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Related: question #879, Most interesting mathematics mistake. But the intent of this question is more pedagogical. In many branches of mathematics, it seems to me that a good counterexample can be ...

The background of my question comes from an observation that what we teach in schools does not always reflect what we practice. Beauty is part of what drives mathematicians, but we rarely talk about ...

This question is a follow up to 74841, and follows from a suggestion by Gian-Carlo Rota that beauty as judged by the educated public differs from that experienced by mathematicians (he gives Euclidean ...

I need examples of problems which use, directly or indirectly, the homomorphism $S_4\to S_3$ in the solution (its kernel is $\mathbb{Z}_2\oplus\mathbb{Z}_2$). Obvious candidates: Lagrange resolvent (...

The other day I was trying to figure out how to explain why isomorphisms are important. I pulled Boyer's A History of Mathematics off the bookshelf and was surprised to find that isomorphism isn't ...