Mathematics of AI       

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Mathematics of AI - Highlights


Historical highlights

 

Algorithms

1990: Fast Matrix Multiplication (Don Coppersmith, Shmuel Winograd)

Following Strassen's breakthrough on matrix multiplication faster than O(n^3), Coppersmith and Winograd developed a more general framework for designing such algorithms using tensor algebra. Their algorithm, which multiplies matrices in time O(n^2.375), was the asymptotically fastest one for 20 years, until recent improvements by Stothers and Vassilevska-Williams. 

Cryptography

1976: DES - Data Encryption Standard (Don Coppersmith)

This encryption technique was developed at IBM in the 1970s and approved as a federal standard by the United States National Bureau of Standards in 1976. It is a symmetric-key block cipher which has remained in use to this day, in various forms and combinations with other encryption schemes. 

Optimization

1950s: Integer Programming & Cutting Planes (Ralph Gomory)

Ralph Gomory was one of the founders of integer programming - solving linear programs in a way that uses only integer numbers. He proposed cutting planes as a method for solving such problems. While the idea was initially not considered practical, it later found broad applicability in conjuction with branch-and-bound methods, and today it is a fundamental component of optimization software packages.