The author of the proof had used a lemma from a famous topology book.

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There are plenty of geometric questions that I would not have any idea how to conjecture what is true.

Perhaps it is just a defect in my abilities, but geometry seems to be orders of magnitude trickier than number theory.

See this for some nice comments on high dimension geometry. Groups My intuition about finite groups is even worse than my geometric intuition. In a sense my intuition about groups is really very good.

It is a quite interesting anonymous blog—it is being written a by a Ph. Over the years I have hit upon a rule in thinking about groups.

A classic example of this is the conjectured behavior of twin primes.

If primes are random, then one would expect that there are about twin primes in where is a constant.

I once had a proof that needed only a lemma about the structure of the primes to be complete.

It was about a communication lower bound that I was working at the time with Bob Sedgewick.

I once lost several months of hard work trying to use a published theorem to solve an open problem. For now let’s turn to the discussion of intuition in mathematics.