## How can we know something exists if we cannot find it?

The probabilistic method was pioneered by the Hungarian mathematician Paul Erdős, famous for his many contributions to combinatorics and graph theory, and it has since become an important tool in these areas of mathematics. Is this article you will learn how it works!

## Does no small structure mean larger homogeneous ones?

A conjecture of Erdős and Hajnal from 1989 says that forbidding any specific substructure results in existence of a very large homogeneous one! In this article you will have a look into one of the most fascinating problems in modern graph theory.

## New breakthrough about Ramsey numbers?

In a seminar talk in Cambridge this week, Julian Sahasrabudhe announced that he, together with his colleagues Marcelo Campos, Simon Griffiths and Rob Morris, had obtained an exponential improvement to the upper bound for Ramsey's theorem.

## Random encounters with Ramsey numbers

It is was the second time yesterday in a one week time and the fourth in a one month time that I came across Ramsey numbers. In the beginning I thought it was just a coincidence.