“I have known a great many intelligent people in my life. I knew Max Planck (Nobel Prize 1918), von Laue (Nobel Prize 1914) and Heisenberg (Nobel Prize 1932). Paul Dirac (Nobel Prize 1933) was my brother in law; Leo Szilard and Edward Teller have been among my closest friends; and Albert Einstein was a good friend, too. But none of them had a mind as quick and acute as John von Neumann. I have often remarked this in the presence of those men and no one ever disputed me.
… But Einstein’s understanding was deeper even than von Neumann’s. His mind was both more penetrating and more original than von Neumann’s. And that is a very remarkable statement. Einstein took an extraordinary pleasure in invention. Two of his greatest inventions are the Special and General Theories of Relativity; and for all of von Neumann’s brilliance, he never produced anything as original.
–Eugene Wigner (Nobel Prize Physics 1963)
Imagination rules! Not speed of thought!
Creativity, freedom of thought, Not genes!
To the question: which philosopher did John follow?
The general answer is that he was a pragmatist, and that in itself is an indication of an underlying philosophy.
But from my perspective he followed, or at least considered, one specific philosopher, Goethe.
After all, Goethe was a philosopher, among many other professions. We studied Faust in school very thoroughly, both in the original and in Hungarian translation. We discussed it for years and reread it occasionally throughout our respective lifetimes.
von Neumann died at the age of 53, in 1957, near Princeton, of cancer. As his mind began to falter, he was, by all accounts in terrifying agony, a screaming, uncontrollable terror. As he neared death, sedated. American guards watched his hospital room, wary that he might babble high-level military secrets, but he began to speak in Hungarian, and the guards didn’t understand it.
His brother was at his side, and John von Neumann, going out of life on this planet, under heavy painkillers, recited Goethe’s Faust from his photographic memory…
It has been said that von Neumann’s intellect was absolutely unmatched. Von Neumann’s ability to instantaneously perform complex operations in his head stunned other mathematicians.
“one had the impression of a perfect instrument whose gears were machined to mesh accurately to a thousandth of an inch.”
“Keeping up with him was … impossible.
The feeling was you were on a tricycle chasing a racing car.”
–Israel Halperin (Von Neumann’s doctoral advisor)
“I never could keep up with him”.
“von Neumann would carry on a conversation with my 3 year old son, and the two of them would talk as equals, and I sometimes wondered if he used the same principle when he talked to the rest of us. Most people avoid thinking if they can, some of us are addicted to thinking, but von Neumann actually enjoyed thinking, maybe even to the exclusion of everything else.”
“One of his remarkable abilities was his power of absolute recall. As far as I could tell, von Neumann was able on once reading a book or article to quote it back verbatim; moreover, he could do it years later without hesitation. He could also translate it at no diminution in speed from its original language into English. On one occasion I tested his ability by asking him to tell me how A Tale of Two Cities started. Whereupon, without any pause, he immediately began to recite the first chapter and continued until asked to stop after about ten or fifteen minutes.”
“I have sometimes wondered whether a brain like von Neumann’s does not indicate a species superior to that of man”
-Nobel Laureate Hans Bethe of Cornell University.
A list of Von Neumann’s accomplishments:
Abelian von Neumann algebra
Arithmetic logic unit
Artificial viscosity (a numerical technique for simulating shock waves)
Axiom of regularity
Axiom of limitation of size
Blast wave (fluid dynamics)
Bounded set (topological vector space)
Class (set theory)
Decoherence theory (Quantum mechanics)
Doubly stochastic matrix
Hilbert’s fifth problem
Hyperfinite type II factor
Inner model theory
Interior point method
Mutual assured destruction
Monte Carlo method
Quantum mutual information
Standard probability space
Von Neumann algebra
Von Neumann architecture
Von Neumann bicommutant theorem
Von Neumann cardinal assignment
Von Neumann cellular automaton
Von Neumann constant (two of them)
Von Neumann interpretation
Von Neumann measurement scheme
Von Neumann Ordinals
Von Neumann universal constructor
Von Neumann entropy
Von Neumann Equation
Von Neumann neighborhood
Von Neumann paradox
Von Neumann regular ring
Von Neumann–Bernays–Gödel set theory
Von Neumann spectral theory
Von Neumann universe
Von Neumann conjecture
Von Neumann’s inequality
Stone–von Neumann theorem
Von Neumann’s trace inequality
Von Neumann stability analysis
Quantum statistical mechanics
Von Neumann extractor
Von Neumann ergodic theorem
Von Neumann–Morgenstern utility theorem
ZND detonation model