Crilly, Tony (A.J. Crilly)

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Crilly, Tony (A.J. Crilly)


Education: B.Sc., M.Sc., A.M., Ph.D.


Office—The School Office, Middlesex University Business School, The Burroughs, Hendon, London NW4 4BT, England. E-mail—[email protected]


Mathematician, educator, and writer. Faculty member at the University of Michigan, Ann Arbor, 1965-67; Enfield College of Technology, London, England, 1967-1972; Middlesex Polytechnic, London, England, 1972-1984; City Polytechnic, Hong Kong, China, 1982-84; and Middlesex University, London, England, 1984—.


(As A.J. Crilly; editor, with R.A. Earnshaw and H. Jones) Fractals and Chaos, Springer-Verlag (New York, NY), 1991.

(As A.J. Crilly; editor, with R.A. Earnshaw and H. Jones) Applications of Fractals and Chaos: The Shape of Things, Springer-Verlag (New York, NY), 1993.

Arthur Cayley: Mathematician Laureate of the Victorian Age, Johns Hopkins University Press (Baltimore, MD), 2006.

Contributor to books, including History of Topology, edited by I.M. James, Elsevier (Amsterdam, Netherlands), 1999; contributor to periodicals, including Historia Mathematica, Mathematical Intelligencer, and Notes and Records of the Royal Society.


Tony Crilly is an educator whose primary interest is the history of mathematics. He has written and edited many works on fractals, chaos, and computing and is also the author of a biography of Arthur Cayley, one of the most significant English mathematicians of the Victorian era. Crilly's book Arthur Cayley: Mathematician Laureate of the Victorian Age provides a comprehensive biography of a mathematician who has largely been forgotten in the modern age. Although Caley published three papers in the Cambridge Mathematical Journal as an undergraduate at the University of Cambridge, and went on to publish more than twenty more papers in the prestigious journal after receiving his graduate degree and teaching at Cambridge for four years, Caley turned to law as a career that could support him. Nevertheless, he remained devoted to mathematics. He wrote or cowrote approximately 250 more papers as an "amateur" mathematician before he returned to teaching mathematics at Cambridge. He subsequently wrote more than 900 papers on every aspect of modern mathematics, including developing the algebra of matrices and working in non-Euclidean geometry and n-geometry. His work was seminal in developing linear algebra.

In his biography of Cayley, Crilly provides the first full-length account of Cayley's life, from his childhood in Russia, where he was born as the child of a successful merchant from Great Britain, on through his many mathematical accomplishments, most of them made as Sadleirian Chair at Cambridge. "When a biographical subject has led a calm, pleasant life, it is the biographer who must suffer, searching for engaging matter," wrote Daniel S. Silver in the American Scientist. "Fortunately for Crilly, the Victorian society in which Cayley moved was close-knit and lively. George Boole, Charles Dickens, Francis Galton, James Clerk Maxwell and William Thomson (later Lord Kelvin) are but a few Cayley intimates found in these pages."

Crilly acknowledges that Cayley has largely disappeared from the popular history of mathematics but delineates his many achievements and how they influenced mathematics far into the twentieth century and even today. For example, the book points out how Cayley's work in n-dimensional geometry has influenced physics and the study of the space-time continuum. Crilly also discusses how Cayley laid foundations for quantum mechanics through his work on matrices. Although Cayley's work in pure mathematics was not considered at the time to be as important as applied mathematics, Crilly relates that Cayley was eventually recognized for his many contributions to science and, in 1883, was elected president of the British Association for the Advancement of Science.

"Anyone interested in the emerging role of the research mathematician in England will find Crilly's book particularly rewarding," wrote Silver in his review of the biography in the American Scientist. A SciTech Book News contributor noted that the author "describes clearly Cayley's accomplishments."



American Scientist, November 1, 2006, Daniel S. Silver, "The Secret History of Mathematicians," review of Arthur Cayley: Mathematician Laureate of the Victorian Age, p. 556.

Biography, winter, 2007, Daniel S. Silver, review of Arthur Cayley, p. 125.

Choice, June, 2006, M.C. Brown, review of Arthur Cayley, p. 1845.

Isis, September, 2007, Francine F. Abeles, review of Arthur Cayley, p. 641.

Mathematics, June, 2006, Paul J. Campbell, review of Arthur Cayley, p. 229.

Nature, June 1, 2006, A.W.F. Edwards, "The Forgotten Mathematician," review of Arthur Cayley, p. 576.

SciTech Book News, March, 2006, review of Arthur Cayley.

Times Higher Education Supplement, March 9, 2007, Peter Neumann, "An Odd Pair with a Passion for All Things Pure," review of Arthur Cayley, p. 22.


Middlesex University Business School London Web site, (February 17, 2008), faculty profile of author.

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