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Bourbaki and Grothendieck-Serre

This time of year I’m usually in France, or at least I was before Covid. This might explain for my recent obsession with French math YouTube interviews.

Today’s first one is about Bourbaki’s golden years, the period between WW2 and 1975. Alain Connes is trying to get some anecdotes from Jean-Pierre Serre, Pierre Cartier, and Jacques Dixmier.

If you don’t have the time to sit through the whole thing, perhaps you might have a look at the discussion on whether or not to include categories in Bourbaki (starting at 51.40 into the clip).

Here are some other time-slots (typed on a qwerty keyboard, mes excuses) with some links.

  • 8.59 : Canular stupide (mort de Bourbaki)
  • 15.45 : recrutement de Koszul
  • 17.45 : recrutement de Grothendieck
  • 26.15 : influence de Serre
  • 28.05 : importance des ultra filtres
  • 35.35 : Meyer
  • 37.20 : faisceaux
  • 51.00 : Grothendieck
  • 51.40 : des categories, Gabriel-Demazure
  • 57.50 : lemme de Serre, theoreme de Weil
  • 1.03.20 : Chevalley vs. Godement
  • 1.05.26 : retraite Dieudonne
  • 1.07.05 : retraite
  • 1.10.00 : Weil vs. Serre-Borel
  • 1.13.50 : hierarchie Bourbaki
  • 1.20.22 : categories
  • 1.21.30 : Bourbaki, une secte?
  • 1.22.15 : Grothendieck C.N.R.S. 1984

The second one is an interview conducted by Alain Connes with Jean-Pierre Serre on the Grothendieck-Serre correspondence.

Again, if you don’t have the energy to sit through it all, perhaps I can tempt you with Serre’s reaction to Connes bringing up the subject of toposes (starting at 14.36 into the clip).

  • 2.10 : 2e these de Grothendieck: des faisceaux
  • 3.50 : Grothendieck -> Bourbaki
  • 6.46 : Tohoku
  • 8.00 : categorie des diagrammes
  • 9.10 : schemas et Krull
  • 10.50 : motifs
  • 11.50 : cohomologie etale
  • 14.05 : Weil
  • 14.36 : topos
  • 16.30 : Langlands
  • 19.40 : Grothendieck, cours d’ecologie
  • 24.20 : Dwork
  • 25.45 : Riemann-Roch
  • 29.30 : influence de Serre
  • 30.50 : fin de correspondence
  • 32.05 : pourquoi?
  • 33.10 : SGA 5
  • 34.50 : methode G. vs. theorie des nombres
  • 37.00 : paranoia
  • 37.15 : Grothendieck = centrale nucleaire
  • 38.30 : Clef des songes
  • 42.35 : 30.000 pages, probleme du mal
  • 44.25 : Ribenboim
  • 45.20 : Grothendieck a Paris, publication R et S
  • 48.00 : 50 ans IHES, lettre a Bourguignon
  • 50.46 : Laurant Laforgue
  • 51.35 : Lasserre
  • 53.10 : l’humour
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the bongcloud attack

In this neverending pandemic there’s a shortage of stories putting a lasting smile on my face. Here’s one.



If you are at all interested in chess, you’ll know by now that some days ago IGMs (that is, international grandmasters for the rest of you) Magnus Carlsen and Hikaru Nakamura opened an official game with a double bongcloud, and couldn’t stop laughing.

The bongcloud attack is the chess opening in which white continues after

1. e2-e4, e7-e5

with

2. Ke1-e2 !

thereby blocking the diagonals for the bishop and queen, losing the ability to castle, and putting its king in danger.

If you are left clueless, you should download the free e-book Winning with the bongcloud immediately.

If you are (or were) a chess player, it is the perfect parody to all those books you had to suffer through in order to build up an ‘opening repertoire’.

If you are new to chess (perhaps after watching The queen’s gambit), it gives you a nice selection of easy mate-in-one problems.

Every possible defence against the bongcloud is illustrated with a ‘game’ illustrating the massive advantage the attack gives, ending with a situation in which … black(!) has a one-move mate.

One example:

In the two knight Copacabana tango defense against the bongcloud, that is the position after



the Haight-Asbury (yeah, well) game (Linares, 1987) continued with:

4. Kg3, Nxe4?
5. Kh3, d6+
6. Qg4!, Bxg4
7. Kxg4, Qf6??
8. Ne2, h5+??
9. Kh3!, Nxf2
10. Kg3!

giving this position



which ‘Winning with the bongcloud’ evaluates as:

White continues his textbook execution of a “pendulum,” swinging back and forth between g3 and h3 to counter every Black threat. With the dynamically placed King, Black’s attack teeters on the edge of petering out. Nxh1 will trap the Black Knight and extinguish the threat.

In the actual game, play took a different turn as Black continued his h-file pressure. Nonetheless, this game is an excellent example of how 2. …Nc6 is often a wasted tempo in the Bongcloud.

Here’s Nakamura philosophising over the game and the bongcloud. Try to watch at least the first 30 seconds or so to see the commentators reaction to the actual Carlsen-Nakamura game.

Now, that put a smile on your face, didn’t it?

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Teapot supremacy

No, this is not another timely post about the British Royal family.

It’s about Richard Borcherds’ “teapot test” for quantum computers.



A lot of money is being thrown at the quantum computing hype, causing people to leave academia for quantum computing firms. A recent example (hitting the press even in Belgium) being the move of Bob Coecke from Oxford University to Cambridge Quantum Computing.

Sure, quantum computing is an enticing idea, and we have fantastic quantum algorithms such as Shor’s factorisation algorithm and Grover’s search algorithm.

The (engineering) problem is building quantum computers with a large enough number of qubits, which is very difficult due to quantum decoherence. To an outsider it may appear that the number of qubits in a working quantum computer is growing at best linearly, if not logarithmic, in sharp contrast to Moore’s law for classical computers, stating that the number of transistors in an integrated circuit doubles every two years.

Quantum computing evangelists assure us that this is nonsense, and that we should replace Moore’s law by Neven’s law claiming that the computing power of quantum computers will grow not just exponentially, but doubly exponentially!

What is behind these exaggerated claims?

In 2015 the NSA released a policy statement on the need for post-quantum cryptography. In the paper “A riddle wrapped in an enigma”, Neil Koblitz and Alfred Menezes carefully examined NSA’s possible strategies behind this assertion.

Can the NSA break PQC? Can the NSA break RSA? Does the NSA believes that RSA-3072 is much more quantum-resistant than ECC-256 and even ECC-384?, and so on.

Perhaps the most plausible of all explanations is this one : the NSA is using a diversion strategy aimed at Russia and China.

Suppose that the NSA believes that, although a large-scale quantum computer might eventually be built, it will be hugely expensive. From a cost standpoint it will be less analogous to Alan Turing’s bombe than to the Manhattan Project or the Apollo program, and it will be within the capabilities of only a small number of nation-states and huge corporations.

Suppose also that, in thinking about the somewhat adversarial relationship that still exists between the U.S. and both China and Russia, especially in the area of cybersecurity, the NSA asked itself “How did we win the Cold War? The main strategy was to goad the Soviet Union into an arms race that it could not afford, essentially bankrupting it. Their GNP was so much less than ours, what was a minor set-back for our economy was a major disaster for theirs. It was a great strategy. Let’s try it again.”

This brings us to the claim of quantum supremacy, that is, demonstrating that a programmable quantum device can solve a problem that no classical computer can solve in any feasible amount of time.

In 2019, Google claimed “to have reached quantum supremacy with an array of 54 qubits out of which 53 were functional, which were used to perform a series of operations in 200 seconds that would take a supercomputer about 10,000 years to complete”. In December 2020, a group based in USTC reached quantum supremacy by implementing a type of Boson sampling on 76 photons with their photonic quantum computer. They stated that to generate the number of samples the quantum computer generates in 20 seconds, a classical supercomputer would require 600 million years of computation.

Richard Borcherds rants against the type of problems used to claim quantum ‘supremacy’. He proposes the ‘teapot problem’ which a teapot can solve instantaneously, but will be impossibly hard for classical (and even quantum) computers. That is, any teapot achieves ‘teapot supremacy’ over classical and quantum computers!

Another point of contention are the ‘real-life applications’ quantum computers are said to be used for. Probably he is referring to Volkswagen’s plan for traffic optimization with a D-Wave quantum computer in Lisbon.

“You could give these guys a time machine and all they’d use it for was going back to watch some episodes of some soap opera they missed”

Enjoy!

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Lockdown reading : Penumbra

In this series I’ll mention some books I found entertaining, stimulating or comforting during these Corona times. Read them at your own risk.



It’s difficult to admit, but Amazon’s blurb lured me into reading Mr. Penumbra’s 24-Hour Bookstore by Robin Sloan:

“With irresistible brio and dazzling intelligence, Robin Sloan has crafted a literary adventure story for the 21st century, evoking both the fairy-tale charm of Haruki Murakami and the enthusiastic novel-of-ideas wizardry of Neal Stephenson or a young Umberto Eco, but with a unique and feisty sensibility that’s rare to the world of literary fiction.” (Amazon’s blurb)

I’m a fan of Murakami’s later books (such as 1Q84 or Killing Commendatore), and Stephenson’s earlier ones (such as Snow Crash or Cryptonomicon), so if someone wrote the perfect blend, I’m in. Reading Penumbra’s bookstore, I discovered that these ‘comparisons’ were borrowed from the book itself, leaving out a few other good suggestions:

One cold Tuesday morning, he strolls into the store with a cup of coffee in one hand and his mystery e-reader in the other, and I show him what I’ve added to the shelves:

Stephenson, Murakami, the latest Gibson, The Information, House of Leaves, fresh editions of Moffat” – I point them out as I go.

(from “Mr Penumbra’s 24-Hour Bookstore”)

This trailer gives a good impression of what the book is about.

Why might you want to read this book?

  • If you have a weak spot for a bad ass Googler girl and her tecchy wizardry.
  • If you are interested in the possibilities and limitations of Google’s tools.
  • If you don’t know what a Hadoop job is or how to combine it with a Mechanical Turk to find a marker on a building somewhere in New-York.
  • If you never heard of the Gerritszoon font, preinstalled on every Mac.

As you see, Google features prominently in the book, so it is kind of funny to watch the author, Robin Sloan, give a talk at Google.

Some years later, Sloan wrote a (shorter) prequel Ajax Penumbra 1969, which is also a good read but does not involve fancy technology, unless you count tunnel construction among those.



Read it if you want to know how Penumbra ended up in his bookstore and how he recovered the last surviving copy of the book “Techne Tycheon”.

More information (together with reading suggestions) can be found at Mr Penumbra’s 24-hour bookstore: a reading map.

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Lockdown reading : the Carls

In this series I’ll mention some books I found entertaining, stimulating or comforting during these Corona times. Read them at your own risk.

An Absolutely Remarkable Thing (AART for the fans) by Hank Green came out in 2018, and recently I reread it when its sequel A Beautifully Foolish Endeavor appeared last summer.


“Protagonist April May discovers a large robot sculpture in Midtown Manhattan. She and her friend Andy Skampt decide to film it and post the video online, which goes viral and makes April an overnight celebrity. All over the world identical structures—known as “Carls”—have appeared in major cities at exactly the same time.” (Wikipedia)

Here’s an artist’s impression of said video, followed by the ‘Queen sequence’ (one of many puzzles in the book). On an audio fragment a faint trace of Queen’s “Don’t Stop Me Now” is heard, and April discovers the code “IAMU” after fixing a series of typos in the Wikipedia article about that song.

Three reasons why you might want to read this book now:

  1. It’s about the dangers and pitfalls of social media and online fame. (Something Hank Green is familiar with as he runs with his brother the YouTube channel Vlogbrothers.)
  2. It’s about a global pandemic. (Not caused by a virus, but by a contagious dream, containing 4096 ‘sequences’=puzzles, each resulting in an HEX-sequence to be combined into a vector-image.)
  3. It’s about the consequences of hate speech. (It’s hard not to draw parallels between ‘Peter Petrawicki’ and a former president, and between the actions of the ‘Defenders’ and the events of January 6th.)

AART doesn’t end well for April May, and it was hard to image Hank Green ever writing a sequel without doing a Bobby Ewing shower scene (showing my age here). And yes, the book ends with a two word text message from April: “Knock Knock”.



The sequel ‘A Beautifully Foolish Endeavour’ is perhaps even more enjoyable than AART. The Dream is now replaced by a Magic Book, and the storytelling (at first) no longer done by April herself but by her four evangelists (Maya, Andy, Miranda and Robin), Green’s very own Mamalujo so to speak.

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G+ recovery 6 : math-history

In April my Google+ account will disappear. Here I collect some G+ posts, in chronological order, having a common theme. Today, math-history (jokes and puns included).

September 20th, 2011

Was looking up pictures of mathematicians from the past and couldn’t help thinking ‘Hey, I’ve seen this face before…’

Leopold Kronecker = DSK (2/7/2019 : DSK = Dominique Strauss-Kahn)

Adolf Hurwitz = Groucho Marx

June 2nd, 2012

The ‘Noether boys’

(Noether-Knaben in German) were the group of (then) young algebra students around Emmy Noether in the early 1930’s. Actually two of them were girls (Grete Hermann and Olga Taussky).

The picture is taken from a talk Peter Roquette gave in Heidelberg. Slides of this talk are now available from his website.

In 1931 Jacques Herbrand (one of the ‘Noether boys’) fell to his death while mountain-climbing in the Massif des Écrins (France). He was just 23, but already considered one of the greatest minds of his generation.

He introduced the notion of recursive functions while proving “On the consistency of arithmetic”. In several texts on Herbrand one finds this intriguing quote by Chevalley (one of the first generation Bourbakis):

“Jacques Herbrand would have hated Bourbaki” said French mathematician Claude Chevalley quoted in Michèle Chouchan “Nicolas Bourbaki Faits et légendes” Edition du choix, 1995. («Jacques Herbrand aurait détesté Bourbaki» in the original French version).

Can anyone tell me the underlying story?

June 26th, 2012

a 3yr old post on Scottish vs. Platonic Solids did hit Reddit/pics

1.4k upvotes. Surreal!

I’d better point them to the latest on this then.

Scottish solids, final(?) comments.

The return of the Scottish solids

December 19th, 2012

Mumford’s treasure map

+Pieter Belmans (re)discovered a proto-drawing of Mumford’s iconic map of Spec(Z[x]) in his ‘red book’.

The proto-pic is taken from Mumford’s ‘Lectures on curves on an algebraic surface’ p.28 and tries to depict the integral projective line. The set-up is rather classical (focussing on points of different codimension) whereas the red-book picture is more daring and has been an inspiration for generations of arithmetical geometers.

Still there’s the issue of dating these maps.

Mumford himself dates the P^1 drawing 1964 (although the publication date is 66) and the red-book as 1967. 

Though I’d love to hear more precise dates, I’m convinced they are about right. In the ‘Curves’-book’s preface Mumford apologises to ‘any reader who, hoping that he would find here in these 60 odd pages an easy and concise introduction to schemes, instead becomes hopelessly lost in a maze of unproven assertions and undeveloped suggestions.’ and he stresses by underlining ‘From lecture 12 on, we have proven everything that we need’.

So, clearly the RedBook was written later, and as he has written in-between his master-piece GIT i’d say Mumford’s own dating is about right.

Still, it is not a completely vacuous dispute as the ‘Curves’ book (supposedly from 1964 or earlier) contains a marvelous appendix by George Bergman on the Witt ring which would predate Cartier’s account…

Thanks to +James Borger i know of George’s take on this

“I was a graduate student taking the course Mumford gave on curves and surfaces; but algebraic geometry was not my main field, and soon into the course I was completely lost.  Then Mumford started a self-contained topic that he was going to weave in — ring schemes — and it made clear and beautiful sense to me; and when he constructed the Witt vector ring scheme, I thought about it, saw a nicer way to do it, talked with him about it and with his permission presented it to the class, and eventually wrote it up as a chapter in his course notes.
I think that my main substantive contribution was the tying together of the various prime-specific ring schemes into one big ring scheme that works for all primes.  The development in terms of power series may or may not have originated with me; I just don’t remember.”

which sounds very Bergmannian to me.

Anyway I’d love to know more about the dating of the ‘Curves’ book and (even more) the first year Mumford delivered his Red-Book-Lectures (my guess 1965-66). Thanks.
Pieter maintains an “Atlas of this picture” here

June 17th, 2013

the birthday of schemes : november 5th 1956

The wikipedia-entry linking Andre Martineau to the origin of the scheme-concept appears to rely on footnote 29 of Cartier’s ‘A mad day’s work, from Grothendieck to Connes and Kontsevich’ which reads:

“Serre first considered the set of maximal ideals of a commutative ring A subject to certain restrictions. Martineau then remarked to him that his arguments remained valid for any commutative ring, provided one takes all prime ideals instead of only maximal ideals. I then proposed a definition of schemes equivalent to the definition of Grothendieck. In my dissertation I confined myself to a framework similar to that of Chevalley, so as to avoid an excessively long exposition of the preliminaries!”

In the 1956/57 Chevalley seminar Cartier gave the first two talks and in the first one, on november 5th 1956, one finds the first published use of the word ‘scheme’, which he refers to as ‘schemes in the sense of Chevalley-Nagata’. On page 9 of that talk he introduces the prime spectrum with its Zariski topology.

In the second talk a week later, on november 12th, he then gives the general definition of a scheme (as we know it, by gluing together affine schemes and including the stalks).

BUT, he did all of this ‘only’ for affine rings over a field, ‘to avoid an excessively long exposition of the preliminaries’…

Grothendieck then made the quantum-leap to general commutative rings.

June 18th, 2013

Correction : scheme-birthday = december 12th, 1955

Claude Chevalley gave already two talks on ‘Schemes’ in the Cartan-Chevalley seminar of 1955/56, the first one on december 12th 1955, the other a week later.

Chevalley only considers integral schemes, of finite type over a field (Cartier drops the integrality condition on november 5th 1956, a bit later Grothendieck will drop all restrictions).

Grothendieck’s quote “But then, what are schemes?” uttered in a Parisian Cafe must date from that period. Possibly Cartier explained the concept to him. In a letter to Serre, dated december 15th 1955, Grothendieck is quite impressed with Cartier:

“Cartier seems to be an amazing person, especially his speed of understanding, and the incredible amount of things he reads and grasps; I really have the impression that in a few years he will be where you are now. I am exploiting him most profitably.”

June 18th, 2013

David Mumford on the Italian school of Geometry

Short version:
Castelnuovo : the good
Severi : the bad
Enriques : the ugly

The longer version:

“The best known case is the Italian school of algebraic geometry, which produced extremely good and deep results for some 50 years, but then went to pieces.
There are 3 key names here — Castelnuovo, Enriques and Severi.

C was earliest and was totally rigorous, a splendid mathematician.

E came next and, as far as I know, never published anything that was false, though he openly acknowledged that some of his proofs didn’t cover every possible case (there were often special highly singular cases which later turned out to be central to understanding a situation).  He used to talk about posing “critical doubts”. He had his own standards and was happy to reexamine a “proof” and make it more nearly complete.

Unfortunately Severi, the last in the line, a fascist with a dictatorial temperament, really killed the whole school because, although he started off with brilliant and correct discoveries, later published books full of garbage (this was in the 30’s and 40’s). The rest of the world was uncertain what had been proven and what not. He gave a keynote speech at the first Int Congress after the war in 1950, but his mistakes were becoming clearer and clearer.

It took the efforts of 2 great men, Zariski and Weil, to clean up the mess in the 40’s and 50’s although dredging this morass for its correct results continues occasionally to this day.” (David Mumford)

June 19th, 2014

Hirune Mendebaldeko – Bourbaki’s muse

After more than 70 years, credit is finally given to a fine, inspiring and courageous Basque algebraic geometer.

One of the better held secrets, known only to the first generation Bourbakistas, was released to the general public in april 2012 at the WAGS Spring 2012, the Western Algebraic Geometry Symposium, held at the University of Washington.

Hirune Mendebaldeko was a Basque pacifist, a contemporary of Nicholas Bourbaki, whom she met in Paris while there studying algebraic geometry. They were rumored to be carrying on a secret affair, with not infrequent trysts in the Pyrenees. Whenever they appeared together in public, however, there was no indication of any personal relationship.

From the comments, by +Sandor Kovacs:

+Chris Brav Chris, just between us: the whole thing is a joke. I just tried to put yet another twist on it. Also, until now we have never admitted that it is, so please don’t tell anyone. 😉

The explanation at the end of +lieven lebruyn’s blog post was indeed the original motivation for the name. We were starting a new “named” lecture series as part of WAGS and wanted to name it after someone not obvious. Basque is a language not related to any other. It seemed a good idea to use that, so very few people would know the meaning of any particular word.

Then we tried all the words in WAGS, but the other three were actually very similar to the English/etc versions. The first name was chosen by vibe. Then we decided that we needed a bio for our distinguished namesake and the connection to Bourbaki presented itself for various reasons that you can guess. But we wanted a pacifist and it seemed a nice contrast to Bourbaki. So Hirune was born and we were hoping that one day she would gain prominence in the world. Finally, it happened. 🙂

June 22nd, 2014

the state of European mathematics in 1927

This map, from the Rockefeller foundation, gives us the top 3 mathematical institutes in 1927 : Goettingen, Paris and … Rome.
The pie-charts per university show that algebra was a marginal topic then (wondering how a similar map might look today).

December 1st, 2015

Did Chevalley invent the Zariski topology?

In his inaugural lecture at #ToposIHES Pierre Cartier stated (around 44m11s):
“By the way, Zariski topology, as we know it today, was not what Zariski invented. He invented a variant of that, a topology on the set of all valuation rings of a given field, which is not exactly the same thing. As for the Zariski topology, the rumour is that it was invented by Chevalley in a seminar given by Zariski, but I have no real proof.”
Do you know more about this?

Btw. the full lecture of Cartier (mostly on sheaf theory) is not on the IHES YouTube channel, but on the channel of +Laurence Honnorat.

The IHES did begin to upload videos of the remaining plenary talks
here (so far, the wednesday talks are available).

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G+ recovery 2 : Grothendieck

My Google+ account is going away on April 2, 2019, so i’ll try to rescue here some posts, in chronological order and around one theme. Here’s Grothendieck-stuff, part two.

March 18th, 2014

crowd-funding Grothendiecks biography?  

+John Baez has a post out at the n-cat-cafe on Leila Schneps’s quest to raise $6000 to translate Scharlau’s 3-volume biography of Grothendieck.

If you care to contribute : go here.

Lots of good stuff in volume 3 on Groths hippy/eco/weirdo years. I’ve plundered Scharlau’s text last year trying to pinpoint the location of Groths hideout in the French Pyrenees.

As far as i know, part 2 (the most interesting part on Groths mathematical years) is still under construction and will be compiled by the jolly group called the “Grothendieck circle”.

There’s a nice series of G-recollections out here (a.o. by Illusie, Karoubi, Cartier, Raynaud, Mumford, Hartshorne, Murre, Oort, Manin, Cartier).

I’m pretty sure Groth himself would prefer we’d try to get his Recoltes et Semailles translated into English, or La Clef des Songes.

November 18th, 2014

Grothendieck’s last hideout

The past ten days I’ve been up in the French mountains (without internet access), not that far from the Ariege, so I’m just now catching up with all (blog)posts related to Grothendieck’s death.

At our place, the morning of thursday november 13th was glorious!

Even though FranceInter kept telling horror stories about flooding in more southern departements, I can only hope that Grothendieck passed away in that morning sun.
About a year ago, on the occasion of Groth’s 85th birthday, I ran a series of posts on places where he used to live, ending with his last known hideout

At the time I didn’t include the precise location of his house, but now that pictures of it are in the French press I feel free to suggest (if you are interested to know where Grothendieck spend his later years) to point your Google-earth or Google-maps (in streetview!) to:
lat 43.068254  lon 1.169080

November 18th, 2014

Mormoiron and Lasserre acknowledge Grothendieck

In the series of post on Grothendieck-places I wrote a year ago (see here and links at the end) I tried to convince these French villages to update their Wikipedia page to acknowledge the existence of Grothendieck under the heading ‘Personnalités liées à la commune’, without much success.

Today it is nice to see that Lasserre added Grothendieck to their page:

“Alexandre Grothendieck (1928-2014), considéré comme un des plus grands mathématiciens du xxe siècle, y a vécu en quasi-ermite de 1990 à sa mort.”

Also Mormoiron, where Grothendieck lived in the 80ties (see picture below) has updated its page:

“Alexandre Grothendieck a habité temporairement à Mormoiron (“Les Aumettes”)”

French villages who still have to follow suit:
Vendargues
Massy
Olmet-et-Villecun

November 19th, 2014

Please keep an eye on the GrothendieckCircle for updates

+Leila Schneps invested a lot of time over the years setting up the Grothendieck Circle website.

Some material had to be removed a few years ago as per Groth’s request.

I’m sure many of you will be as thrilled as I was to get this message from Leila:

“I have already started modifying the Grothendieck circle website and it will of course eventually return completely.  Plus many things will be added, as we will now have access to Grothendieck’s correspondence and many other papers.”

Leila already began to update the site, for example there’s this new page on Groth’s life in Lasserre.

I understand Leila is traveling to Lasserre tomorrow, presumably for Grothendieck’s funeral. Hopefully she will eventually post something about it on the GrothendieckCircle (or, why not here on G+).

December 4th, 2014

 
Nicolas Bourbaki is temporarily resurrected to announce the death of Grothendieck in the French newspaper Le Monde.

You may recall that Bourbaki passed away on november 11th 1968, see +Peter Luschny’s post on his death announcement.

December 6th, 2014

The ‘avis de décès’ released by Grothendieck’s family and friends, published in the local French newspaper ‘La Depeche’, on saturday november 15th.

It announces Grothendieck’s cremation, on november 17th at 11.30h in the village of Pamiers, bordering the ‘Camp du Vernet’, where Grothendieck’s father Sasha was imprisoned, before being deported to Auschwitz and murdered by the Nazis in 1942. 

June 12th, 2015

Grothendieck’s later writings  

Next week there’s a Grothendieck conference at Montpellier. George Maltsiniotis will give a talk thursday afternoon with the  exciting title “Grothendieck’s manuscripts in Lasserre” (hat tip +Pieter Belmans ).

You may recall that G’s last hideout was in the Pyrenean village of Lasserre.

After a bit of sleuthing around I’ve heard some great news.

Grothendieck’s family have donated all of his later writings (apart from his correspondences and other family-related stuff) to the Bibliotheque Nationale. The BNF have expressed their intention of scanning all this material (thousands of pages it seems) and making them (eventually) available online!

Rumour has it that the donation consists of 41 large folders containing G’s reflections, kept in the form of a diary (a bit like ‘Clef des Songes’), on G’s usual suspects (evil, Satan, the cosmos), but 2 or 3 of these folders contain mathematics (of sorts).

Probably, Maltsiniotis will give a preview on this material. To anyone lucky enough to be able to go down south next week and to attend his talk, please keep me in the loop…

June 19th, 2015

Maltsiniotis’ talk on Grothendieck’s Lasserre-gribouillis

Yesterday, George Maltsiniotis gave a talk at the Gothendieck conference in Montpellier with title “Grothendieck’s manuscripts in Lasserre”.

This morning, +David Roberts  asked for more information on its content, and earlier i gave a short reply on what i learned, but perhaps this matter deserves a more careful write-up.

+Damien Calaque  attended George’s talk and all info below is based on his recollections. Damien stresses that he didn’t take notes so there might be minor errors in the titles and order of the parts mentioned below.

EDIT: based on info i got from +Pieter Belmans  in the comments below (followed up by the picture he got via +Adeel Khan  taken by Edouard Balzin) i’ve corrected the order and added additional info.

The talk was videotaped and should become public soon.

As i mentioned last week Grothendieck’s family has handed over all non-family related material to the Bibliotheque Nationale. Two days ago, Le Monde wrote that the legacy consists of some 50.000 pages.

Maltsiniotis insisted that the BNF wants to make these notes available to the academic community, after they made an inventory (which may take some time).

I guess from the blackboard-picture i got from Pieter, the person responsible at the BNF is Isabelle le Masme de Chermont.

The Lasserre-griboillis themselves consists of 5 parts:

1. Géométrie élémentaire schématique. (August 1992)
This is about quadratic forms and seems to be really elementary.

2. Structure de la psyché. (12/10/1992-28/09/1993) 3600 pages
This one is about some combinatorics of oriented graphs with extra-structure (part of the structure are successor and predecessor operators on the set of arrows).

3. Psyché et structures (26/03/93-20/06/93) 700 pages
This one is non-mathematical.

4. Maxwell equations.
Maltsiniotis mentioned that he was surprised to see that there was at best one mathematics book in G’s home, but plenty of physics books.

5. Le problème du mal. (1993-1998) 
This one is huge (30.000 pages) and is non-mathematical.

Note that also the Mormoiron-gribouillis will be made public by the University of Montpellier, or if you prefer video.

Finally, is the photo below what you think it is? Yep!

January 20th, 2016

where are the videos of the Grothendieck conference?

Mid june 2015 a conference “Mathematics of the 21st century: the vision of Alexander Grothendieck” was held in Montpellier. In a comment to a post here on Maltsiniotis’ talk i mentioned that most of the talks were video-taped and that they would soon be made public.

When they failed to surface on the Montpellier website, i asked +Damien Calaque  for more information. Some months ago Damien told me the strange (and worrying) tale of their fate.

At that moment Damien was in a process of trying to recover the videos. Two weeks ago he told me things were looking good, so i now feel free to post about it.

Michael Wright is the head of the Archive for Mathematical Sciences & Philosophy. He arranged with the organizers of the conference that he would send someone over to video-tape the lectures and that he would make them available on his Archive. He also promised to send a copy of the videos to Montpellier, but he never did. Nor did the tapes appear on his site.

Damien Calague emailed Wright asking for more information and eventually got a reply. It appears that Wright will not be able to edit the videos nor put them online in a reasonable time.

They agreed that Damien would send him a large capacity USB-drive. Wright would copy the videos on it and send it back. Damien will arrange for the videos to be edited and the University of Montpellier will put them online. Hopefully everything will work out smoothly.

So please keep an eye on the website of l’Institut Montpelliérain Alexander Grothendieck

May 6th, 2017

Grothendieck’s Montpellier notes will hit the net May 10th

At last there is an agreement between the university at Montpellier and Grothendieck’s children to release the ‘Montpellier gribouillis’ (about 28000 pages will hit the net soon).
Another 65000 pages, found at Lasserre after Grothendieck’s death, might one day end up at the IHES or the Bibliotheque Nationale.
If you are interested in the history of Grothendieck’s notes, there is this old post on my blog.

(h/t Theo Raedschelders for the Liberation link)

May 11th, 2017

Buy a Grothendieck painting to get the Lasserre notes online!

As of yesterday, most of Grothendieck’s Montpellier notes are freely available at this site.

There’s much to say about the presentation (eg. It is not possible to link directly to a given page/article, it is scanned at only 400 dpi etc. etc.) but hey, here they are at last, for everyone to study.

By far the most colourful (in my first browsing of the archive) is cote No. 154, on ‘systeme de pseudo-droites’. You can download it in full (a mere 173 Mb).

As you know, the Montpellier notes are only a fraction of the material Grothendieck left behind. By far the largest (though probably not the most interesting, mathematically) are the Lasserre notes, which to the best of my knowledge are in the care of a Parisian bookseller.

Here’s an idea:
almost every page of No. 154 (written on ancient computer-output) looks like a painting. No doubt, most math departments in the world would love to acquire one framed page of it. Perhaps this can raise enough money to safeguard the Lasserre notes…

July 13th, 2017

le Tour de France in Grothendieck’s backyard

If you want to see the scenery Grothendieck enjoyed in his later years, watch the Tour de France tomorrow.

It starts in Saint-Girons where he went to the weekly market (and died in hospital, november 13th 2014), ending in Foix with 3 category 1 climbs along the way (familiar to anyone familiar with Julia Stagg’s expat-lit set at ‘Fogas’ or you can read my own post on Fogas).

It will not pass through Lasserre (where G spend the final 20 years of his life) which is just to the north of Saint-Girons.

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G+ recovery 1 : Grothendieck

My Google+ account is going away on April 2, 2019, and all attempts to automatically backup my G+ posts seem to fail so far. So i’ll try to rescue here some of them, in chronological order and around one theme. Today, Grothendieck-stuff, part one.

May 30th, 2013

Recordings of a 1972 talk by Grothendieck at Cern “Réflexions sur la science- responsabilité du savant”.
If you don’t have time to listen to all 138 minutes, try to grab from part1 the fragment 29:10 – 30:40 on “the strange ritual of inviting experts to give a talk on some esoteric subject for an audience of 50 to 100 people, one or two of whom will perhaps be able to painfully understand a few bits and pieces, and all others find themselves in a position of humiliation, as they gave in to social pressure to be there, even though the topic itself didn’t interest them at all” (poor translation on my part)
These recordings are illustrative for Grothendieck’s talks in his ‘Survivre’ period, early 70ties. 
(h/t Matilde Marcolli on FB)

June 8th, 2013

Grothendieck’s christmas tree

In the pdf-version of “Recoltes et Semailles” Grothendieck writes on page 463 in the Yin-Yang chapter:

“j’ai fini par aboutir à un diagramme, vaguement en forme d’arbre de Noël”

Here’s the actual diagram, from the original typescript of “Les portes sur l’univers”, the appendix to the ‘Clef du Yin et du Yang’.

Sadly, this appendix (and the many drawings contained in it) didn’t make it into the pdf-release of RecS…

June 9th, 2013

Grothendieck’s yin-yang sunflower

Grothendieck’s ‘Les Portes sur l’Univers’ (Gateways to the Universe(?)) is a truly fascinating text, containing several mysterious drawings (and even a bit of icosahedral-math towards the end).

On PU46, he draws the sunflower of yin and yang, having 12 leafs (he claims, corresponding to 12 yin-terms on the inner circle, 12 yang-terms on the outer circle, as well as to the 12 signs of the zodiac…).

He continues: “On l’appellera, au choix, l’accordeon cosmique, ou l’harmonica cosmique, ou (pour mettre tout le monde d’accord) l’harmonium cosmique”.
(One might call it, as one prefers, the cosmic accordion, or the cosmic harmonica, or (in order to seek general consensus) the *cosmic harmony*).

June 10th, 2013

Grothendieck’s icosahedral theorem

On april 12th 1986, Grothendieck decides to add a mathematical annexe to his esoteric text ‘Les portes sur l’univers’. 

“Par contre, c’est peu pour mon ardeur de mathématicien, laquelle s’est a nouveau réveillée ces jours derniers – et voila repartie ma réflexion sur l’icosaèdre, cet amour mathématique de mon âge mur! Je vais donc peut-être rajouter a ces notes quelques compléments sur la combinatoire de l’icosaèdre et sur la géométrie des ensembles a six éléments…”

He starts with a set S of 6 elements (the vertices), any pair of elements is an edge and any triple a triangle. He then calls a set of triangles F an *icosahedral structure* provided every edge is contained in exactly two triangles in F.

His main result is that all such icosahedral structures are isomorphic (and has exactly 60 isomorphisms), an icosahedral structure consist of exactly 10 triangles and a choice of triangle determines the structure uniquely. Moreover, there are exactly 12 different such octahedral structures and there is an involution on this set coming from ‘complementary’ structures.

At a first glance, Grothendieck’s result appears to be closely related to one of the surprises in finite group theory: the outer automorphism of the symmetric group on 6 letters.

For more on this and related mathematical mysteries of the octahedron, try:

+John Baez  ‘Some Thoughts on the Number 6’  

+Noah Snyder  ‘The Outer Automorphism of S_6’

my own ‘Klein’s dessins d’enfant and the buckyball’

December 18th, 2013

for Grothendieck aficionados

a chance discovery last month en route from Les Vans – Lablachere (in the Ardeche region), a ‘ferronnerie d’art’ (a wrought-iron workshop) called ‘La Clef des Songes’.

All 315 pages of this Grothendieck meditation from 1987 can be found here.

The 691 pages of ‘Notes pour la clef des songes’ are a bit harder to get. Fortunately, the mysterious website ‘l’astree’ offers them as a series of 23 pdfs here. Enjoy the read!

January 3rd, 2014

Why did Grothendieck quit mathematics?

After yesterday’s post on the striking similarities between the lives of Grothendieck and JD Salinger it sure felt weird to stumble upon this footnote in “La Clef des Songes”  

Probably I’m reading way too much into it, but it appears to indicate that Grothendieck stopped doing mathematics to become … a writer!

April 23rd, 2014

Grothendieck documentary available on DVD

+catherine aira and Yves Le Pestipon made a 90 minute long documentary “Alexander Grothendieck, sur les routes d’un genie” which had successful showings in universities, at the Novela science festival, on Toulouse television, and elsewhere. It will be shown in Nantes, Toulouse, Montpellier, and Montreal.

Yves Le Pestipon is one of the people behind the mysterious website lastree.net which has (among many other things) posts on Grothendieck containing hints to his present whereabouts…

Here are some YouTube clips:
clip1

clip2

Here’s the tumblr page of the project:

All of us who cannot attend the viewings can still order the DVD for 25 Euros (20 Euros in France) by sending an email to catherine.aira@gmail.com.

A new release of the DVD, containing English subtitles, will be available soon.

Thanks to +Adeel Khan Yusufzai +David Roberts and +catherine aira 

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