# neverendingbooks

• ## Mamuth to Elephant (3)

Until now, we’ve looked at actions of groups (such as the $T/I$ or $PLR$-group) or (transformation) monoids (such as Noll’s monoid) on special sets of musical elements, in particular the twelve pitch classes $\mathbb{Z}_{12}$, or the set of all $24$ major and minor chords. Elephant-lovers recognise such settings as objects in the presheaf topos on […]

• ## Mamuth to Elephant (2)

Last time, we’ve viewed major and minor triads (chords) as inscribed triangles in a regular $12$-gon. If we move clockwise along the $12$-gon, starting from the endpoint of the longest edge (the root of the chord, here the $0$-vertex) the edges skip $3,2$ and $4$ vertices (for a major chord, here on the left the…

• ## From Mamuth to Elephant

Here, MaMuTh stands for Mathematical Music Theory which analyses the pitch, timing, and structure of works of music. The Elephant is the nickname for the ‘bible’ of topos theory, Sketches of an Elephant: A Topos Theory Compendium, a two (three?) volume book, written by Peter Johnstone. How can we get as quickly as possible from…

• ## Hexboards and Heytings

A couple of days ago, Peter Rowlett posted on The Aperiodical: Introducing hexboard – a LaTeX package for drawing games of Hex. Hex is a strategic game with two players (Red and Blue) taking turns placing a stone of their color onto any empty space. A player wins when they successfully connect their sides together…

• ## Learners’ logic

In the Learners and Poly-post we’ve seen that learners from $A$ to $B$ correspond to set-valued representations of a directed graph $G$ and therefore form a presheaf topos. Any topos comes with its Mitchell-Benabou language, allowing us to speak of formulas, propositions and their truth values. Two objects play a special role in this: the…

• ## Yet more topos news

Every topos has its own internal language, the so called Mitchell-Bénabou language, allowing us to speak about formulas and their truth values. Sadly, Jean Bénabou died last week. Here’s a nice interview with Bénabou (in French) on category theory, Grothendieck, logic, and a rant on plagiarism among topos theorists (starting at 1:00:16). Yesterday, France Culture’s…

• ## The hype cycle of an idea

These three ideas (re)surfaced over the last two decades, claiming to have potential applications to major open problems: (2000) $\mathbb{F}_1$-geometry tries to view $\mathbf{Spec}(\mathbb{Z})$ as a curve over the field with one element, and mimic Weil’s proof of RH for curves over finite fields to prove the Riemann hypothesis. (2012) IUTT, for Inter Universal Teichmuller…

• ## Chevalley’s circle of friends

Last week, Danielle Couty ArXiVed her paper Friendly views on Claude Chevalley (in French). From the abstract: “We propose to follow the itinerary of Claude Chevalley during the last twenty years of his life, through the words of Jacques Roubaud, Denis Guedj and Alexander Grothendieck. Our perspective is that of their testimonies filled with friendship.”…

• ## Christine Bessenrodt (1958-2022)

We were pretty close once. It is a shock to read about her passing on Twitter. EWM mourns Christine Bessenrodt, who passed away on January 24 after a serious illness. Christine held the Chair of Algebra and Number Theory at The University of Hannover and she worked in many ways to promote equality for women…

• ## Grothendieck stuff

January 13th, Gallimard published Grothendieck’s text Recoltes et Semailles in a fancy box containing two books. Here’s a G-translation of Gallimard’s blurb: “Considered the mathematical genius of the second half of the 20th century, Alexandre Grothendieck is the author of Récoltes et semailles, a kind of “monster” of more than a thousand pages, according to…