Abel Quote by Niels Henrik Abel

Perhaps the greatest paradox of all is that there are paradoxes in mathematics.

— Edward Kasner

Even in pure mathematics they can't remove all paradox, and the rest of us should also recognize we are going to have to endure…

— Charlie Munger

“The implication is that logical or mathematical proofs cuts no ice in adjudicating competing claims of fact.[101] Analytic propositions “are entirely devoid of factual…

— Stephen R.C. Hicks

“The paradox of illuminating complexity is that it is inherently difficult to do so without erasing all of the nuance.”

— David Shenk

Mathematics does not grow through a monotonous increase of the number of indubitably established theorems but through the incessant improvement of guesses by speculation…

— Imre Lakatos

One cannot really argue with a mathematical theorem.

— Stephen Hawking

That's the problem with false proofs of true theorems; it's not easy to produce a counterexample.

— Jeffrey Shallit

“However, one cannot really argue with a mathematical theorem.”

— Stephen Hawking

It is not so much whether a theorem is useful that matters, but how elegant it is.

— Stanislaw Ulam

The development of mathematics towards greater precision has led, as is well known, to the formalization of large tracts of it, so that one…

— Kurt Gödel

“It is an unfortunate fact that proofs can be very misleading. Proofs exist to establish once and for all, according to very high standards,…

— Herbert S. Gaskill

“Mathematicians have, according to Wright, been "unreasonably successful" in finding applications to apparently useless theorems, and often years after the theorems were first discovered.”

— Alex Bellos