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Results tagged with mathematical-philosophy
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user 17907
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.
5
votes
Sine and Archimedes' derivation of the area of the circle
To answer your question 1: it really depends on which set of axioms you consider 'canonical'. If you look at it from the viewpoint of the first-year courses in calculus and vector analysis and the lik …
- 4,746
0
votes
Is pure mathematics useful outside of mathematics itself?
I think you're right to have these doubts, that is to say, I have had similar misgivings about the "usefulness" of my work in pure mathematics, and not only that, but the "usefulness" of pure mathemat …
14
votes
Pressure to defend the relevance of one's area of mathematics
Let me address the very final part of your question, concerning "one’s own internalized sense of what is proper research". I have definitely encountered this form of internal doubt during my years as …