What binds us to space-time is our rest mass, which prevents us from flying at the speed of light, when time stops and space loses meaning. In a world of light there are neither points nor moments of time; beings woven from light would live "nowhere" and "nowhen"; only poetry and mathematics are capable of speaking meaningfully about such things. -Yuri Manin

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.

I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways." -Godfrey H. Hardy on Srinivasa Ramanujan

The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight. -Dantzig

Suppose we loosely define a religion as any discipline whose foundations rest on an element of faith, irrespective of any element of reason which may be present. Quantum mechanics for example would be a religion under this definition. But mathematics would hold the unique position of being the only branch of theology possessing a rigorous demonstration of the fact that it should be so classified. -F. DeSua

A Mathematician is a machine for turning coffee into theorems. -Paul Erdos

This is not mathematics, this is theology. -Gordan about Hilbert's Proof of the Basis Theorem

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane. -Richard Hamming

It was a dark and stormy night when R H Bing volunteered to drive some stranded mathematicians from the fogged-in Madison airport to Chicago. Freezing rain pelted the windscreen and iced the roadway as Bing drove on - concentrating deeply on the mathematical theorem he was explaining. Soon the windshield was fogged from the energetic explanation. The passengers too had beaded brows, but their sweat arose from fear. As the mathematical description got brighter, the visibility got dimmer. Finally, the conferees felt a trace of hope for their survival when Bing reached forward - apparently to wipe off the moisture from the windshield. Their hope turned to horror when, instead, Bing drew a figure with his finger on the foggy pane and continued his proof - embellishing the illustration with arrows and helpful labels as needed for the demonstration. - Remembrance at UT Austin

That non-Abelian gauge fields are conceptually identical to ideas in the beautiful theory of fiber bundles, developed by mathematicians without reference to the physical world, was a great marvel to me. In 1975 I discussed my feelings with Chern, and said "this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere." He immediately protested: "No, no. These concepts were not dreamed up. They were natural and real." - C. N. Yang

One evening at a Joint Summer Research Congerence in the early 1990's Nicholai Reshetikhin and I button-holed Flato, and explained at length Shum's coherence theorem and the role of categories in "quantum knot invariants". Flato was persistently dismissive of categories as a "mere language". I retired for the evening, leaving Reshetikhin and Flato to the discussion. At the next morning's session, Flato tapped me on the shoulder, and, giving a thumbs-up sign, whispered, "Hey! Viva les categories! These new ones, the braided monoidal ones." - David Yetter

Mathematicians are like Frenchman: whatever you say to them they translate into their own language, and forthwith it is something entirely different. -Johann Goethe