Landau kept a printed form for dealing with proofs of Fermat's last theorem. 'On page blank, lines blank to blank, you will find there is a mistake.' - John Edensor Littlewood

[For an unproved Lemma] I had what looked like a promising idea for this, but it was fallacious. In the middle of a three week holiday - mathematics completely below the horizon - the idea came again out of the blue when I was in bed. I forgot it had been rejected as fallacious, and this forgetting did the trick; because this time I noticed that it did prove something, and, by what was nearly, or quite, automatic writing, a proof got written down which deduced the Lemma from the something. ... I did experience automatic writing again. ... my pencil wrote down the formula [omitted] for no reason at all, and almost unattended by consciousness. On the face of it the formula has no apparent connexion with the problem, but it turns out to be an essential key to the proof. ... as if my subconsciousness knew the thing all the time, and finally got impatient.

Besicovitch and Harry Williams asked me what God was doing before the Creation. I said: 'Millions of words must have been written on this; but he was doing Pure Mathematics and thought it would be a pleasant change to do some Applied.'

My research began, naturally, in the Long Vacation of my 3rd year, 1906. My director of studies (and tutor) E. W. Barnes suggested the subject of integral functions of order 0... [After success,] Barnes was now encouraged to suggest a new problem: 'Prove the Riemann Hypothesis'.