All Questions

In a previous post I asked (Which theorems have Pythagoras' Theorem as a special case?). Are there any compelling examples where it is significantly "easier"/"simpler" to prove ...

I was looking at a bio-movie of Ramanujan last night. Very poignant. Also impressed by Jeremy Irons' portrayal of G.H. Hardy. In G.H. Hardy's wiki page, we read: . . . "Hardy cited as his most ...

Denote by $\pi(x)$ the number of primes $\leq x$. I'm interested in knowing who came up with the first elementary proof that $\pi(x)=o(x)$. I know that Chebyshev demonstrated elementarily before ...

In a few days I will be giving a talk to (smart) high-school students on a topic which includes a brief overview on the notions of curvature and of gedesic lines. As an example, I will discuss flight ...

Every real symmetric matrix has at least one real eigenvalue. Does anyone know how to prove this elementary, that is without the notion of complex numbers?

This is one of those recreational questions that aren't really about research. I found a curious remark in an old volume of American Mathematical Monthly (1922) which I'll quote below: In the ...