The key to speed, researchers have determined, is to reduce the number of multiplication steps, lowering that exponent from n3 (for the standard method) as much as they can. The lowest possible value, n2, is basically as long as it takes just to write the answer. Computer scientists refer to that exponent as omega, ω, with nω being the fewest possible steps needed to successfully multiply two n-by-n matrices as n grows very large. “The point of this work,” said Zhou, who also co-authored the January 2024 paper, “is to see how close to 2 you can come, and whether it can be achieved in theory.”

After proving the existence of this loss, Duan’s team modified the way that the laser method labeled blocks, reducing the waste substantially. As a result, they set a new upper bound for omega at around 2.371866 — an improvement over the previous upper bound of 2.3728596, set in 2020 by Josh Alman and Vassilevska Williams. That may seem like a modest change, lowering the bound by just about 0.001. But it’s the single biggest improvement scientists have seen since 2010. Vassilevska Williams and Alman’s 2020 result, by comparison, only improved upon its predecessor by 0.00001.