# Mathematician:Arthur Cayley

## Contents

## Mathematician

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

The first to study groups as an abstract concept in their own right.

Also one of the pioneers of matrix algebra, and hence sometimes cited as one of the "fathers" of matrix theory.

## Nationality

English

## History

- Born: 16 August 1821 in Richmond, Surrey, England
- Died: 26 January 1895 in Cambridge, Cambridgeshire, England

## Theorems and Definitions

- Cayley's Theorem (Group Theory)
- Cayley's Theorem (Graph Theory), also known as Cayley's Formula
- Cayley's Theorem (Category Theory)
- Cayley Numbers, also known as octonions.
- Cayley Algebra
- Cayley Table
- Cayley Diagram
- Cayley-Dickson Algebra (with Leonard Eugene Dickson)
- Cayley-Dickson Construction (with Leonard Eugene Dickson)
- Cayley-Hamilton Theorem (with William Rowan Hamilton)
- Grassmann-Cayley Algebra (with Hermann Günter Grassmann)
- Cayley-Menger Determinant (with Karl Menger)

Results named for **Arthur Cayley** can be found here.

Definitions of concepts named for **Arthur Cayley** can be found here.

## Publications

- 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 $\theta^n - 1$*(*Phil. Mag.***Ser. 4****Vol. 7**: 40 – 47) - 1857:
*On the Theory of the Analytical Forms called Trees* - 1858:
*A Memoir on the Theory of Matrices*(*Phil. Trans.***Vol. 148**: 17 – 37) - 1859:
*Sixth Memoir on Quantics*(*Phil. Trans.***Vol. 149**: 61 – 90) - 1865:
*Note on Lobatchevsky's Imaginary Geometry*(*Phil. Mag.***Ser. 4****Vol. 29**: 231 – 233) - 1870:
*A Memoir on Abstract Geometry*(*Phil. Trans.***Vol. 160**: 51 – 63) - 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*(*Amer. J. Math.***Vol. 11**,*no. 2*: 139 – 157) www.jstor.org/stable/2369415 - 1889:
*A theorem on trees*(in which Cayley's Formula is introduced).

## Notable Quotes

*It is difficult to give an idea of the vast scope of modern mathematics. The word "scope" is not the best; I have in mind an expanse swarming with beautiful details, not the uniform expanse of a bare plain, but a region of a beautiful country, first seen at a distance, but worthy of being surveyed from one end to the other and studied even in its smallest details: its valleys, streams, rocks, woods and flowers.*

## Sources

- 1937: Eric Temple Bell:
*Men of Mathematics*: Chapter $\text{XXI}$ - 1952: T. Ewan Faulkner:
*Projective Geometry*(2nd ed.) ... (previous) ... (next): $1.1$: Historical Note - 1971: Allan Clark:
*Elements of Abstract Algebra*... (previous) ... (next): Introduction - 1971: Allan Clark:
*Elements of Abstract Algebra*... (previous) ... (next): Chapter $2$: The Symmetric Groups: $\S 77 \alpha$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Epigraph to Part $\text {B}$: Memorable Mathematics - 1996: John F. Humphreys:
*A Course in Group Theory*... (previous) ... (next): Chapter $2$: Maps and relations on sets: Summary - 2008: David Joyner:
*Adventures in Group Theory*(2nd ed.) ... (previous) ... (next): $\S 2.2.1$: History