Before we start the quest for the final G-spot, hopefully in time for Grothendieck’s 85th birthday, one more post on Alexandre’s ‘hippy-days’. In the second part of Allyn Jackson’s “The Life of Alexandre Grothendieck” she tells the story that AG, while touring the US to spread the gospel of the eco-mouvement “Survivre et Vivre” (the deal was that he gave… Read more →

# G-spots : Massy

One week from now, Alexandre Grothendieck will turn 85. Today, we’ll have a glance at his ‘wilder years’, the early 70ties, when he resigned from the IHES and became one of the leading figures in the French eco-movement. This iconic picture is from those days The text reads: “Schurik entre les “frères ennemis” Gaston Galan et Dyama, rue Polonceau. Derrière,… Read more →

# G-spots : Mormoiron

With Grothendieck’s 85th brithday coming up, march 28th, we continue our rather erratic quest to locate the spots that once meant a lot to him. Ever wondered what Grothendieck’s last-known hideout looked like? Well, here’s the answer: (h/t gruppe eM) And, here’s the story. One of the stranger stories to be found on the web is the Grothendieck quest by… Read more →

# G-spots : Vendargues

In a couple of days, on march 28th, Alexandre Grothendieck will turn 85. To mark the occasion we’ll run a little series, tracking down places where he used to live, hoping to entice some of these villages in the south of France to update their Wikipedia-page by adding under ‘Personnalités liées à la commune’ the line – Alexandre Grothendieck (né… Read more →

# 16 ways to capture a lion (in 1938)

A classic among mathematical jokes is the paper in the August/September 1938 issue of the American Mathematical Monthly “A contribution to the mathematical theory of big game hunting” by one Hector Petard of Princeton who would marry, one year later, Nicolas Bourbaki’s daughter Betti. claimtoken-511b561b7a5a2 There are two main sources of information on the story behind this paper. There are… Read more →

# The empty set according to bourbaki

The footnote on page E. II.6 in Bourbaki’s 1970 edition of “Theorie des ensembles” reads If this is completely obvious to you, stop reading now and start getting a life. For the rest of us, it took me quite some time before i was able to parse this formula, and when i finally did, it only added to my initial… Read more →

# 5 unfortunate French logicians

According to Jean van Heijenoort, the sad state of logic in France after WW2 was largely caused by the untimely death of several key French logicians/mathematical philosophers. Prepping for my course on the history of mathematics, starting next week, i’m trying out a couple of tools, such as Timeline JS. Below, a mini timeline of the deaths of these 5… Read more →

# Scottish solids, final(?) comments

In the spring of 2009 I did spend a fortnight dog-sitting in a huge house in the countryside, belonging to my parents-in-law, who both passed away the year before. That particular day it was raining and thundering heavily. To distract myself from the sombre and spooky atmosphere in the house I began to surf the web looking for material for… Read more →

# From the Noether boys to Bourbaki

Next year I’ll be teaching a master course on the “History of Mathematics” for the first time, so I’m brainstorming a bit on how to approach such a course and I would really appreciate your input. Rather than giving a chronological historic account of some period, I’d like this course to be practice oriented and focus on questions such as… Read more →

# Farey symbols in SAGE 5.0

The sporadic second Janko group $J_2$ is generated by an element of order two and one of order three and hence is a quotient of the modular group $PSL_2(\mathbb{Z}) = C_2 \ast C_3$. This Janko group has a 100-dimensional permutation representation and hence there is an index 100 subgroup $G$ of the modular group such that the fundamental domain $\mathbb{H}/G$… Read more →

# a hamlet with avg. 0.2 kB/sec internet-connection

# Aaron Siegel on transfinite number hacking

One of the coolest (pure math) facts in Conway’s book ONAG is the explicit construction of the algebraic closure $\overline{\mathbb{F}_2}$ of the field with two elements as the set of all ordinal numbers smaller than $(\omega^{\omega})^{\omega}$ equipped with nimber addition and multiplication. Some time ago we did run a couple of posts on this. In transfinite number hacking we recalled… Read more →

# Quiver Grassmannians and $\mathbb{F}_1$-geometry

Reineke’s observation that any projective variety can be realized as a quiver Grassmannian is bad news: we will have to look at special representations and/or dimension vectors if we want the Grassmannian to have desirable properties. Some people still see a silver lining: it can be used to define a larger class of geometric objects over the elusive field with… Read more →

# bookworm arXiv

One of the nicer tools around is bookworm arXiv which ‘is a collaboration between the Harvard Cultural Observatory, arxiv.org, and the Open Science Data Cloud. It enables you to explore lexical trends in over 700,000 e-prints, spanning mathematics, physics, computer science, and statistics’ posted on the arXiv. One possible use is to explore the popularity of certain topics. Below is… Read more →

# the matrix reloaded

The dinosaurs among you may remember that before this blog we had the ‘na&g-forum’ to accompany our master-class in noncommutative algebra & geometry. That forum ran on an early flat-panel iMac G4 which was, for lack of a better name, baptized ‘the matrix’. The original matrix did survive the unification of the three Antwerp universities and a move to a… Read more →