William Werner Boone

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Born: 16 Jan 1920 in Cincinnati, Ohio,USA
Died: 14 Sept 1983 in Urbana, Illinois, USA

Bill Boone trained as an accountant after leaving high school. As his family did not have much money he had to earn his way working as a barman. However his real ambition at this time was to become a writer and he attended workshops on writing and wrote a short story.

Bill turned to mathematics taking a part-time degree at the University of Cincinnati. He graduated in 1945 and, the same year, began graduate studies at Princeton.

He obtained a doctorate from Princeton in 1952 having failed to carry out Post's suggestion of constructing a finitely presented group with insoluble word problem. Post and Markov had independently constructed semigroups with this property in 1947. In fact Boone had constructed for his doctoral thesis an example of a finitely presented group with no way to decide if a given element lies in the subsemigroup generated a fixed finite set. Boone's doctoral supervisor at Princeton was Church and his thesis was entitled Several Simple, Unsolvable Problems of Group Theory Related to the Word Problem.

In 1950 Turing gave an example of a cancellative semigroup with insoluble word problem (having at one stage believed incorrectly that he could solve the group problem). Following these ideas of Turing's Boone finally proved the insolubility of the word problem for groups in 1957, two years after Novikov published his proof.

Boone proved in 1959 that many other decision problems for groups were insoluble. From 1958 Boone worked at Illinois, Urbana where he was based for the rest of his life. However he liked Europe and spent much time there.

He spent the years 1972-73 and 1978-79 at Oxford and wrote a joint paper with G Higman during the first of these visits which is of major importance. It gives an algebraic characterisation of groups with soluble word problem connecting this property with embeddability in a simple group.