Alfred W. Hales

Alfred Washington Hales (born November 30, 1938 in Pasadena, California) is an American mathematician who deals with combinatorial and algebra.

Hales studied at Caltech and was there as a student twice 1958/59 Putnam Fellow. In 1960 he received his bachelor's degree and in 1962 he was promoted to Robert Dilworth at Caltech (On the nonexistence of free complete Boolean algebras). He was a postdoctoral student at the University of Cambridge in 1962/63. From 1963 to 1966 he was Benjamin Peirce Instructor at Harvard University. From 1966 he was assistant professor and then professor at the University of California, Los Angeles, where he temporarily headed the faculty. In 1992, he became Professor Emeritus and headed the Center for Communications and Computing at the Institute for Defense Analysis.

In 1977/78 he was a guest scientist at the University of Warwick, 1986/97 at MSRI, whose board of trustees he was from 1995 to 1999, and 1970/71 at the University of Washington

He is known for the theorem of Hales-Jewett (1963, with Robert I. Jewett) from Ramsey theory. The theorem assures the existence of regular structures at sufficiently high dimensions and was considered and proved by them for the example of a generalized Tic-Tac-Toe-type game. If you play the game on a sufficiently high-dimensional cube with a given page length n and number of players c, there is always a winning solution (row, column or diagonal of the same color).

He contributed to the book Shift Register Sequences by Solomon W. Golomb. He also dealt with group theory and theory of modules and associations.

In 1971 he was one of the first recipients of the George Pólya Prize with Jewett and others. He is a fellow of the American Mathematical Society (2012) and the American Association for the Advancement of Science.

He has been married to Virginia Green since 1962 and has a son and two daughters. Single-level Edit source text

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