Chelsie Folsom

Chelsie Folsom

Published: 02 Oct 2023


Arthur Cayley was a remarkable mathematician whose contributions to the field of mathematics are still celebrated today. Born in 1821, Cayley’s work revolutionized numerous branches of mathematics and laid the foundation for many important theories that are still studied and revered by mathematicians worldwide.

In this article, we will dive into the fascinating life and achievements of Arthur Cayley. From his influential work in algebra and geometry to his groundbreaking research in the theory of matrices, Cayley’s legacy has left an indelible mark on the world of mathematics.

So, hold on to your mathematical hats as we uncover 12 astounding facts about the brilliant mind of Arthur Cayley!

Table of Contents

Cayley was born on August 16th, 1821.

Arthur Cayley, whose full name is Arthur Cayley Sturm, was born on August 16th, 1821, in Richmond, Surrey, England. His early interest in mathematics paved the way for his future achievements.

He attended Trinity College, Cambridge.

Cayley received his education at Trinity College, Cambridge, where he excelled in mathematics. He graduated in 1842 and went on to become one of the most influential mathematicians of all time.

Cayley made significant contributions to matrix theory.

One of Cayley’s most important contributions was his development of matrix theory. He introduced the concept of matrices and laid the groundwork for their use in a wide range of mathematical applications.

He pioneered the study of abstract algebra.

Cayley played a crucial role in the development of abstract algebra. He introduced the concept of a group and made significant advancements in the study of groups, rings, and fields.

Cayley’s theorem revolutionized graph theory.

Cayley’s theorem, also known as Cayley’s formula, provides a fundamental result in graph theory. It states that the number of labeled trees in a complete graph on n vertices is equal to n^(n-2).

He published over 900 mathematical papers.

Cayley was an incredibly prolific mathematician and published over 900 papers in his lifetime. His works covered a wide range of topics, from geometry and algebra to number theory and mathematical physics.

Cayley was the first to use the term “matrix”.

In his influential paper “A Memoir on the Theory of Matrices,” Cayley introduced the term “matrix” to describe rectangular arrays of numbers. This term has become a fundamental concept in mathematics and various scientific fields.

He was a founding member of the London Mathematical Society.

Cayley played a crucial role in the formation of the London Mathematical Society in He served as the first president of the society and actively promoted the advancement of mathematical research.

Cayley was knighted for his contributions to mathematics.

In recognition of his outstanding contributions to mathematics, Arthur Cayley was knighted by Queen Victoria in He became Sir Arthur Cayley, a title that reflected his significant achievements in the field.

He made groundbreaking discoveries in invariant theory.

Cayley made significant contributions to invariant theory, particularly in the study of forms and invariant theory. His work laid the foundation for modern developments in this area of mathematics.

Cayley was a Fellow of the Royal Society.

Arthur Cayley was elected as a Fellow of the Royal Society in This prestigious honor recognized his remarkable contributions to mathematical research and his impact on the field.

His legacy continues to inspire mathematicians worldwide.

Even after his passing in 1895, Cayley’s work continues to inspire and influence generations of mathematicians. His groundbreaking theories and innovative approaches remain foundational in various branches of mathematics.


In conclusion, Arthur Cayley was a brilliant mathematician who made significant contributions to the field of algebra and group theory. His work on matrices and linear transformations laid the foundation for modern algebraic structures and has had a profound impact on various branches of mathematics and science.

Through his groundbreaking research and publications, Cayley revolutionized the study of abstract algebra and paved the way for future generations of mathematicians to explore new frontiers in the field. His work continues to be studied and admired by mathematicians around the world, solidifying his legacy as one of the most influential mathematicians of his time.

In addition to his mathematical accomplishments, Cayley was also a respected lawyer and lawmaker, proving that brilliance in mathematics can coexist with success in other fields.

The remarkable achievements of Arthur Cayley serve as an inspiration to aspiring mathematicians and highlight the power of perseverance, curiosity, and innovation in pushing the boundaries of human knowledge.


1. Who was Arthur Cayley?

Arthur Cayley was a British mathematician and lawyer who lived from 1821 to 1895. He was known for his groundbreaking work in algebra and group theory.

2. What were Arthur Cayley’s contributions to mathematics?

Arthur Cayley made significant contributions to the field of algebra, particularly in the areas of matrices, linear transformations, and group theory. He developed important concepts and theorems that laid the foundation for modern algebraic structures.

3. How did Arthur Cayley’s work impact mathematics?

Cayley’s work had a profound impact on modern algebra and various branches of mathematics. His discoveries and theories provided a solid framework for understanding and solving complex mathematical problems.

4. How are Arthur Cayley’s achievements recognized?

Arthur Cayley is widely recognized as one of the most influential mathematicians of the 19th century. His contributions to the field have been acknowledged through various honors and awards, including the prestigious Sylvester Medal.

5. Was Arthur Cayley only a mathematician?

No, Arthur Cayley was also a lawyer and lawmaker in addition to being a mathematician. His versatile skills and achievements in multiple fields showcase his brilliance and intellectual prowess.