Does intuition play an important role in the field of mathematics? The essay seems to suggest that mathematicians use their intuition a great deal. Terence Tao seems to agree that it is important:
...“fuzzier” or “intuitive” thinking (such as heuristic reasoning, judicious extrapolation from examples, or analogies with other contexts such as physics) gets deprecated as “non-rigorous”. All too often, one ends up discarding one’s initial intuition and is only able to process mathematics at a formal level, thus getting stalled at the second stage of one’s mathematical education.
The point of rigour is not to destroy all intuition; instead, it should be used to destroy bad intuition while clarifying and elevating good intuition. It is only with a combination of both rigorous formalism and good intuition that one can tackle complex mathematical problems;
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.
It still might be a good idea to post it there. Afaik, duplication in quotes threads is discouraged, but not between the quotes threads and the rest of the site.
Does intuition play an important role in the field of mathematics? The essay seems to suggest that mathematicians use their intuition a great deal. Terence Tao seems to agree that it is important:
What is intuition?
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.
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It still might be a good idea to post it there. Afaik, duplication in quotes threads is discouraged, but not between the quotes threads and the rest of the site.