Integer multiplication is one of the oldest mathematical operations and still a central problem for computer arithmetic. The complexities of many other basic operations such as division, base conversion, gcds, computing e and pi, FFTs, etc. can be expressed in terms of the complexity of integer multiplication. In our talk, we will survey a new algorithm for multiplying two n-digit integers in time O(n log n).

Joris van der Hoeven and David Harvey received the de Bruijn Medal 2022 for this work.