"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 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." - William Jaco, from an ingenious collection of quotes.
"If I had been swimming the backstroke, I would have quit right away." - swimmer Matt Zelen's promise to his Grandmother after his decision to continue on in his 100m butterfly race when his suit came off diving in.
"We often hear that mathematics consists mainly of 'proving theorems'. Is a writer's job mainly that of 'writing sentences'?" - Gian-Carlo Rota.
"Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity." - Alan Turing, Systems of Logic Based on Ordinals, Proceedings of the London Mathematical Society, (2) 45, 1939.
"Research is the process of going up alleys to see if they are blind." - Marston Bates.