181–182 of 182 posts
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Is this what humans do?
No. Not in my experience. Anyone with experience in research mathematics will tell you that making progress at the research level is driven by intuition - intuition honed from years of training with formal rules and rigor but intuition nonetheless - with the final step being to reframe the argument in formal/rigorous language and ensure consitency and so forth. Infact the more experience and skill I get in supposedly…
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Think of all the algebra problems you got in school where the solution started with "get all the x's on the same side of the equation." You then applied a bunch of rules like "you can do anything to one side of the equals sign if you also do it to the other side" to reiterate the same abstract concept over and over, gradually altering the symbology until you wound up at something that looked like the quadratic formul…
People don't uncover new mathematics with formal rules and symbols pushing, at least not for the most part. They do so first with intuition and vague belief. Formalisation and rigour is the final stage of constructing a proof or argument.