## The return of the cat CEILIDH

By in Stories

I couldn’t believe my eyes. I was watching an episode of numb3rs, ‘undercurrents’ to be precise, and there it was, circled in the middle of the blackboard, CEILIDH, together with some of the key-exchange maps around it…

## Aaron Siegel on transfinite number hacking

By in Games

Aaron Siegel has now dramatically extended our previous list and calculated the $\alpha_p$ for all primes $p \leq 181$. He mails :

## A cat called CEILIDH

The sad story of Alice Silverberg‘s cat when she came too close to tori-cryptography…

## Extending Lenstra’s list

By in Games

After more than 30 years we make a small addition to Hendrik Lenstra’s list of Conway’s mystery elements $\alpha_p$:

## Elliptic Curve Systems Too Risky

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Of course, they’re not. It’s an Arjen Lenstra joke on the abbreviation of the tori key-compression system ECSTR.

## Conway’s nim arithmetics

By in Games

John Conway defined the simplest possible addition and multiplication on the class of all ordinal numbers, turning it magically into an algebraically closed field…

## Tori and more efficient key-exchange

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What has Hilbert’s Satz 90 to do with finding more efficient ways to exchange keys?

## Transfinite number hacking

By in Games

Alain Connes asked for a concrete realisation of the algebraic closure $\overline{\mathbb{F}_2}$ of the finite field on two elements. Well, here it is:

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According to Wikipedia the Russell paradox was discovered a year before by Ernst Zermelo but he did not publish the idea, which remained known only to Hilbert, Husserl and other members of the University of Göttingen.

## Devilish symmetries

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The fractal nature of the devil’s staircase has a large group of (self)symmetries.

## The taxicab story

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There’s this classic Hardy story on his visit to Ramanujan in a taxicab numbered 1729:

## Algebraic tori and cryptography

Did Diffie and Hellman discover the key-exchange principle, or was this one of the hidden secrets of GCHQ?

## Only space for $\exists !$ topos book

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For the first time in 15 years both PD1 & PD2 will join us on vacation. Space is crammed, so drastic decisions are required…

## The father of all beamer talks

By in Games

Who was the first mathematician to give a slide show talk? I don’t have the definite answer to this question, but would like to offer a strong candidate : Hermann Minkowski.

## $\mathbf{Ext}(\mathbb{Q},\mathbb{Z})$ and the solenoid $\widehat{\mathbb{Q}}$

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Note to self: check Jack Morava’s arXiv notes on a more regular basis!

## Crowdfund subtitling of interviews?

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Four months ago, Leila Schneps started a crowd-funding project to translate part 3 of Scharlau’s biography of Grothendieck. So far, she raised 3350 of the required 6000 dollars from 45 donations.

## Fresh(wo)men’s course on Foundations

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In two months I’ll be teaching ‘Logic and Set Theory’ for the first time, a first year, first semester course on Foundations. And no (though I considered it for a nanosecond) I will not trow HoTT at them…

## On categories, go and the book $\in$

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A nice interview with Jacques Roubaud (the guy responsible for Bourbaki’s death announcement) in the courtyard of the ENS. He talks about go, categories, the composition of his book $\in$ and, of course, Grothendieck and Bourbaki.

## Why I didn’t post yesterday today

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At times it is far more rewarding to enter into an exchange on G+ than to try to write yet another blog post here…

## A noncommutative moduli space

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Supernatural numbers also appear in noncommutative geometry via James Glimm’s characterisation of a class of simple $C^*$-algebras, the UHF-algebras.

## The origins of HoTT

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Below, a great G+-post by Allen Knutson, pointing to a talk given by Voevodsky in which he explains why  some errors (by himself and others) convinced him that mathematics needed a new foundation.

## Erna Bannow, octonions and the Leech?

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Erna Bannow was born october 6th1911 in Schlawe (Pommern), now Sławno in Poland. In 1930 she finished her secondary studies at the Oberlyzeum Merseburg (near Leipzig). She then continued her studies at the universities of Marburg, Bonn, and Göttingen.

## Oulipo’s use of the Tohoku paper

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Many identify the ‘Tohoku Mathematical Journal’ with just one paper published in it, affectionately called the Tohoku paper: “Sur quelques points d’algèbre homologique” by Alexander Grothendieck.

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## Hilbert’s heartbreak hotel

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A post by Nature is causing some ripples at Google+.

## 4 generations of mathematicians

By in History

Bourbaki’s death announcement mentions ‘Respectively their father, brother, son, grandson, great-grandson, and grand-cousin’ giving us 5 generations, among which 4 generations of Bourbakis.

## Noncommutative boundary to Langlands

Here’s the punchline : a large chunk of the Connes-Marcolli book Noncommutative Geometry, Quantum Fields and Motives can be read as an exploration of the noncommutative boundary to the Langlands program (at least for $GL_1$ and $GL_2$ over the rationals $\mathbb{Q}$).

## Bourbaki & Le Tour de France

By in Stories

During the 1952 summer-congress in Pelvoux-le-Poët, Bourbaki fervently followed the Tour de France, and was an avid supporter of one of the greatest cyclists ever: Fausto Coppi.

## Where is Fogas?

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A (reading) suggestion for Grothendieck-stalkers touring around small villages in the Ariège region, near Saint-Girons, in search of ‘another house’ : better bring along the Fogas Chronicles by Julia Stagg.

This time we will describe the points of the arithmetic site with Steinitz’ supernatural numbers and adele-classes.

## Bourbaki’s cause of death: May 68

By in History

In Bourbaki est mort, CQFD, Pierre Cartier asserts: “Yes, Bourbaki is dead. He was killed by May 68!”

## Who discovered the Leech lattice? (1)

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The Leech lattice was, according to wikipedia, ‘originally discovered by Ernst Witt in 1940, but he did not publish his discovery’ and it ‘was later re-discovered in 1965 by John Leech’. However, there is very little evidence to support this claim.

## The points of the arithmetic site

Now that Alain Connes’ talk at the IHES is online, giving hints to prove some of the statements of the arithmetic site, we can continue our story.

## Where is Bourbaki’s hotel in Pelvoux?

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From left to right: Jacques Dixmier, Jean Dieudonné, Pierre Samuel, André Weil, Jean Delsarte and Laurent Schwartz on some terrace during the 1951 ‘Ecumenical’ Bourbaki summer-conference in Pelvoux. Where, exactly, was this?

## Cartier on Grothendieck, again

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Last week, the IHES shared Pierre Cartier “Les mathématiques de Grothendieck (un survol)” (talk in English though). I don’t know whether this was part of the evening activities of the conference for Maxim Kontsevich 50th birthday (one Groth-activity/conference is quickly becoming the standard…).

## Who discovered the Leech lattice? (2)

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For the better part of the 30ties, Ernst Witt (1) did hang out with the rest of the ‘Noetherknaben’, the group of young mathematicians around Emmy Noether (3) in Gottingen.

## according to Groth. IV.22

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Roubaud’s motif (pardon the expression) for writing the announcement of Bourbaki’s death in 1968 can be read between the lines in his book Mathematics, a novel from which all quotes below are taken.

## topological theology

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The announcement of Bourbaki’s death ends with the remarkable line:

“For God is the Alexandrov compactification of the universe.” Groth. IV.22

What has this to do with Simone Weil attending Bourbaki congresses?

## Grothendieck’s Café

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“A story says that in a Paris café around 1955 Grothendieck asked his friends “what is a scheme?”. At the time only an undefined idea of “schéma” was current in Paris, meaning more or less whatever would improve on Weil’s foundations.” (McLarty in The Rising Sea)

## the ‘Cemetery for Random Functions’

By in History

Perhaps the fact that Bourbaki died on November 11th, 1968 (exactly 50 years after the end of WW1) is an allusion to the mandatory retirement age for members of Bourbaki, as suggested by the Canulars Bourbaki.

## the announcement of Bourbaki’s death

By in History

Even though the Bourbaki group dissolved itself in the late 90ties, the (premature) death of N. Bourbaki was already announced in november 1968…

## Entonnoirs a.k.a. Spectral Sequences

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“Sammy Eilenberg was suggesting (as a joke) that it should be called “entonnoir” : each step (“page” as one says now) is smaller than the preceding one, and what comes out at the end is delicious.” (Serre on AlgTop)

## $\neg$ the Bourbaki couch potatoes

By in History

At the 1951 Pelvoux-congress a schism between the mountaineers and couch potatoes threatened Bourbaki.

## Sheaves and Carapaces

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“I sat in the seminaire Cartan, as a stupified witness to his discussions with Serre, loaded with ‘Spectral Sequences’ (brr!) and drawings (called ‘diagrams’) full of arrows covering the blackboard. It was the heroic age of the theory of ‘sheaves’ and ‘carapaces’ and of a whole arsenal whose sense entirely escaped me.” (Grothendieck, ReS, p.19)

## Tropical – the French view of Brazil

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“The adjective tropical was coined by French mathematicians in honor of their Brazilian colleague Imre Simon. There is no deeper meaning in the adjective tropical. It simply stands for the French view of Brazil.” (From Speyer-Sturmfels)

## Maxim Kontsevich – Jeux de Mots

By in Algebra

A very nice talk by Maxim Kontsevich, intended for a general audience, on formal languages, free groups and algebraic power series.

## Grothendieck quest – the (road) movie

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A movie by Catherine Aira and Yves Le Pestipon “Alexande Grothendieck, sur les routes d’un genie” is touring mathematical departments and conferences in the south(-west) of France.

## the birthday of Grothendieck topologies

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This is the story of the day our notion of ‘neighbourhood’ changed forever (at least in the geometric sense).

## Herbrand’s fatal mountain hike

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Jacques Herbrand was considered one of the greatest younger logicians and number-theorists when he fell to his death on july 27th 1931, only 23 years old, while mountain-climbing in the Massif des Ecrins.

By in History

## The Log Lady and the Frobenioid of $\mathbb{Z}$

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“Sometimes ideas, like men, jump up and say ‘hello’. They introduce themselves, these ideas, with words. Are they words? These ideas speak so strangely.”

Note to fellow library users: I’ve taken out SGA4, Mac Lane-Moerdijk and the Elephants. There’s an arithmetic site I need to check out.

## Hirune Mendebaldeko-Bourbaki’s muse

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

## Alain in toposland

An (at times) hilarious interview on the dangers of category theory and Alain’s conversion to topoi. Here, an attempt to provide subtitles for 2 minutes (50.36-52.27):

By in GeoTag

## Bloomsday 2014 – a mad day’s work

Welcome to my new blog – a mad day’s work.