Michael Atiyah at 1996 Chern symposium (Source: Wikimedia)

On January 11, 2019 Michael Atiyah passed away at the age of 89. He was a British-Lebanese mathematician, his mother was Scottish and his father a Lebanese Orthodox Christian. There is no doubt that he was one of the greatest and most innovative mathematicians of the 20th century. He introduced numerous new concepts and theories, which were involved in the groundbreaking theories and answers to many important problems in mathematics as well as in physics. He earned many distinctions in his career due to his outstanding contributions, notably, Abel prize (2004), Fields Medal (1966) and Royal Medal (1968). Dr. Atiyah said:

If you attack a mathematical problem directly, very often you come to a dead end, nothing you do seems to work and you feel that if only you could peer round the corner there might be an easy solution. There is nothing like having somebody else beside you, because he can usually peer round the corner.

As an undergraduate, Atiyah was interested in classical projective geometry, he did his PhD research under the supervision of the great W. V. D. Hodge (father of Hodge theory). Micheal Atiyah was fond of discussing and building the understanding of geometry to broader communities of researchers. Atiyah along with Friedrich Hirzebruch discovered Topological K-theory. His work on Index theory is recognized due to one of the most celebrated theorems in mathematics, Atiyah-Singer Theorem. In the 1980s, methods derived from the index theorem unexpectedly played a role in the development of string theory, particularly with the work of Edward Witten, a string theorist. Witten and Atiyah began an extended collaboration, and in 1990 Witten won the Fields Medal, the only physicist ever to win the prize, with Atiyah as his champion. Micheal Atiyah published a study in 2014, with Semir Zeki, a neurobiologist at University College London, and other collaborators, on The Experience of Mathematical Beauty and Its Neural Correlates. This study revealed that the part of brain that appreciates beauty in music, art and poetry is also involved in the appreciation of mathematical beauty. This is what Attiyah had to say about algebra:

Algebra is the offer made by the devil to the mathematician. The devil says: “I will give you this powerful machine; it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvelous machine.”

His mathematical writing include 15 books, covering a broad range of context on geometry and algebra. Michael Atiyah’s article Advice to a young Mathematiciain contains many valuable teachings. Last year, he gave a memorable talk on The future of mathematical physics: new ideas in old bottles in the International Congress of Mathematicians. At the 2018 Heidelberg Laureate Forum (HLF), Sir Michael Atiyah gave a lecture in which he claimed to have found a proof for one of the most famous open problem of the time, namely, the Riemann hypothesis. Sadly, the claim was not so convincing, and in response, he had to undertake a lot of unpleasant criticism. When he was questioned in an interview about risking his reputation on his claim, he replied:

My reputation is established as a mathematician. If I make a mess of it now, people will say, “All right, he was a good mathematician, but at the end of his life he lost his marbles.” 

Michael Atiyah was instrumental in his approach. He was an ambitious and brave mathematician. He actively stayed in working and building his mathematical empire, even when he turned 89. He was a self-driven personality which was well reflected in his statements. The news about the death of Michael Atiyah has not only saddened the mathematical but the whole scientific community. He would be remembered as an highly ambitious mathematician:

 In the broad light of day, mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigor. But at night, under the full moon, they dream, they float among the stars and wonder at the mystery of the heavens: they are inspired. Without dreams, there is no art, no mathematics and no life.                                  

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