Analysis Quote by Johann Heinrich Lambert

The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines…

— John Maynard Keynes

In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is…

— Martin Gardner

What a mathematical proof actually does is show that certain conclusions, such as the irrationality of , follow from certain premises, such as the…

— Timothy Gowers

Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions.

— Anonymous

The once-surprising existence of non-Euclidean models of Euclid's first four axioms can be seen as a sort of mathematical joke.

— John Allen Paulos

Certainly it is permitted to anyone to put forward whatever hypotheses he wishes, and to develop the logical consequences contained in those hypotheses. But…

— Giuseppe Peano

It would be foolish to give credit to Euclid for pangeometrical conceptions; the idea of geometry deifferent from the common-sense one never occurred to…

— George Sarton

Postulates are based on assumption and adhered to by faith. Nothing in the Universe can shake them.

— Isaac Asimov

We cannot ... prove geometrical truths by arithmetic.

— Aristotle

Any good theorem should have several proofs, the more the better.

— Michael Atiyah

Proofs exist only in mathematics and logic, not in science.

— Satoshi Kanazawa

Many of the proofs in mathematics are very long and intricate. Others, though not long, are very ingeniously constructed.

— Edward Charles Titchmarsh