A quotation by Jacques Hadamard
The shortest path between two truths in the real domain passes through the complex domain.
Quoted in The Mathematical Intelligencer 13 (1991).
Practical application is found by not looking for it, and one can say that the whole progress of civilization rests on that principle.
Quoted in H Eves Mathematical Circles Squared (Boston 1972).
To parents who despair because their children are unable to master the first problems in arithmetic I can dedicate my examples. For, in arithmetic, until the seventh grade I was last or nearly last.
Quoted in D MacHale, Comic Sections (Dublin 1993)
Logic merely sanctions the conquests of the intuition.
Quoted in M Kline, Mathematical thought from ancient to modern times (New York, 1972).
Can the existence of a mathematical entity be proved without defining it ?