
At the Bourbaki Seminar in November 1968 the participants were handed the following (premature) announcement of Bourbaki’s death. The French text can be found at the Canulars Bourbaki, and the English translation below is from Maurice Mashaal’s book Bourbaki, a secret society of mathematicians, page 115. I’ve underlined a couple of riddles in the text…. Read more »

Chasing one story, one sometimes tumbles into a different one. For some time I’m trying to debunk the story that Wolfgang Krull was close to inventing the notion of schemes in the early 1930’s. I guess my first encounter with it was through The Rising Sea: Grothendieck on simplicity and generality I by Colin McLarty… Read more »

You better subscribe to the French newspaper Liberation if you’re interested in the latest whereabouts of Grothendieck’s ‘gribouillis’. And even then it is hard to turn this info into a consistent tale. A futile attempt… [section_title text=”In the Bibliotheque Nationale de France?”] A year ago it all seemed pretty straightforward. Georges Maltsiniotis gave a talk… Read more »

We know embarrassingly little about the symmetries of the roots of all polynomials with rational coefficients, or if you prefer, the absolute Galois group $Gal(\overline{\mathbb{Q}}/\mathbb{Q})$. In the title picture the roots of polynomials of degree $\leq 4$ with small coefficients are plotted and coloured by degree: blue=4, cyan=3, red=2, green=1. Sums and products of roots… Read more »

We left the story of Grothendieck’s Lasserre notes early 2015, uncertain whether they would ever be made public. Some things have happened since. Georges Maltsiniotis gave a talk at the Gothendieck conference in Montpellier in june 2015 having as title “Grothendieck’s manuscripts in Lasserre”, raising perhaps even more questions. Philippe Douroux, a journalist at the… Read more »

Summer of 2012. Suddenly several “integerasaserviceproviders” spring from nowhere. They deliver “artisanal integers”. Integers which (they claim) are “handcrafted and guaranteed to be unique and hellabeautiful”. Are you still with me? Perhaps it helps to have a look at one of the three such services still operational today: Brooklyn Integers, Mission Integers (after San Francisco’s… Read more »

absolute, geometry, number theory, stories
The Log Lady and the Frobenioid of $\mathbb{Z}$
Posted on by lievenlb“Sometimes ideas, like men, jump up and say ‘hello’. They introduce themselves, these ideas, with words. Are they words? These ideas speak so strangely.” “All that we see in this world is based on someone’s ideas. Some ideas are destructive, some are constructive. Some ideas can arrive in the form of a dream. I can… Read more »

Absolute geometry is the attempt to develop algebraic geometry over the elusive field with one element $\mathbb{F}_1$. The idea being that the set of all prime numbers is just too large for $\mathbf{Spec}(\mathbb{Z})$ to be a terminal object (as it is in the category of schemes). So, one wants to view $\mathbf{Spec}(\mathbb{Z})$ as a geometric… Read more »

Apologies to Joachim Roncin, the guy who invented the slogan “Je suis Charlie”, for this silly abuse of his logo: I had hoped the G+ post below of end december would have been the last I had to say on this (non)issue: (btw. embedded G+post below, not visible in feeds) A quick recap : –… Read more »

. Michele Audin has written a book on the history of the Julia seminar (hat tip +Chandan Dalawat via Google+). The “Julia Seminar” was organised between 1933 and 1939, on monday afternoons, in the Darboux lecture hall of the Institut Henri Poincare. After good German tradition, the talks were followed by tea, “aimablement servi par… Read more »

If Chad Orzel is able to teach quantum theory to his dog, surely it must be possible to explain schemes, stacks, toposes and motives to hipsters? Perhaps an idea for a series of posts? It’s early days yet. So far, I’ve only added the tag sga4hipsters (pun intended) and googled around for ‘reallife’ applications of… Read more »

Nature (the journal) asked David Mumford and John Tate (of Fields and Abel fame) to write an obituary for Alexander Grothendieck. Probably, it was their first experience ever to get a paper… rejected! What was their plan? How did they carry it out? What went wrong? And, can we learn from this? the plan Mumford… Read more »

A mathstory well worth following in 2015. What will happen to Grothendieck’s unpublished notes, or as he preferred, his “gribouillis” (scribbles)? Here’s the little I know about this: 1. The Mormoiron scribbles During the 80ties Grothendieck lived in ‘Les Aumettes’ in Mormoiron In 1991, just before he moved to the Pyrenees he burned almost all… Read more »

math, number theory
$\mathbf{Ext}(\mathbb{Q},\mathbb{Z})$ and the solenoid $\widehat{\mathbb{Q}}$
Posted on by lievenlbNote to self: check Jack Morava’s arXiv notes on a more regular basis! It started with the G+post below by +David Roberts: Suddenly I realised I hadn’t checked out Morava‘s “short preprints with ambitious ideas, but no proofs” lately. A couple of years ago I had a brief email exchange with him on the Habiro… Read more »

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. Clearly there are popmath books like dedicated to $\pi$ or $e$, but I don’t know just one novel having… Read more »

Supernatural numbers also appear in noncommutative geometry via James Glimm’s characterisation of a class of simple $C^*$algebras, the UHFalgebras. A uniformly hyperfine (or, UHF) algebra $A$ is a $C^*$algebra that can be written as the closure, in the norm topology, of an increasing union of finitedimensional full matrix algebras $M_{c_1}(\mathbb{C}) \subset M_{c_2}(\mathbb{C}) \subset … \quad… Read more »

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. In this paper, Grothendieck reshaped homological algebra for Abelian categories, extending the setting of CartanEilenberg (their book and the paper both appeared in 1957). While working on the Tohoku… Read more »

A reading suggestion for Grothendieckstalkers crawling around the Ariège region, near SaintGirons, in search of ‘another house’ : better bring along the Fogas Chronicles by Julia Stagg.

“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) Finding that particular café in Paris, presumably in the… Read more »

This is the story of the day the notion of ‘neighbourhood’ changed forever (at least in the geometric sense). For ages a neighbourhood of a point was understood to be an open set of the topology containing that point. But on that day, it was demonstrated that the topology of choice of algebraic geometry, the… Read more »

Here’s a map of the (major) mathematical centers in Europe (in 1927), made for the Rockefeller Foundation. Support by the Rockefeller foundation was important for European Mathematics between the two world wars. They supported the erection of the Mathematical Institute in Goettingen between 19261929 and creation of the Institut Henri Poincare in Paris at about… Read more »

A standard Grassmannian $Gr(m,V)$ is the manifold having as its points all possible $m$dimensional subspaces of a given vectorspace $V$. As an example, $Gr(1,V)$ is the set of lines through the origin in $V$ and therefore is the projective space $\mathbb{P}(V)$. Grassmannians are among the nicest projective varieties, they are smooth and allow a cell… Read more »

For me this quest is over. All i did was following breadcrumbs left by others. Fellowtravelers arrived there before. What did they do next? The people from the esoteric site L’Astrée, write literary texts on Grothendieck, mixing strange details (such as the kiosque de la place Pinel, the village of FougaxetBarrineuf and even ‘Winnie’ or… Read more »

Roy Lisker (remember him from the Mormoiron post?) has written up his Grothendieckquest(s), available for just 23$, and with this strange blurbtext: “The author organized a committee to search for him that led to his discovery, in good health and busily at work, in September, 1996. This committee has since become the Grothendieck Biography Project…. Read more »

We would love to conclude this series by finding the location of the “final” Grothendieckspot, before his 85th birthday, this thursday. But, the road ahead will be treacherous, with imaginary villages along the way and some other traps planted by the nice people of the Grothendieck Fan Club It is wellknown that some members (if… Read more »
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