“The goys have proven the following theorem…”

— John Von Neumann

Statement at the start of a classroom lecture, as quoted in 1,911 Best Things Anyone Ever Said (1988) by Robert Byrne.

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John Von Neumann 19

Hungarian-American mathematician and polymath 1903–1957

Richard Hamming (1915–1998) American mathematician and information theorist

The Unreasonable Effectiveness of Mathematics (1980)
Context: The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.

“A mathematician, then, will be defined in what follows as someone who has published the proof of at least one non-trivial theorem.”

Jean Dieudonné

Mathematics and Mathematicians (1992); published in Is Mathematics Inevitable? A Miscellany (2008), edited by Underwood Dudley, p. 3. ISBN 0883855666

“If for the entire universe we conceive the same magnitude to be determined, consistently and with due regard to all circumstances, which for a single body I have called entropy, and if at the same time we introduce the other and simpler conception of energy, we may express in the following manner the fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat.
1. The energy of the universe is constant.
2. The entropy of the universe tends to a maximum.”

Rudolf Clausius (1822–1888) German mathematical physicist

Ninth Memoir. On Several Convenient Forms of the Fundamental Equations of the Mechanical Theory of Heat.
The Mechanical Theory of Heat (1867)

“In general, people only ask for advice that they may not follow it; or, if they should follow it, that they may have somebody to blame for having given it.”

Alexandre Dumas book The Three Musketeers

Variant: As a general rule... people ask for advice only in order not to follow it; or if they do follow it, in order to have someone to blame for giving it.
Source: The Three Musketeers

“The positive energy theorem was for half a century or more an open challenge to relativists. Many attempts were made to prove flat spacetime was stable, but none completely succeeded completely until a majestic tour de force of geometric reasoning of Shoen and Yau. This was followed two years later by a proof of Witten, which was as elegant as it was short. It is this proof of Witten’s that we take as a template here for the quantum theory.”

Lee Smolin (1955) American cosmologist

"Positive energy in quantum gravity" arXiv (Jun 10, 2014)

“You have the right to follow your dreams. I'm giving you permission to follow your dreams.”

Martin de Maat (1949–2001) American theatre director

The Mysterious Martin de Maat (2001)

“Follow your heart, follow your dreams. If writing is your passion, put everything you have into it.”

J.M. DeMatteis (1953) comics illustrator

A Conversation With The Legendary J.M. DeMatteis! (2004)
Context: Follow your heart, follow your dreams. If writing is your passion, put everything you have into it. Let that passion, that joy, lead you. In the end it might not lead you to exactly the place you thought you were heading... but it will absolutely lead you someplace wonderful. And don’t let the Nay-Sayers, the Practical People, stop you or wear you down. Follow your dreams... and you can’t go wrong.