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Poincare, Henri - Discovering arithmetic transformations of indefinite ternary quadratic forms



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A description of the experience

An Essay on the Psychology of Invention in the Mathematical Field – Jacques Hadamard

I turned my attention to the study of some arithmetical questions apparently without much success…….. Disgusted with my failure, I went to spend a few days at the seaside and thought of something else.

One morning, walking on the bluff, the idea came to me, with just the same characteristics of brevity, suddenness and immediate certainty, that the arithmetic transformations of indefinite ternary quadratic forms were identical with those of non Euclidian geometry.’

These two results showed to Poincare that there existed other fuchsian groups and consequently, other fuchsia functions than those which he had found during his sleeplessness.

The source of the experience

Poincare, Henri

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