A set of integers greater than 1 is primitive if no number in the set divides another. Erdős proved in 1935 that the series of $1/(n \log n)$ for $n$ running over a primitive set A is universally bounded over all choices of A. In 1988 he conjectured that the universal bound is attained for the set of prime numbers. In this research case study, Oxford's Jared Duker Lichtman describes recent progress towards this problem:
Alongside the mathematics, the Andrew Wiles Building, home to Oxford Mathematics, has always been a venue for art, whether on canvas, sculpture, photography or even embedded in the maths itself.
However, lockdown has proved especially challenging for the creative arts with venues shut. Many have turned to online exhibitions and we felt that not only should we do the same but by so doing we could stress the connection between art and science and how both are descriptions of our world.