Anurag Bishnoi
One of the oldest open problem in Ramsey theory has been solved. We now know the asymptotics of Ramsey numbers , for any fixed , up-to log factors. Last month, Domagoj Bradač showed that for any fixed and (where the term is hiding log factors), using a beautiful finite-geometric...
Anurag Bishnoi
The following post is (partly) based on discussions with Dion Gijswijt and Ananth Ravi from September 2025. The famous cap set problem has attracted the attention of various mathematicians from different areas over the last few decades. It asks for the largest possible size, , of a 3-term...
Anurag Bishnoi
In this post, I will discuss a recent breakthrough of Hunter, Pohoata, Verstraete and Zhang on an old problem in finite geometry, which also has interesting consequences outside this area. For example, it improves constructions in a minimal distance problem in and it has been adapted by Ihringer...
Anurag Bishnoi
What is the minimum number of colors needed to color the points of the Fano plane such that there is no monochromatic line? It is a nice exercise to prove that two colors do not suffice. This fact has been known at least since the 1956 paper of Richardson that introduced the notion of...
Anurag Bishnoi
How many swaps do you need to sort objects on a circle in clockwise order? This fairly simple and natural question quickly leads to some deep mathematics that I would like share. Let’s start with an example for : After swapping 2 with 6, 1 with 4, and then 4 with 5, we get the...
Anurag Bishnoi
The Ramsey number is the smallest such that every graph on vertices either contains a clique of size or an independent set of size . Ramsey’s theorem implies that these numbers always exist, and determining them (precisely or asymptotically) has been a major challenge in mathematics for the...