William Boone

Abstract William Werner Boone (1920-1983) was a logician whose research centered on algebraic decision problems, particularly in group theory. He received his doctorate from Princeton University in 1952, and in 1954-1956 he was at the Institute for Advanced Study, where he got to know Gödel. During this period, he was occupied with the word problem for groups, and in 1956 he achieved his goal of constructing a finitely presented group whose word problem is undecidable (Boone 1957 and 1957a). The same result was obtained independently, by a different construction, slightly earlier, by P. S. Novikov (Novikov 1955). Consequently, the recursive undecidability of the word problem for groups is often called the Boone-Novikov theorem. Over the next few years, Boone worked at improving and refining his proof; the end product was the long paper Boone 1959. In 1958 Boone joined the mathematics department of the University of Illinois, becoming professor in 1960. He remained on the faculty there until his death. Boone had a second two-year stint at the Institute for Advanced Study in 1964-1966.