He helped found the modern British school of pure mathematics, and was a professor at Trinity College, Cambridge for 35 years.

The young Cayley enjoyed complex maths problems, and the school's master observed indications of his mathematical genius.

At the age of 17 Cayley began residence at Trinity College, Cambridge, where he excelled in Greek, French, German, and Italian, as well as mathematics.

The cause of the Analytical Society had now triumphed, and the Cambridge Mathematical Journal had been instituted by Gregory and Robert Leslie Ellis.

To this journal, at the age of twenty, Cayley contributed three papers, on subjects that had been suggested by reading the Mécanique analytique of Joseph Louis Lagrange and some of the works of Laplace.

He continued to reside at Cambridge University for four years; during which time he took some pupils, but his main work was the preparation of 28 memoirs to the Mathematical Journal.

Because of the limited tenure of his fellowship it was necessary to choose a profession; like De Morgan, Cayley chose law, and was admitted to Lincoln's Inn, London on 20 April 1846 at the age of 24.

[5] His friend J. J. Sylvester, his senior by five years at Cambridge, was then an actuary, resident in London; they used to walk together round the courts of Lincoln's Inn, discussing the theory of invariants and covariants.

[5] Around 1860, Cambridge University's Lucasian Professor of Mathematics (Newton's chair) was supplemented by the new Sadleirian professorship, using funds bequeathed by Lady Sadleir, with the 42-year-old Cayley as its first holder.

He gave up a lucrative legal practice for a modest salary, but never regretted the exchange, since it allowed him to devote his energies to the pursuit that he liked best.

Maxwell wrote an address praising Cayley's principal works, including his Chapters on the Analytical Geometry of

In 1881, he received from the Johns Hopkins University, Baltimore, where Sylvester was then professor of mathematics, an invitation to deliver a course of lectures.

As the President's address is one of the great popular events of the meeting, and brings out an audience of general culture, it is usually made as little technical as possible.

[9] A number of mathematical terms are named after him: This article incorporates text from the 1916 Lectures on Ten British Mathematicians of the Nineteenth Century by Alexander Macfarlane, which is in the public domain.