Mathematical bridge-builder


Michael F. Atiyah PHOTO/TIFR Archives

Michael F. Atiyah (1929-2019) was a prominent member of the scientific establishment in Britain, where he dominated the mathematical scene and established Oxford as a major centre for geometry.

Sir Michael Francis Atiyah was one of the major figures of 20th century mathematics. He was a master of modern geometry and a crucial agent in its rapprochement with theoretical physics. He passed away on January 11, a few months short of his 90th birthday.

Michael Atiyah’s father, Edward Selim Atiyah, was Lebanese and a civil servant in Khartoum, the capital of Sudan, then a British colony. His mother, Jean Levens, was Scottish. Of his father, Atiyah said: “My father’s main dream was to go to Oxford. He wanted to convert himself into an Englishman. It didn’t quite work out. When he came back to Sudan, he found he wasn’t part of the English class structure; he was regarded as one of the lower classes although he was Oxford-educated and regarded himself as culturally English. That turned him over a bit. He became an Arab nationalist to some extent. All his life was divided between wanting passionately to be English and yet sympathising with the Arab political position within the British Empire.” (I have relied on the incomparable biography available at for information on Atiyah’s life.)

Those who met Atiyah in his prime would have recognised a certain brisk British type: always impeccably dressed and who spoke in confident, clear, declarative sentences, with a twinkling sense of humour that put the listener at ease. His was a short, slightly stocky figure, but through force of personality he dominated any room he was in. Although he was an internationalist by temperament and held for three years a prestigious professorship at the Institute for Advanced Study in Princeton, New Jersey, United States, it was clear that he felt most at home in Britain, where he was a prominent member of the scientific establishment and where he dominated the mathematical scene and eventually established Oxford as a major centre for geometry. After retirement from Oxford, he moved to Edinburgh and back to his Scottish roots.

It is often said that there are two tribes of mathematicians: the problem-solvers and the theory-builders. There is in fact a third group, the bridge-builders, of whom Atiyah was the archetypical example. It is this aspect of the man that I would like to convey in this article.

(An aside: In the 1990s, Atiyah gave a public lecture at the Tata Institute of Fundamental Research (TIFR) in the Homi Bhabha Auditorium, a majestic structure perched on the rocky south Bombay shore facing the Arabian Sea. Unfortunately, I do not have access to the text, but I remember well his description of the roles of the theoretical physicist and mathematician in the exploration of the mathematical universe, or at least those parts of it that were of interest to him at that time. A theoretical physicist is an explorer who jumps from island to island and reports back on the flora and fauna that she has seen; a mathematician then builds the bridges linking the islands. The physicist roams far and wide and gets impatient with the mathematician who is in it for the bridge-building—a punchline, somewhat self-deprecating and clearly only half-meant.)

To set the stage, one first needs to understand how mathematics, like the natural sciences, took its modern form in a process that began in the 19th century and culminated in the emergence of some grand narratives in the 20th century. Most of this happened in Europe.

Euclid’s construction of geometry was concerned with the deduction of mathematical truths by systematic reasoning from a set of axioms. In spite of this, for much of the ensuing two millennia, mathematics proceeded on the basis of ingenious calculations based on intuitive justifications. As these became more and more baroque, the practitioners began to feel the need to moor their reasoning in solid ground. This resulted in careful constructions of mathematical objects and subtle definitions.

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