Some branches of math are really nice and everything seems seem to fit together and be true for a reasonhave reasoning which is more global. There is a lot of symmetry and efficiency in the proofs because the reasoning transfers easily between proofs. For other branches of math, a lot of things truths seem to end up being true by accident or by luckbe more local. The proofs feel like we are beating the truth into submission with tend to have lots of sub-cases and exceptions. There are fewer general principles. Does anybody know why branches of math vary like this? Can you place different branches of math on this scale from being dominated by more ad hoc to being dominated by less ad hoc proofs?
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Why do branches of math vary in proof styles and what category are different branches in?Some branches of math are really nice and everything seems to fit together and be true for a reason. There is a lot of symmetry and efficiency in the proofs. For other branches of math, a lot of things seem to end up being true by accident or by luck. The proofs feel like we are beating the truth into submission with lots of sub-cases and exceptions. Does anybody know why branches of math vary like this? Can you place different branches of math on this scale from being dominated by more ad hoc to being dominated by less ad hoc proofs?
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