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Stuart_Armstrong comments on [LINK] What is it like to have an understanding of very advanced mathematics? - Less Wrong Discussion
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Intuition is vital. Theorems can take paragraphs and proofs can go for pages; without intuition, the combinatorics would annihilate you. Interestingly, I'm starting to develop new intuitions (in logic, rather than my old field, differential geometry) which means I might soonbe able to do some work in the field.