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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.
23
votes
Extremely messy proofs
This is not about measure theory or Dynkin's lemma or Caratheodory's extension theorem, but it is hard for me to resist sharing one of my favorite examples of improving proofs with modern machinery: t …
10
votes
Why do we teach calculus students the derivative as a limit?
A problem I like to give students to solve shortly after introducing the derivative is to evaluate $f'(2)$ for $f(x) = x^x$. Of course, this function can be rewritten as $f(x) = e^{x\ln x}$ but in my …