While away on vacation, I heard last week the sad news of the death last week of Michael Atiyah, at the age of 89. Atiyah was both a truly great mathematician and a wonderful human being. In his mathematical work he simultaneously covered a wide range of different fields, often making deep connections between them and providing continual new evidence of the unity of mathematics. This unifying vision also encompassed physics, and the entire field of topological quantum field theory was one result.

I had the great luck to be at MSRI during the 1988-89 academic year, when Atiyah spent that January there. Getting a chance to talk to him then was a remarkable experience. He had one of the quickest minds I’ve ever seen, often grasping what you were trying to explain before the words were out of your mouth. At one point that month I ran into Raoul Bott walking away from an ongoing discussion with Atiyah and Witten at a blackboard. Bott shook his head, saying something like “it’s just too scary listening to the two of them”.

Any question, smart or stupid, would lead to not just an answer, but a fascinating explanation of all sorts of related issues and conjectures. For Atiyah, his love of discussing mathematics was something to be shared at all times, with whoever happened to be around.

The last time I met him was in September 2016 in Heidelberg. He was his usual cheerful and engaging self, still in love with mathematics and with discussing it with anyone who would listen. I did notice though that age had taken its toll, in the sense that he no longer would engage with anything that got into the sort of complexities that in the past he had been quick to see his way through. It’s unfortunate that near the end of his life far too much attention was drawn to implausible claims he started making that he could see how to solve some of the most difficult and intractable open problems of the subject.

There’s a lot more I could write here about Atiyah and his remarkable career, but I’ve realized that most of it I’ve already gotten to in one post here or another. So, for more, see some of the following older posts, which discussed:

Interviews and profiles here, here and here.

Atiyah and his work with Raoul Bott.

Atiyah and topological quantum field theory.

**Update**: In recent years Andrew Ranicki had been maintaining a page with Atiyah-related links.

In a previous blog posting you wrote “Atiyah favored “new-fangled” abstraction, only writing down formula when forced to by Bott”. As an analyst (who finds themselves having to write down each step of a proof) I find this amazing. Do you have any more details as to how he was able to do this?

T,

I’m paraphrasing Atiyah himself there. My interpretation of what he was saying is that it’s not about the details of a proof, just that he was happy working more abstractly with arbitrary solutions (e.g. in the index theorem, where you can show that there are solutions, without having them explicitly), where Bott wanted to work out what happened for explicit solutions in order to get more insight into what was going on (and ultimately convinced Atiyah he needed to do this).

Actually I think analysis was the field where both Atiyah and Bott were weakest, and the papers he is discussing in that quote were written with an analyst (Garding). Atiyah characterizes their role in the paper as a “subcontract”, presumably meaning they were handling just certain more topological and geometrical issues.

He was amazing. A long and useful life!

-drl

Mathilde Marcolli collaborated with Michael Atiyah and was a friend of him up to the end of his life. She paints a moving portrait of him and engages the mathematical community with her refined “aqua fortis” way at https://listeningtogolem.blogspot.com/2019/01/the-polar-star-and-life-endgame-elegy.html.

Blessed are you Sir for showing us there is more than one way for geometry and physics to interact with each other!

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Sad.

One of my goals in life is to understand

whythe index theorem is true (yes, I know the various proofs, but I want to see why it should be obvious).It seems that he was one of the good guys, and it is nice to know the good guys do often get the recognition they deserve.

Dave Miller in Sacramento

I have now put on my website a short note on an idea of Michael Atiyah.

http://www.alainconnes.org/docs/watertoyourmill1.pdf