Raoul Bott
2009Edit
What is known about the large exceptional Lie groups and geometric models of various elliptic cohomology theories?
One way of looking at Bott Periodicity is that tensor operations between non-octal division algebras close leaving Cayleys as a remainder.
Then the issue becomes "can we do anything with tensor products involving Octonians?" which seems to be the Raison d'ĂȘtre for F4, E6-8.
An issue would then be whether Elliptic cohomology is a k-theoretic refinement requiring an extension of tensor products using exceptionals.
2016Edit
I read about great mathematical lineages & get sad. I don't know other selfadvised PhDs. Something wants to belong.
The great Harvard mathematician Raoul Bott lent me his name as advisor as a mensch lends a surname to a bastard. I didn't know 2 say thanks.
Because I view my needing a PhD as a sign of my own weakness, I have not yet been able to say "Thank You" to the 2 brave men who stood 4 me.
So let me finally say it: my thanks 2 @drorbarnatan & the late Raoul Bott, for heroically saving me & my PhD from my own university 20y ago.
2019Edit
One of the worldâs greatest men has died. Most of you will have no idea who this is. I just donât know how to bridge that gap yet to tell you what he did.
I was very close with his top collaborator. They were the Watson and Crick of mathematics to me. They rewrote my whole life.
Michael Atiyah OM FRS, President of the Royal Society 1990 -1995, died today. He was "a wonderful person who was a true internationalist and a fervent supporter for investing in talent â themes which resonate very clearly today." Read the full tribute https://royalsociety.org/news/2019/01/tribute-to-former-president-of-the-royal-society-sir-michael-atiyah/
There is a little known stone wall on Long Island. While flawed, it is a gift to all mankind that should be a pilgrimage site, as an understanding of the contents is nesessary to understand our world. Think of it as transcendent graffiti. Atiyahâs spray-paint is everywhere here.
Imagine watery planets with holes and twists. Knotted donut planets called base spaces. Crazy oceans called âVector bundlesâ and âPrincipal bundlesâ.
He told us about how the twists and holes determine what waves must live on them and which cannot.
He helped direct Ed Witten and Graeme Segal to truly tell us what Quantum Field Theory really was beyond being a physical theory. These men took a grab bag of techniques developed for calculation and showed us that they were a mellifluous whole of geometry, topology and physics.
If you want to know why I am so passionate about resisting the reign of terror against true scholarship it is this. Universities housed REAL scholarship beyond your wildest dreams. This kind of scholarship is not socially constructed. Almost no one can even do this level of work.
I completely agree with your assessment of the magnitude of the world's loss here. But who, in your view, was Atiyah's "top collaborator"? Bott, perhaps? Singer? Someone else? He shared credit with a large number of co-workers in his published work. (I'd vote for Bott, myself.)
I knew Bott and Singer pretty well myself, and I agree that it's not even close.
What a lunch we could have. Would love to hear your perspective.
They were such extraordinary persons, and their influence on me was exceeded only by that of Chern. I miss them all more than I can say. And perhaps we should indeed have lunch. Pretty sure we'd both enjoy it.
Are you anywhere near SF? I gotta hear your argument for Atiyah Bott. The main flaw on that wall IMO is the absence of Bott Periodicity. Other issues: Tits Freudenthal, the main Elliptic Deformation Complexes, Hopf Fibration, etc..
But Bott Periodicity is beyond mind blowing.
Yes, I reside in Mountain View, and get up to SF with some frequency. And I don't mean to make an argument for Atiyah-Bott, exactly; it's more of a feeling, born mostly of personal observation, that Atiyah-Bott had a much deeper aesthetic affinity than did Atiyah-Singer (say.)
@BraneRunner @MathPrinceps Some would put it higher.
He helped direct Ed Witten and Graeme Segal to truly tell us what Quantum Field Theory really was beyond being a physical theory. These men took a grab bag of techniques developed for calculation and showed us that they were a mellifluous whole of geometry, topology and physics.
If you want to know why I am so passionate about resisting the reign of terror against true scholarship it is this. Universities housed REAL scholarship beyond your wildest dreams. This kind of scholarship is not socially constructed. Almost no one can even do this level of work.
@vanest SUNY Stony Brook, Simons Center for Geometry and Physics. Itâs blocked partially by a staircase now.
Very sad news indeed - I knew Michael from when I was at @TrinCollCam he was brilliant, warm & amazing. Was at a conference where he was supposed to speak on thursday #higgscentre - he cancelled at the last minute....
More recently we talked about dark matter and black holes (2 yrs ago now) he was very excited about astro... b4 when i was a student he was just very encouraging and warm
2020Edit
Sometimes people take pride in being self taught. But in my case this is defensive.
I would have been honored to have been a part of a chain. I just never found my mentor in time. Isadore Singer should have been my advisor.
Here is Herbie on Miles Davis:
If you arenât lucky enough to find a master, as Herbie says, who can lead you to your own voice, you need to be your own advisor and there are so many problems youâll have to overcome because you are always living in your own blind spot.
Itâs an inferior road. But itâs possible.
I donât know that Iâve spoken publicly about it like this. So Iâm trying it out. This is real Kung Fu Panda stuff.
It bothers me that Raoul Bott is listed as my supervisor on my Wikipedia entry. He wasnât.
What he was, was my hero who rescued me. A far more impressive role.
Iâm considering telling the story but Iâve never felt comfortable telling it in public. We oddly resent those who rescue us; Iâll never know if I could have done it alone. Knowing me, he essentially tricked me into accepting help to spare me the wound to my pride. A great man. đ
Tom Lehrer
Noam Elkies
@LauraDeming
@MarcusduSautoy
@patrickc
@lishali88
@peterthiel
@thegoodtomchi*
@SamHarrisOrg
@joerogan
@tylercowen
@MsMelChen
James Simons
Jared Diamond
@StephenAtHome
@tferriss
@FutureJurvetson
@naval
Jimmy Kaltreider
@mkonnikova
@pmarca
Etc...
[no family]
Who's the most knowledgeable person you can think of? Think of "knowledgeable" as 2D space: it factors in both horizontal breadth across a wide range of topics and vertical depth within those topics. Who are some people whose knowledge covers an extraordinary amount of 2D space?
Freeman Dyson
@brookedallas
Sydney Coleman
@adamgazz
@balajis
@stephstem
Kevin Harrington
Jordan Greenhall
Daniel Schmachtenberger
@nntaleb
@annakhachiyan
@seanonolennon
@DavidYezzi
Raoul Bott
@DouglasKMurray
@jordanbpeterson
Isadore Singer
R Gomory
R Feynman
And on & on & on...
2021Edit
Isadore Singer & Raoul Bott worked in almost exactly the same area. They collaborated with exactly the same people. They worked in adjacent zip codes (02138 vs 02139). They both had claims to the "greatest topological theorem" of the 20th century.
They never co-authored a paper.
I've known only three minds personally who I'm convinced will be discussed 1000 years from now if humans survive: James Watson, Raoul Bott and Isadore Singer (I met Atiyah & Witten but did not know them).
Is & Raoul however both collaborated on my rescue in Graduate school.
Perhaps with both of these giants now gone it is time to tell my story. I'm not sure. I have never told it publicly in full. But they both are heroic men beyond being great minds.
Had they surmounted their personal difficulties their collaborations could have changed the world.
They worked down the same street. I was at times a ping pong ball they sent back & forth between Building 2 at MIT & Harvard Science Center rm 508 (I think) along a 45 minute walk. I very much respected that they chose not to air any difficulties. They had respect for each other.
One reason I largely kept quiet about my story is respect for both men. They both defended and believed in the system. But, in part they believed in it BECAUSE they were so powerful that they could act as an underground railroad when that system failed:
So, in part, I'm their collaboration. Raoul was not my advisor. He had no real idea what I was doing. But he was far more than that. Is was my shtarker. My ace in the hole. They worked as a team to help me; their failure to talk directly was the main clue I had of anything amiss.
Lastly, there is the matter of my wedding. Is came to our event but I didn't invite Raoul. I did not understand what he had done for me. It is one of the biggest mistakes of my life. When the internet tries to insist to me that I am his student, I want to tell them what happend.
The truth is that I would have been proud to be the student of Raoul Bott. I would have a storied lineage to claim.
The truth is Raoul gave me his name for a self-advised thesis. And like a fool I resented it. Yet how much greater is the man who lends his last name to a Bastard.
In any event. I miss Is very much, but never expected to see him again. And I'm wrestling w the idea that I'm now free to tell my own story after 25yrs of saying very little in public. One of the reasons I don't take kindly to internet warfare is that I have large debts to pay.
The more I subject myself to mindless politics, catfighting, shadowbanning & trolling, the harder it is to fight for others/myself and to pay the debts to the giants who rescued me along my way. I don't know how I'd have done w/o them.
But I needed to grow this voice to do it.
Lastly, I used to have a relationship to a very different @nytimes. Thus when I read Is' obituarty I was shocked to see @julierehmeyer's beautiful tribute including my own quotes on Is. It made me sad to think about how much has been lost. Sadly, those quotes came from long ago.
If you haven't read her piece, I think it is quite moving even though it is no more than a sketch. End.
https://www.nytimes.com/2021/02/12/science/isadore-singer-dead.html
[Not to be crass: but I can usually tell within the 1st minute what is happening to the throttling of my tweets: this is not being widely seen. I'm trying to say something meaningful about a departed friend @jack. Could you please take a personal interest & stop the throttling?!]
2022Edit
@anisomorphism @Javlaskitstovel Sure it starts with Bott & Tu. With a little May. Before you know it? Youâre. hitting the harder stuff. Hartshorne leads to EGA & SGA. Next? They find you in a gutter, begging to do even just a little of Jacksonâs E&M to make the withdrawal symptoms go away.
Even for a momentâŠ
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