John von Neumann

John von Neumann Quotes, Verified Against Primary Sources

Von Neumann's own words on entropy, computing, and a finite Earth — checked against the original magazine, report, and book pages, plus two famous anecdotes and one line he never said.

Fact-checked · last reviewed 2026-07-13

Most "von Neumann quotes" reach you secondhand — a colleague's memory of a hallway remark, printed decades later. This page separates what he actually wrote, checked against the original publication, from what others remember him saying, and from a line that belongs to someone else entirely.

Verified quotes, with sources

Advice to Claude Shannon, recounted by Shannon in 1961 (Myron Tribus & Edward C. McIrvine, "Energy and Information," Scientific American 225, no. 3, September 1971, p. 180):

"You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. In the second place, and more important, no one knows what entropy really is, so in a debate you will always have the advantage."

Note the exact wording: many quote sites insert an extra "really" ("no one really knows"). The original page has no second "really" — just "no one knows what entropy really is."

From First Draft of a Report on the EDVAC, June 30, 1945 — his own definition of a stored-program computer (primary text, Archive.org):

"[An automatic computing system is] a (usually highly composite) device, which can carry out instructions to perform calculations of a considerable order of complexity."

From the preface to Theory of Games and Economic Behavior, with Oskar Morgenstern, 1944 (primary text, Archive.org):

"This book contains an exposition and various applications of a mathematical theory of games. The theory has been developed by one of us since 1928 and is now published for the first time in its entirety."

From "Can We Survive Technology?", Fortune, June 1955 — von Neumann on a crowding planet (primary text, Fortune):

"The great globe itself is in a rapidly maturing crisis—a crisis attributable to the fact that the environment in which technological progress must occur has become both undersized and underorganized."

"Literally and figuratively, we are running out of room. At long last, we begin to feel the effects of the finite, actual size of the earth in a critical way."

Two beloved anecdotes — reported, not transcribed

Not every famous line clears that bar. Two of the most quoted "von Neumann quotes" survive only as other people's recollections:

  • "In mathematics you don't understand things. You just get used to them." Reportedly his reply to a physicist who didn't follow a method he'd proposed, as told to Gary Zukav for The Dancing Wu Li Masters (1979) — not a von Neumann publication (source).
  • "With four parameters I can fit an elephant, and with five I can make him wiggle his trunk." A two-hop chain: Fermi told this to Freeman Dyson in 1953 as a von Neumann saying; Dyson published it in Nature in 2004 (Wikipedia's account of the citation).

Both are almost certainly close to something he really said. Neither is a transcript.

A quote he never said

"It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in five years." This is a Stanislaw Ulam line, from Ulam's 1958 memorial tribute to von Neumann in the Bulletin of the American Mathematical Society — routinely reassigned to von Neumann on quote-aggregator sites (sourcing notes, Wikiquote).

Hear him reason it out

Reading these lines is one thing; hearing the reasoning behind them is another. Our AI recreation of von Neumann — clearly labeled as a recreation — will walk you through why "entropy" was the right word for Shannon's problem, or what "undersized and underorganized" meant about a planet in 1955.

More in this cluster: von Neumann hub · biography · death · facts.

John's verified quotes

Every quote below is checked against a primary or scholarly source — the citation sits right under it.

This book contains an exposition and various applications of a mathematical theory of games. The theory has been developed by one of us since 1928 and is now published for the first time in its entirety.
Theory of Games and Economic Behavior, Preface to the First Edition — Internet Archive
I think that it is a relatively good approximation to truth — which is much too complicated to allow anything but approximations — that mathematical ideas originate in empirics, although the genealogy is sometimes long and obscure.
The Mathematician (1947) — MacTutor History of Mathematics, University of St Andrews
Literally and figuratively, we are running out of room. At long last, we begin to feel the effects of the finite, actual size of the earth in a critical way.
Can We Survive Technology? — Fortune (June 1955)
Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin.
John von Neumann — Quotations — Today in Science History
Von Neumann told Claude Shannon to name his new uncertainty measure 'entropy' — the term already had a meaning in statistical mechanics, and since almost nobody truly understands what entropy is, Shannon would always have the advantage in any argument about it.
Energy and Information — Scientific American, Vol. 225, No. 3 (September 1971)
With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.
Von Neumann's elephant — Wikipedia
Portrait of John von Neumann

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