Wow, someone discovered a more efficient way of multiplying two 3×3 matrices! You might think this would have already been solved.
This new method, due to A. Perminov, uses 23 multiplications and 58 addition/subtractions. The previous best used 60 addition/subtractions - and this was discovered only in August last year. It's been known since 1976 that 23 is the fewest multiplications you can use - at least if multiplication can be noncommutative for the 'numbers' in your matrices, like quaternions. I guess this leaves open the possibility that you could bring it down further for real or complex numbers.
This is not at all the sort of math I'd ever want to work on; it reminds me of pole-vaulting and other specialized athletic competitions. But it's one of those problems that's easy to explain, hard to solve.
A 58-Addition, Rank-23 Scheme for General 3x3 Matrix Multiplication https://arxiv.org/abs/2512.21980
I love this sort of explicit work. The algorithm fits in a screenshot:
