In 1969 Strassen showed surprisingly that it is possible to multiply two 2 x 2 matrices using seven multiplications and 18 additions, instead of the naive eight multiplications and four additions. The number of additions was later reduced to 15. Karstadt and Schwartz further reduced the number of additions to 12 using a change-of-basis method. Both the number of multiplications and the number of additions have been shown to be optimal for the 2 x 2 case. For multiplying 3 x 3 matrices, the lowest number of multiplications found so far is 23. Using 23 multiplications, Schwart et al. showed how to reduce the number of additions to 61 using a change-of-basis method. Mårtensson and Stankovski Wagner showed how to achieve 62 additions, without changing basis. Using the optimization method by Mårtensson and Stankovski Wagner, Stapleton found an algorithm requiring only 60 additions. In this work we continue to combine the methods of Mårtensson, Stankovski Wagner and Stapleton, finding an algorithm requiring only 59 additions, still without a basis change. Technical details on the method and tools used for finding this scheme, and a discussion on the impact of this discovery, will come in an upcoming publication.

翻译：1969年，Strassen出人意料地证明，两个2×2矩阵的乘法可以通过7次乘法和18次加法完成，而非朴素的8次乘法和4次加法。加法次数后来被减少到15次。Karstadt和Schwartz通过基变换方法进一步将加法次数降至12次。对于2×2情形，乘法次数和加法次数均已被证明是最优的。对于3×3矩阵乘法，目前已知的最低乘法次数是23次。Schwart等人利用23次乘法，通过基变换方法将加法次数减少至61次。Mårtensson和Stankovski Wagner展示了如何在不变换基的情况下实现62次加法。Stapleton运用Mårtensson和Stankovski Wagner的优化方法，找到了一种仅需60次加法的算法。在本研究中，我们继续结合Mårtensson、Stankovski Wagner和Stapleton的方法，发现了一种仅需59次加法的算法，且仍无需基变换。关于该方案所用方法及工具的技术细节，以及此发现影响的讨论，将在后续出版物中呈现。