As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

Albert Einstein (1879 - 1955), "Geometry and Experience", January 27, 1921

Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.

Albert Einstein (1879 - 1955)

Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.

Bertrand Russell (1872 - 1970), Mysticism and Logic¹ (1917) ch. 4

Mathematics, rightly viewed, possesses not only truth, but supreme² beauty - a beauty cold and austere³, like that of sculpture.

Bertrand Russell (1872 - 1970)

Mathematics is the queen of the sciences.

Carl Friedrich Gauss (1777 - 1855), from Sartorius von Waltershausen, "Gauss zum Gedachtniss" [1856]

I went off to college planning to major in math or philosophy-- of course, both those ideas are really the same idea.

Frank Wilczek (1951 - )

In mathematics you don't understand things. You just get used to them.

Johann von Neumann (1903 - 1957)

I have hardly ever known a mathematician⁴ who was capable of reasoning.

Plato (427 BC - 347 BC), The Republic

Proof is the idol⁵ before whom the pure mathematician tortures himself.

Sir Arthur Eddington (1882 - 1944), The Nature of the Physical World

The mathematics is not there till we put it there.

Sir Arthur Eddington (1882 - 1944), The Philosophy of Physical Science

We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about 'and'.

Sir Arthur Eddington (1882 - 1944), The Harvest of a Quiet Eye (A. L. Mackay), 1977

If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker⁶ entirely⁷ by the use of the mathematics of probability.

Vannevar Bush (1890 - 1974)