Rigor's place in mathematics


Found in Hubbard and Hubbard's vector calculus textbook.

Rigor is ultimately necessary in mathematics, but it does not always come first, as Archimedes acknowledged in his own work, in a manuscript discovered in 1906. In it, Archimedes reveals that his deepest results were found using dubious infinitary arguments, and only later proved rigorously, because "it is of course easier to supply the proof when we have previously acquired some knowledge of the questions by the method, than it is to find it without any previous knowledge".

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