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Arthur Cayley

, 784 pages

50 halftones, 7 line drawings

December 2005



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Arthur Cayley

Mathematician Laureate of the Victorian Age

Arthur Cayley (1821–1895) was one of the most prolific and important mathematicians of the Victorian era. His influence still pervades modern mathematics, in group theory (Cayley's theorem), matrix algebra (the Cayley-Hamilton theorem), and invariant theory, where he made his most significant contributions. Yet Cayley's life has been overlooked by historians, who have lavished far more attention on lesser figures. Mathematician and biographer Tony Crilly, the world's leading authority on Cayley, rectifies this oversight with the first definitive account of his life.

Born in England, Cayley spent his childhood in St. Petersburg, where his father was a commercial agent. After returning to England in 1828, Cayley received a first-rate education. As an undergraduate at Trinity College in Cambridge, he was named "Senior Wrangler," the top mathematics student of his year. After graduating, he found himself at the vanguard of the revolution in British mathematics which included William Rowan Hamilton, George Boole, and James Joseph Sylvester. At the same time, needing a reliable income, he trained for the bar and became a barrister at Lincoln's Inn in 1849. Though a successful lawyer, Cayley devoted all his free time to mathematics and confirmed his reputation as one of the era's leading minds with a procession of brilliant articles on key aspects in pure mathematics. Only after 1863, when he was appointed to the Sadleirian Chair at Cambridge, could he fully pursue mathematical investigations, and he continued to publish influential papers until his death.

Comprehensive and elegantly composed, this biography makes clear the scope of Arthur Cayley's prodigious achievements, firmly enshrining him as the "Mathematician Laureate of the Victorian Age."

Tony Crilly is a Reader in mathematical sciences at Middlesex University.

"The real subject of Crilly's monumental biography is the surrounding galaxy of British mathematicians and milieu in which they operated."

"Fluid, readable style... Highly recommended."

"This well-written biography... is full of shrewd observation and careful analysis. "

"First full-length account of Cayley's life... Anyone interested in the emerging role of the research mathematician in England will find Crilly's book particularly rewarding."

"Crilly's book is a beautifully written account of Cayley's life and of British mathematics in the 19th century."

"I highly recommend Arthur Cayley: Mathematician Laureate of the Victorian Age as a valuable addition to one's personal or institutional library. There is everything to enjoy about this book: the writing, the content, the essential tribute to Cayley's life and contributions."

"The reader of Crilly's book will come away with an appreciation of the quality and breadth of Cayley's mathematical writings."

"A well-written and thorough account of its subject... a wealth of useful and well-researched information that is difficult to find elsewhere."

"Recommended to those who are not specialists in mathematics and are interested in historico-cultural or social science aspects... An instructive book accessible to the reader."

"A scholarly work of the highest quality. It should be in every university library, and I recommend it to all who wish to delve deeply into the life of Arthur Cayley."

"[ Arthur Cayley] gives a broad picture of the developments in mathematics and society over the nineteenth century."

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