Algebraic expert renowned as Britain’s best mathematician since Isaac Newton

Sir Michael Atiyah, a mathematician and former president of the Royal Society, who has died aged 89, was widely regarded as Britain’s greatest living mathematician. Atiyah was an expert in the abstruse field of algebraic topology, which concerns the interconnections between equations and geometrical shapes. He was interested in the arcane mathematical properties of these links, and his first major contribution (in collaboration with F Hirzebruch) was the development of a new and powerful analytical technique known as K-theory.

Subsequently, in collaboration with I M Singer, he established another important analytical tool known as the

Index theorem.

These theories became valuable tools for solving problems not just in mathematics but in theoretical physics, especially particle physics. The theories of superspace and supergravity, and the string theory of fundamental particles, were all developed using Atiyah’s ideas.

One of the fields in which his work has been applied is in the search for the ‘‘Holy Grail’’ of physics, a single theory that would account for all the forces and particles in the universe, an endeavour that, among other things, routinely calls on the properties of 11-dimensional spaces.

Atiyah’s brother Joe remarked: ‘‘He has been described to me by more than one professor of mathematics as the best mathematician in this country since Sir Isaac Newton.’’

Michael Francis Atiyah was born in London, the son of a distinguished Lebanese civil servant and a Scottish artist. He was educated in Egypt, and later at Manchester Grammar School.

He claimed never to have been very happy with science at school. ‘‘I wasn’t keen on physics,’’ he said, ‘‘because I wasn’t very good at practicals. I did some serious chemistry when I was 15 and that was exciting. But the thing that put me off was inorganic chemistry, where there were masses of facts you had to know and an awful lot of memory work that didn’t appeal to me.’’

In mathematics, however, he found his true metier: ‘‘In mathematics, if you understand the principles, you get along fine. You don’t need a good memory for mathematics.’’

Atiyah wrote his first original paper, concerning a branch of geometry, while still a second-year undergraduate at Trinity College, Cambridge. That, and a double first, convinced him to dig more deeply into mathematics.

After completing his doctorate, he became a fellow of Trinity in 1954, then spent 1955 as a Commonwealth Fellow at the Institute for Advanced Study at Princeton. Returning to Cambridge, he was a college lecturer from

1957 and a fellow of Pembroke College from

1958. In 1961 he moved to a readership at Oxford University, where he became a fellow of St Catherine’s College. He was elected a fellow of the Royal Society in 1962, aged 32.

He was elected master of Trinity College, Cambridge, in 1990 and was appointed the first director of the new Isaac Newton Institute for Mathematical Sciences.

Despite the abstruse nature of his field, Atiyah was no unworldly academic, but had a sound instinct for public relations. He was also a man who believed strongly that science could not be divorced from morality.

He argued that scientists had a duty to voice their concerns on issues relating to the application of science, and that they should distance themselves from governments and demonstrate independence of thought.

While president of the Royal Society, he used his position to launch a series of scathing attacks on the government’s neglect of Britain’s science base, and set up a committee to address key issues such as the brain drain.

In 1995 he launched an unprecedented attack on Britain’s nuclear weapons programme, describing it as ‘‘fundamentally misguided, a total waste of resources and a significant factor in our relative economic decline’’. He was equally dismissive of Britain’s conventional arms industry: ‘‘As a scientist, I cannot by my silence condone a policy which uses the scientific skills of this country to export potential death and destruction to poorer parts of the world.’’

He was not a particularly good committee man; he found it difficult to deal with people who held views opposing his own. In 1997 he resigned as master of Trinity earlier than had been expected after a disagreement with the college’s garden committee over a planting scheme for the fellows’ garden.

Atiyah received numerous honours during his career. There is no Nobel Prize for mathematics, but in 1966 he won the discipline’s equivalent, the Field Medal. He received the Royal Medal of the Royal Society in 1968, the Copley Medal in 1988 and the Abel Prize in 2004.

In September 2018, at the Heidelberg Laureate Forum, Atiyah claimed to have come up with a simple proof of the Riemann hypothesis, one of mathematics’ most notoriously unyielding problems. His claim was met with scepticism.

He wrote many original papers in mathematical journals and several books on mathematics, including The Geometry and Physics of Knots in 1992 and We are all Mathematicians in 2007.

Michael Atiyah served as chancellor of Leicester University from 1995 until 2005 and as president of the Royal Society of Edinburgh from 2005 until 2008. He was knighted in 1983 and became a member of the Order of Merit in 1992. In 2011 he was made a Grand Officier of the Legion d’honneur.

He married, in 1955, Lily Brown; she died in March 2018. They had three sons, one of whom died on a walking holiday in the Pyrenees in 2002. – Telegraph Group

‘‘In mathematics, if you understand the principles, you get along fine. You don’t need a good memory for mathematics.’’ Sir Michael Atiyah on how he found his metier