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by freehorse
1 day ago
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New techniques and abstractions is how mathematics expand. Mathematics is about studying structures, proving statements is a part of it but it is not all what mathematics is about. If anything, proofs themselves are a means to an end (understanding). Eg Galois developed some techniques and abstractions to prove that there is no general solution to polynomial equations of degree >=5, but these techniques and abstractions gave rise to whole new mathematical fields. Mathematics has to be also understood from the perspective of theory building, not just problem solving. |
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