Quote by Ellen J. Langer

It is by logic we prove. It is by intuition we discover.

— Henri Poincare

It is through science that we prove, but through intuition that we discover.

— Henri Poincare

The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing.

— George Polya

It is with logic that one proves; it is with intuition that one invents.

— Henri Poincare

“a few centuries earlier. At that time the humans still knew pretty well when a thing was proved and when it was not; and…

— C.S. Lewis

Mathematicians create by acts of insights and intuition. Logic then sanctions the conquests of intuition.

— Morris Kline

Intuition is the source of scientific knowledge.

— Aristotle

“The first successes were such that one might suppose all the difficulties of science overcome in advance, and believe that the mathematician, without being…

— Joseph Bertrand

Like Molière's M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being…

— Ernest Nagel

“Somewhere out there is a theory that would explain my empirical observations, and this theory has yet to be discovered. Mathematics thrives on such…

— Henri Darmon

Intuition is more important to discovery than logic.

— Henri Poincare

“There is no such thing as a logical method of having new ideas. Discovery contains an irrational element or a creative intuition. Karl Popper1”

— Frans P.B. Osinga