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Results tagged with mathematical-philosophy
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user 29316
Philosophical aspects of logic and set theory; truth status of mathematical axioms; Philosophy of Mathematics; philosophical aspects of mathematics in general; relation of mathematics to philosophy; etc. Consider also posting at http://philosophy.stackexchange.com/, where philosophy-of-mathematics is one of the most popular tags.
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Is rigour just a ritual that most mathematicians wish to get rid of if they could?
"No". That was my answer till this afternoon! "Mathematics without proofs isn't really mathematics at all" probably was my longer answer. Yet, I am a mathematics educator who was one of the panelists …
22
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Is rigour just a ritual that most mathematicians wish to get rid of if they could?
Here is an "uncommon" answer in favor of rigour from an old paper of Atiyah (Bull. Inst. Math. App. 10 (1974), 232-234): "How research is carried out?" In particular, I like the first part of the quot …
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History of the abstract method in mathematics
Recently I have "finished" a 13-year on and off research on the history of the mathematical notion of equivalence. At the end of which, I learned that we owe the nowadays rather elementary process of …
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Did Euler prove theorems by example?
Not sure if this answer adds anything to the ones already given. I write it because It is an example where Euler explicitly writes about the necessity of giving a proof, and more importantly, calls a …