Poincare, Henri - Discovering functions without realising it
Type of spiritual experience
This is a fascinating observation, as it shows that although some of Poincare's work proceeded with him knowing he had been given insight, he also proceeded without realising that he had been given more insight than he realised.
A description of the experience
An Essay on the Psychology of Invention in the Mathematical Field – Jacques Hadamard
In Poincare’s Methodes Nouvelles de la Mecanique Celeste Volume III , he has to deal with the calculus of variations and he uses a sufficient condition fr a minimum, equivalent to the one which results from Weierstrass’s method. But he does not give a proof of that condition; he speaks of it as a known fact. Now, as we have said, Weierstrass’s method was not published at the time when that volume of the Methode Nouvelles was written. Moreover, he does not make any mentin of Weierstrasse’s discovery, which he should have necessarily done if he had received any private communication of it. Above all, it must be added that the condition is formulated in a form slightly different (though basically equivalent) from the ne which is classically known as resulting from Weierstrasse’s method. Must we think that Weierstrasse’s argument or an analogous one was found by Poincare and remained unconscious in his mind?