Alicia Boole Stott, a self-taught mathematician, was one of the first people to explore four-dimensional geometrical figures, for which she was awarded an honorary doctorate.
Born in Cork City in 1860, Alicia was the third of five daughters of logician and mathematician George Boole and his wife, educational psychologist Mary Everest.
When George died in 1864, Mary and four of their children moved to London, where Mary worked as a librarian in the Queen’s College, London.
Her daughters attended the college’s junior school, except Alicia, who remained in Cork with relatives for some seven years before joining her mother and sisters in London.
None of the Boole sisters went to university, but at age 18, Alicia’s brother-in-law Charles Howard Hinton introduced her to his wooden geometric models. Fascinated, she began to experiment with them.
Alicia developed an ability to visualise in the fourth dimension. She was particularly interested in the convex regular solids in four dimensions, and coined the term ‘polytopes’ to describe them.
By manipulating models, she discovered that in four dimensions there are six regular ‘hypersolids’, or as she called them, polytopes.
Despite never learning any analytical geometry, she made three-dimensional central cross-sections of all six using Euclidean constructions and synthetic methods.
Working alone and as an amateur, she was unaware the six polytopes had been discovered by Ludwig Schlaefli in 1840, rediscovered by Washington Irving Stingham and other mathematicians, and then by herself. She had constructed her models purely from curiosity.
Boole worked as a secretary, married Walter Stott, an actuary, in 1890, and they had two children. Then, some years later, a paper by a Dutch mathematics professor in the Proceedings of the Amsterdam Academy caught her attention.
Pieter Hendrik Schoute had approached Boole Stott’s problems by purely analytical means, and his results were identical with hers. When she learned of this, Boole Stott constructed a set of her cardboard models, photographed them and sent the prints to Schoute at Groningen University. He was so impressed he came to England to visit, and so began a collaboration.
Boole Stott published her main work in 1900 and 1910 but left her mathematical work when Schoute died in 1913. The following year, Groningen University conferred her with an honorary doctorate.
In 1930, she resumed her work when her nephew, Geoffrey Ingram Taylor, introduced her to a noted geometer, Harold Scott MacDonald Coxeter. He was 23 and she was 70, yet they began to collaborate.
Together, they investigated the Gosset four-dimensional polytope. Boole Stott again made models of its sections, and was the first to point out that its vertices lie on the edges of another polytope, dividing them in golden section.
She suggested the idea of partial truncation and invented the processes of expansion and contraction, which led her to discover various uniform polytopes.
Boole Stott and Coxeter delivered a joint paper in Cambridge University, and she donated a set of models for permanent exhibition in the department of mathematics.
She died in Middlesex in 1940.
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With thanks to Mary Mulvihill of Ingenious Ireland for providing the material for this profile from her book Lab Coats and Lace (2009).
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