ProofWiki:Mathematicians/Arthur Cayley

English mathematician most famous for his work in group theory and graph theory.

Nationality

English

History

• Born: 16 August 1821
• Died: 26 January 1895

Theorems and Definitions

• Cayley's Theorem (Group Theory)
• Cayley's Theorem (Graph Theory), also known as Cayley's Formula
• Cayley Numbers, also known as octonions.
• Cayley Table
• Cayley Diagram
• Cayley-Dickson Algebra (with L.E. Dickson)
• Cayley-Dickson Construction (with L.E. Dickson)
• Cayley-Hamilton Theorem (with William Rowan Hamilton)
• Grassmann-Cayley Algebra (with Hermann Grassmann)

Books and Papers

• 1854: On a property of the caustic by the refraction of a circle
• 1854: On the theory of groups, as depending on the symbolic equation $\theta^n - 1$
• 1857: On the Theory of the Analytical Forms called Trees
• 1875: On the Analytical Forms called Trees, with Applications to the Theory of Chemical Combinations
• 1881: On the Analytical Forms called Trees
• 1889: On the Theory of Groups (American Journal of Mathematics, Vol. 11, No. 2)
• 1889: A theorem on trees (in which Cayley's Formula is introduced).

Also See

• John J. O'Connor and Edmund F. Robertson: "Arthur Cayley": MacTutor History of Mathematics archive

• Eric Temple Bell: Men of Mathematics (1937): Chapter $\text{XXI}$
• Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): Introduction
• John F. Humphreys: A Course in Group Theory (1996): $\S 2$: Summary