Saturday, January 12, 2019

Michael Atiyah: 1929-2019

Sadly, yesterday, just months after his lecture about his efforts to prove the Riemann Hypothesis, the Lebanese-British mathematician Michael Atiyah died at age of 89.7. See The Telegraph or some press in Bangladesh (that reprinted the New York Times).

He died 10 months after his wife (from 1955), Lily Brown, also a mathematician, who was 90.

Atiyah articles at TRF...

He was born in London. His mother was Scottish and his father was a Lebanese Orthodox Christian. I guess that the Lebanese people with these European world views are closer to us – the average unbanned TRF commenters – than e.g. the U.S. and Western European left-wingers – in particular, I have Sarah Abdallah in mind. Her sensible Western views are so shockingly pleasing, especially if you compare them with the hostile, anti-Western rubbish that the likes of D.H. try to spread within our civilization. And D.H. doesn't stand just for any Richard Head but for a particular one. (If you dared to read the previous sentence, D.H. will add some extra punishment for you in the Gulag.)

But back to the main topic.

Michael grew like an Englishman, got his PhD in the U.K., and spent time in Oxford, Cambridge, and Princeton, among other places. He spoke English almost everywhere but he had an extended family and was capable to speak Arabic to them. The clicky hacky (that's a loanword borrowed from Czech) script known as written Arabic turned out to be more difficult than algebraic geometry for him.

He got the Fields Medal in 1966 and the Abel Prize in 2004.

He was considered Britain's greatest living mathematician. His list of collaborators was also impressive – Bott, Singer, Witten, Maldacena, Vafa, Hitchin, Drinfeld, and other big shots. I guess most of those would still think that his and Singer's contribution to the index theorems was the most important insight (Atiyah described the power of the index theorems as the ability to say a lot about differential equations without solving them; the Atiyah-Singer index theorem is religiously treated as a gem in the Green-Schwarz-Witten textbook of superstring theory, as a tool to understand multiloop amplitudes – I guess it was Witten's chapter) but he has done lots of other things, especially in algebraic geometry.

Atiyah was the main father of K-theory, too: it was really his first famous work.

Around 2000, Witten introduced K-theory to string theory as the "superior" classification method for D-brane charges – K-theory is a refined property of the manifold that is physically linked to tachyon and gauge fields and that superseded homology (before it was replaced with derived categories, some folks would add). K-theory may be used in this way because the spacetime-filling or high-dimensional D-branes with tachyon fields may decay to nothing, as Ashoke Sen originally figured out, but if there are some topological "knots" on the tachyonic fields before the decay, some lower-dimensional D-branes survive the decay.

Sadly, it doesn't look like a proof of the Riemann Hypothesis is one of the victorious triumphs but his courage to semi-sensibly attack the difficult problem at such a high age, months before the death, is incredible at the human level.

As Witten stresses in the New York Times, Atiyah has totally transformed the character of interactions between mathematics and physics. Those disciplines began to sleep with each other again and passionately so. He was clearly interested in physically interpreted and heuristic mathematical ideas (he was the lead author of the big written discussion about heuristic ideas in mathematics) and the newest developments in physics, especially those close to quantum field theory and string theory. While in Pugwash, Atiyah has defused the nuclear standoff between India and Pakistan. He has done and represented lots of other things.

I actually loved his and Witten's 2001 paper about M-theory on \(G_2\) holonomy manifolds. They studied one class of shapes – the moduli space itself looked like the pants diagram because three different topologies could have been transformed to each other via smooth transitions (the moduli space is smooth while topology change shouldn't be; the resolution of the paradox is that points near the juncture of the pantsy moduli space don't describe smooth large 7-dimensional geometries). It's probably not a paper transforming the whole field but it's an excellent example of topology change in M-theory and an explicit example of quarter-realistic physics on \(G_2\) holonomy manifolds. If you're a refined person who appreciates beauty in physics rather than a savage who gets lost in math, you should look at the paper.

One year earlier, he, Vafa, and Maldacena also used M-theory on \(G_2\) manifolds to give an elegant geometric derivation of a 4D large \(N\) duality. You see that like in the case of index theorems, one may derive cool and powerful properties of complicated systems by looking at nice and novel geometric realizations of those systems. That was the way of looking and discovering that he preferred and that excited him and I understand that spirit very well.

(I think that I met him only once during his talk in Santa Barbara either in 2000 or 2001.)

The New York Times even indirectly encourages young men affected by hair loss not to lose their smile, self-confidence, and not to prepare for death: Atiyah became almost bald as a young man.

RIP Prof Atiyah.

P.S.: As you could see above, I will try to revive the occasional embedding of some Amazon links. Jeff wrote me that after he reached the fine-structure constant of wealth, around $137 billion, his wife decided to rob him of one-half of that constant. So I should better embed the Amazon links, he told me, to compensate for the hungry wife's effect on the revenue. In the past, Bezos changed the code for these Amazon picture-links and my old ones ceased to work. I could only update a small fraction of them.

One reason for the revival is that Bezos also wrote me that if there were some revenue, it won't be sent as an Amazon gift card anymore but I could define an IBAN for a Czech EUR banking account instead. So let me try.

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