I probably did a Stallings. I spent the whole of last night ‘proving’ some thing which bothered me off and on for forty years. When the mind is calmer, mistakes will emerge but not in the current state. As Stallings said in ‘How not to prove the Poincaré conjecture’ some excitement and blindness takes over: “I was unable to find flaws in my ‘proof’ for quite a while, even though the error is very obvious. It was a psychological problem, a blindness, an excitement, an inhibition of reasoning by an underlying fear of being wrong. Techniques leading to the abandonment of such inhibitions should be cultivated by every honest mathematician.” May be the body needs rest too. In any case I got some training from Stallings writing his Tata Notes which I wrote in 1967 adding many mistakes of mine to his. He describes the genesis of those Noted towards the end here in Remambering John Stallings
“Early in my career, when I was starting to teach at Princeton, I got to give some seminar talks on my work on PL manifolds, involving the Engulfing Theorem and high-dimensional Poincaré Conjecture. I did not do a good job of this; there were many details, such as general position, which I did not really know how to do; the typical proof was just by hand-waving. I do recall “great” topologists in the audience, such as Milnor. And I think I called it off eventually, finally getting the proofs of some details in my Tata notes of 1967 or so.”
“Early in my career, when I was starting to teach at Princeton, I got to give some seminar talks on my work on PL manifolds, involving the Engulfing Theorem and high-dimensional Poincaré Conjecture. I did not do a good job of this; there were many details, such as general position, which I did not really know how to do; the typical proof was just by hand-waving. I do recall “great” topologists in the audience, such as Milnor. And I think I called it off eventually, finally getting the proofs of some details in my Tata notes of 1967 or so.”
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