# neverendingbooks

• ## Finnegans Wake’s geometry lesson

The literary sensation that spring of 1939 no doubt was the publication of Finnegans Wake by James Joyce. On May 4th 1939 FW was published simultaneously by Faber and Faber in London and by Viking Press in New York, after seventeen years of composition. In 1928-29, Joyce started publishing individual chapters from FW, then known […]

• ## Princeton’s own Bourbaki

In the first half of 1937, Andre Weil visited Princeton and introduced some of the postdocs present (notably Ralph Boas, John Tukey, and Frank Smithies) to Poldavian lore and Bourbaki’s early work. In 1935, Bourbaki succeeded (via father Cartan) to get his paper “Sur un théorème de Carathéodory et la mesure dans les espaces topologiques”…

• ## Cambridge, spring 1939

One of the few certainties we have on the Bourbaki-Petard wedding invitation is that it was printed in, and distributed out of Cambridge in the spring of 1939, presumably around mid April. So, what was going on, mathematically, in and around Trinity and St. John’s College, at that time? Well, there was the birth of…

• ## the Bourbaki code revisited

The fictitious life of Nicolas Bourbaki remains a source of fascination to some. A few weeks ago, Michael Barany wrote an article for the JStor Daily The mathematical pranksters behind Nicolas Bourbaki. Here’s one of the iconic early Bourbaki pictures, taken at the Dieulefit-meeting in 1938. More than a decade ago I discovered the exact…

• ## Ghost metro stations

In the strange logic of subways I’ve used a small part of the Parisian metro-map to illustrate some of the bi-Heyting operations on directed graphs. Little did I know that this metro-map gives only a partial picture of the underground network. The Parisian metro has several ghost stations, that is, stations that have been closed…

• ## Lockdown reading : Bacon

In this series I’ll mention some books I found entertaining, stimulating or comforting during these Corona times. Read them at your own risk. In an attempt to raise the level of this series, I tried to get through the latest hype in high-brow literature: The Death of Francis Bacon by Max Porter. It’s an extremely…

• ## Boolean and Heyting islands

Raymond Smullyan‘s logic puzzles frequently involve Knights (who always tell the truth) and Knaves (who always lie). In his book Logical Labyrinths (really a first course in propositional logic) he introduced islands where the lying or truth-telling habits can vary from day to day—that is, an inhabitant might lie on some days and tell the…

• ## Know thy neighbours

Two lattices $L$ and $L’$ in the same vector space are called neighbours if their intersection $L \cap L’$ is of index two in both $L$ and $L’$. In 1957, Martin Kneser gave a method to find all unimodular lattices (of the same dimension and signature) starting from one such unimodular lattice, finding all its…

• ## The Leech lattice neighbour

Here’s the upper part of Kneser‘s neighbourhood graph of the Niemeier lattices: The Leech lattice has a unique neighbour, that is, among the $23$ remaining Niemeier lattices there is a unique one, $(A_1^{24})^+$, sharing an index two sub-lattice with the Leech. How would you try to construct $(A_1^{24})^+$, an even unimodular lattice having the same…

• ## Lockdown reading : Centenal

In this series I’ll mention some books I found entertaining, stimulating or comforting during these Corona times. Read them at your own risk. The Centenal Cycle is a trilogy written by Malka Older. A Centenal is the basic political unit of a future micro-democracy. It is a neighbourhood consisting of 100.000 people which can vote…