
Close date updated to 2087-11-13 6:59 pm
The possibility of achieving O(n^2.15) time for multiplying two n x n matrices is an ongoing research topic in computational complexity theory. While there is no definitive answer as to whether or not it is possible, there are several mathematicians and computer scientists who believe that it may be achievable.
The Strassen algorithm, the fastest known algorithm for matrix multiplication with a time complexity of O(n^2.807), was discovered in 1969.
Since then, there have been many attempts to improve upon this algorithm, but no one has yet been able to achieve a time complexity better than O(n^2.373).
Reference facts: the current exponent is 2.3728596
https://en.wikipedia.org/wiki/Matrix_multiplication#Computational_complexity