Ben Green

Richard Guy's book "Unsolved Problems in Number Theory" was one of the first mathematical books I owned. I will discuss a selection of my favorite problems from the book, together with some of the progress that has been made on them in the 30 years...

Abstract:The Sylvester-Gallai Theorem states that, given any set P of n points in the plane not all on one line, there is at least one line through precisely two points of P. Such a line is called an ordinary line. How many ordinary lines must there...

Abstract : Colour {1,..,N} red and blue, in such a manner that no 3 of the blue elements are in arithmetic progression. How long an arithmetic progression of red elements must there be? It had been speculated based on numerical evidence that there...