It is possible to improve the exponent further; however, the exponent must be at least 2 (because an <math>n \times n</math> matrix has <math>n^2</math> values, and all of them have to be read at least once to calculate the exact result).
In 2010, Andrew Stothers gave an improvement to the algorithm, <math>O(n^{2.374}).</math><ref>{{Citation | last1=Stothers | first1=Andrew | title=On the Complexity of Matrix Multiplication | url=httphttps://www.mathsera.lib.ed.ac.uk/pghandle/thesis1842/stothers.pdf4734 | year=2010}}.</ref><ref>{{Citation | last1=Davie | first1=A.M. | last2=Stothers | first2=A.J. | title=Improved bound for complexity of matrix multiplication|journal=Proceedings of the Royal Society of Edinburgh|volume=143A|pages=351–370|year=2013|doi=10.1017/S0308210511001648}}</ref> In 2011, Virginia Williams combined a mathematical short-cut from Stothers' paper with her own insights and automated optimization on computers, improving the bound to <math>O(n^{2.3728642}).</math><ref>{{Citation | last1=Williams | first1=Virginia | title=Breaking the Coppersmith-Winograd barrier | url=http://theory.stanford.edu/~virgi/matrixmult-f.pdf | year=2011}}</ref> In 2014, François Le Gall simplified the methods of Williams and obtained an improved bound of <math>O(n^{2.3728639}).</math><ref>"Even if someone manages to prove one of the conjectures—thereby demonstrating that ω = 2—the wreath product approach is unlikely to be applicable to the large matrix problems that arise in practice. (...) the input matrices must be astronomically large for the difference in time to be apparent."{{Citation | last1=Le Gall | first1=François | contribution=Powers of tensors and fast matrix multiplication | year = 2014 | arxiv=1401.7714 | title = Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation ([[ISSAC]] 2014)}}</ref>
The Coppersmith–Winograd algorithm is frequently used as a building block in other algorithms to prove theoretical time bounds.
