[430] Likewise Albert Tucker claimed he never noticed von Neumann Focus on just about anything he would simply call "topological" and described how once von Neumann was supplying a evidence of a topological theorem, which he considered, though ingenious, was the kind of proof an analyst would give as opposed to someone who worked on combinatorial topology.[423]

Von Neumann proved that the most effective means of doing substantial-scale mining functions including mining a complete moon or asteroid belt will be through the use of self-replicating spacecraft, Profiting from their exponential growth.[312]

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Von Neumann held a lifelong enthusiasm for historical historical past and was renowned for his historical know-how. A professor of Byzantine historical past at Princeton when explained that von Neumann experienced larger know-how in Byzantine background than he did.[seventy eight] He realized by heart A lot of the material in Gibbon's Drop and Slide and following dinner favored to engage in different historical conversations.

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In between 1935 and 1937, von Neumann labored on lattice principle, the speculation of partially requested sets in which every two features Possess a finest reduced certain and a minimum upper sure. Garrett Birkhoff described his perform, "John von Neumann's excellent head blazed over lattice idea just like a meteor".

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Even though dying of cancer, von Neumann continued his get the job done whilst he however could. Lewis Strauss, who at some time was chairman of the AEC and a close friend, described many of his ultimate Recollections of von Neumann in his memoir.

Lots of the similar entropy actions in classical facts principle can be generalized to the quantum case, which include Holevo entropy and conditional quantum entropy. Quantum mutual information and facts[edit]

He recognized in 1926 that a state of a quantum system might be represented by a degree in the (elaborate) Hilbert space that, in general, could be infinite-dimensional even for a single particle. During this formalism of quantum mechanics, observable quantities including situation or momentum are look here represented as linear operators acting around the Hilbert Place related to the quantum system.[226]

Employing his past Focus on measure principle von Neumann created numerous contributions to the theory of topological teams, starting having a paper on Pretty much periodic capabilities on groups, where by von Neumann prolonged Bohr's concept of virtually periodic features to arbitrary groups.

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