X-posted from the SIMO X-Men blog

A math teacher from Primary school once told me that “lazy people make good mathematicians”. This is one story of laziness-inspired mathematics.

X-posted from the SIMO X-Men blog, but I think I will rewrite it in multiple parts for followability. This version is suitable for folks fluent in linear algebra.

In this post I want to share a really interesting factoring algorithm that I learnt while taking an advanced cryptography class, and it will serve as a good springboard into talking about the mathematics and algorithms of lattices.

X-posted from the SIMO X-Men blog

I’m going to explore various versions of an idea, starting from where I first saw it in Olympiads, and going beyond.

For a long time now I’ve been searching for some intuitive reasons on why we should expect minimax duality to hold. One approach to this seems to come from online learning algorithms.

We put together the puzzle pieces from the various definitions of “conjugates” and “duality” (convex, Lagrange and minimax) to get a better picture of what duality is. In particular, we will look at

• how minimax duality is a special case of convex duality by constructing a “partial conjugate” function;
• implications for the existence of estimators/constructions with minimax guarantees.