A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so.
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Source, in full
"The Role of Mathematics in the Sciences and in Society" (1954) an address to Princeton alumni, published in John von Neumann : Collected Works (1963) edited by A. H. Taub ; also quoted in Out of the Mouths of Mathematicians : A Quotation Book for Philomaths (1993) by R. Schmalz