Theory consisted not only of having proposed a new elegant axiomatic system (extending the system of Zermelo-Fraekel ZFC) but also of having proposed several innovations elevating the system of ZFC; in particular the deﬁnition of ordinal and cardinal numbers and the theory of deﬁnitions by transﬁnite introduction. The deﬁnition of ordinals and cardinals was given by von Neumann in the paper “Zur Einfu¨hrung der transﬁniten Zahlen” (1923) – it was his second publication. In this example, one obtains the sequence ∅,{∅},{∅,{∅}},{∅,{∅},{∅,{∅}}}}, ... – i.e., von Neumann’s ordinal numbers. Those sets – as representatives – are in fact very useful, especially in the axiomatic set theory because they can be easily deﬁned in terms of the relation ∈ only and they are well order by the relation ∈. They also enable an elegant deﬁnition of cardinal numbers. In the paper (1928) one ﬁnds the following deﬁnition: a well ordered set M is said to be an ordinal (number) if and only if for all x ∈ M, x is equal to the initial segment of M determined by x itself (as von Neumann wrote: x = A(x;M)). Elements of ordinal numbers are also ordinal numbers. An ordinal number is said to be a cardinal number if and only if it is not equipollent to any of its own elements.
He also did groundbreaking work in lattice theory, continuous geometry, measure theory, ergodic theory, and then he tackled more complicated areas, introducing propositional calculus. Dr. von Neumann was very influential in the field of nuclear physics as well.

## The death of a genius-

John von Neumann was diagnosed with terminal cancer in 1955. Even though he was 51, he was still the life of the party, spurting limericks and entertaining regularly. His second wife, Klara, said “he could count everything except calories”. Despite his ailment and weakness, he took part in the ceremonies organized to honor him, in a wheel chair, and kept contact with family and friends during this time. The cancer reached his brain, and he passed away on February 8, 1957 in Washington, D.C.