Facts Quote by Emile Borel

All results of the profoundest mathematical investigation must ultimately be expressible in the simple form of properties of the integers.

— Leopold Kronecker

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

— Kurt Gödel

Integers are the fountainhead of all mathematics.

— Hermann Minkowski

The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been…

— G. H. Hardy

. . . we have overcome the notion that mathematical truths have an existence independent and apart from our own minds. It is even…

— Anonymous

Mathematics in general is fundamentally the science of self-evident things.

— Felix Klein

As far as I know, only a small minority of mathematicians, even of those with Platonist views, accept the idea that there may be…

— Abraham Robinson

Mathematics and logic have been proved to be one; a fact from which it seems to follow that mathematics may successfully deal with non-quantitative…

— Alfred Korzybski

One of the chief triumphs of modern mathematics consists in having discovered what mathematics really is.

— Bertrand Russell

For mathematics, even to the logical forms in which it moves, is entirely dependent on the concept of natural number.

— Hermann Weyl

Can the existence of a mathematical entity be proved without defining it ?

— Jacques Hadamard

All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to…

— Anonymous