Arthur Cayley

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Cayley, Arthur

Cayley, Arthur (kāˈlē), 1821–95, English mathematician. He was admitted to the bar in 1849. In 1863 he was appointed first Sadlerian professor of mathematics at Cambridge. His researches, which covered the field of pure mathematics, included especially the theory of matrices (see matrix) and the theory of invariants. The algebra of matrices was the tool Heisenberg used in 1925 for his revolutionary work in quantum mechanics (see quantum theory). The concept of invariance is important in modern physics, particularly in the theory of relativity. Cayley's collected papers were published in 13 volumes (1889–98).
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Cayley, Arthur


Born Aug. 16, 1821, in Richmond; died Jan. 26, 1895, in Cambridge. British mathematician.

Cayley was appointed professor at Cambridge University in 1863. His major works were devoted to the theory of algebraic quadratic forms. He established a connection between the theory of invariants and projective geometry. His studies in this field are the basis for an interpretation of Lobachevskii’s geometry (the Cayley-Klein interpretation). Cayley was also the author of works on the theory of determinants, differential equations, and elliptic functions. He also conducted investigations in spherical astronomy and astrophysics.


Noether, M. “Arthur Cayley.” Mathematische Annalen, 1895, vol. 46, pp. 462–80.
The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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Arthur Cayley was one of the most prolific and important mathematicians of the Victorian era.
The mathematician Arthur Cayley published this as a conjecture in 1879, and in that same year Alfred Kempe published a proof that remained in force until 1890, when an error was discovered.
13 Arthur Cayley (1821-95), the distinguished mathematician (Honorary Fellow of Trinity 1872; Fellow 1875) had his portrait painted in 1874; see DNB XXII, 402.