SIMO Retiree Blog

(Jit here.) I am going to write about some recent ideas in diophantine geometry. Consider a curve $C$ inside $\mathbb{C}^2$ given by some polynomial $P(x,y) = 0$. Can there be infinitely many points $(x,y)$ lying on our curve $C$ such that both $x$ and $y$ are roots of unity?

(David here.) A math teacher from Primary school once told me that "lazy people make good mathematicians". This is one story of laziness-inspired mathematics.

(This is Yan Sheng.) At some point I came up with a new idea to prove the famous identity$$\zeta(2)\coloneqq\sum_{n=1}^\infty\frac1{n^2}=\frac{\pi^2}6.$$