Two years ago I blogged about recent developments about multiplying integers. The next most important operation in (applied) mathematics is multiplying matrices.

The usual way of doing this requires \(n^3\) multiplications (and some additions) for multiplying two \((n\times n)\)-matrices. But there is actually a way of doing it with less than this: the current record by Alman-Williams from last October is roughly at \(\mathcal{O}(n^{2.37286})\)-multiplications (arXiv:2010.05846).

There is a nice, short article on the QuantaMagazine about this: link.