**Bill Boone** worked on word problems in Groups.

- One book he much admired was Thomas Wolfe's 'Of Time and the River' whose hero, afflicted with a Faustian thirst for knowledge, moves from the rural South of the United States to Boston and then to England and France, and there is a superficial parallel to this in Bill's all-inquisitive progress from the Mid-West to sophisticated Princeton and subsequent regular visits to Europe.
- However, Bill never lost the directness and openness that one thinks of as characteristic of the provincial America of his youth, and his vigorous personality and broad Mid-West accent left an abiding impression on all who knew him.
- Despite his literary interests, Bill decided to turn to mathematics, a subject which seemed to grow in importance for him around this time in his life, and he studied part-time for a degree at the University of Cincinnati.
- 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.
- Following these ideas of Turing's, Boone finally proved the insolubility of the word problem for groups in 1957, two years after Petr Sergeevich Novikov published his proof.
- Bill's strength as a mathematician was his ability to master, painstakingly and thoroughly, a mass of intricate combinatorial detail and this strength was severely sapped by routine distractions.
- This was the most carefree time in Bill's career - though he was, by temperament, a man never entirely free from worries - for he had a major result behind him and time to think.
- Bill was gregarious in the extreme and made many friends among European mathematicians, notably G Hasenjaeger in Germany and J L Britton, G Higman and B H Neumann in England, to name only a few.
- Boone's first inclination after proving his insolubility theorem was not to move on to other problems but rather to keep on polishing and improving his proof.
- Boone proved in 1959 that many other decision problems for groups were insoluble which was published in a joint publication Some unsolvable problems about elements and subgroups of groups with Gilbert Baumslag and Bernhard Neumann.
- From 1958 Boone worked at the University of Illinois, Urbana, first as an Associate Professor, and from 1960 as a full professor.

Born 16 January 1920, Cincinnati, Ohio, USA. Died 14 September 1983, Urbana, Illinois, USA.

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Algebra, Group Theory, Origin Usa

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive