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It is not typical that being good in one area of mathematics makes one proficient in another — mathematics has a lot of depth, and to reach the frontier in any
by svat 2y ago
It is not typical that being good in one area of mathematics makes one proficient in another — mathematics has a lot of depth, and to reach the frontier in any specialization requires years of study. However:
- There are skills that carry over; these are usually known by the name "mathematical maturity" https://en.wikipedia.org/w/index.php?title=Mathematical_maturity&oldid=1268743726 https://en.wikipedia.org/w/index.php?title=Mathematical_matu...
- There is a story/legend told about Erdős, where he was so good at problem-solving/proofs that he once solved a problem in another area after asking for the definitions of the terms in the problem. (The fact that this story is told illustrates that it is not commonplace.)