I posted a question on MathOverflow about understanding Kleene's construction of a computable tree with an infinite branch but no infinite hyperarithmetical branch: mathoverflow.net/q/513712/17064

Unwrapping the proof of the fact that an infinite branch of a computable tree can fail to be hyperarithmetical

(Experts can skip the following two paragraphs, which are written for the sake of completeness of MathOverflow.) Standard definitions (recalled for convenience): In this question, a tree means a su...

mathoverflow.net

mathstodon.xyz/@jeanas/1169...

Jean Abou Samra (new account) (@jeanas@mathstodon.xyz)

Attached: 1 image @jpoiret@types.pl I wonder if this comment will make it through moderation… (CC @antoinechambertloir and @patrick_massot)

mathstodon.xyz

I hope you are sitting down… mathoverflow.net/a/513385/

Could the Jacobian conjecture be undecidable?

Most of us know the Jacobian conjecture. Here's a version below for fixed positive integers $d$ and $n$: $J(d,n)$: If $f: C^n \rightarrow C^n$ is a polynomial map of degree $d$, and if the Jacob...

mathoverflow.net

This had me in fits of laughter: www.math.columbia.edu/~woit/wordpr... “Gross started off the talk by complaining that he had had to work hard for the few days before his talk, since he had found that his slides were so old that the file formats now had compatibility problems with current software.”

Various and Sundry

Some things that might be of interest: The ICM is starting next week in Philadelphia. One traditional aspect of the ICM is the announcement of the Fields Medal winners. This year there won’t …

math.columbia.edu

People told me that the small wiki I run (https:// wiki.lilypond.community) was regularly down or unresponsive. After peeking into the request log, I blocked the crawler that feeds Meta's AI. Load average instantly down from around 50 to under 0.5.

Article bouleversant. www.lemonde.fr/internationa...

« Si on m’attrape, c’est la fin pour moi » : au Sénégal, l’effroi quotidien des homosexuels sous le coup de la répression

Alors qu’en mars, une loi a durci les peines encourues pour relations homosexuelles, les Sénégalais LGBT+ vivent dans la peur. Sous le couvert de l’anonymat, plusieurs d’entre eux témoignent d’un quot...

lemonde.fr

I just signed the TCS4F manifesto tcs4f.org . This is the text I added to my website: I am panicked about climate change, and so should you be. I have signed the Theoretical Computer Scientists for Future (TCS4F) pledge for sustainable research in theoretical computer science. …

TCS4F Manifesto - Theoretical Computer Scientists for Future

TCS4F is an initiative aimed at theoretical computer scientists for a significant reduction of carbon emissions and evolve towards more sustainable practices.

tcs4f.org

mathstodon.xyz/@jeanas/1168...

The standard encoding of pairs in the untyped λ-calculus is pair := λ x y f ⋅ f x y, fst := λ p ⋅ p (λ x y ⋅ x), snd := p (λ x y ⋅ y). This validates the β-rules fst (pair x y) = x and snd (pair x y) = y but not the η-rule p = pair (fst p) (snd p). Is there another encoding with η?

The page en.wikipedia.org/wiki/Semanti... is taking shape. Feedback very much appreciated, especially on pedagogy (I don't find this topic very easy to explain).

mathstodon.xyz/@jeanas/1167...

“There's a semantics for graded students — it's the constant function ‘fail’.” (Viktor Bense)

I asked a question on MathOverflow about category theory, requesting help in clarifying a confusion of mine regarding the reg/lex and ex/lex constructions on the category of assemblies and how they relate to “extensional realizability”: mathoverflow.net/q/511959/17064

Confusion concerning the reg/lex and ex/lex constructions on the category of assemblies

While trying to gain some understanding on how extensional realizability relates to the reg/lex and ex/lex completions of assemblies, I came to believe the following mutually contradictory statemen...

mathoverflow.net

Looks interesting: arxiv.org/abs/2606.00861

The Axiom of Double Complement and its opposites

Powell introduced the Axiom of Double Complement ($\mathsf{DCom}$) to give his double-negation interpretation of $\mathsf{ZF}$ into $\mathsf{IZF_{Rep}}$. However, the consistency, strength, and compat...

arxiv.org

I completely disagree 🙂 If you are lucky enough to take a course in the beautiful area of descriptive set theory (as I recently did), one thing it teaches you is that expanding your view to spaces beyond just the reals practically doesn't complicate matters and gives many new interesting examples.

A descriptive set theory question: mathstodon.xyz/@jeanas/1166...

Here's a question I've meant to ask for a long time: mathoverflow.net/q/511737/

How bad can papering over universe issues be?

Many introductions to category theory brush over size issues (by which I mean paying attention to which categories are small, locally small, dealing with facts like there being no category of all

mathoverflow.net

I added a definition of the effective topos to Wikipedia. I think it's incomprehensible for a newcomer (as it was to me two years ago), but since I ran out of time, pedagogy will have to wait for later or someone else. en.wikipedia.org/wiki/Effecti...

Every summer I repost this article on how to spot drowning. Please read it and pass on. In the last few years I’ve had SIX messages from people who saved a kid’s life after clicking on the link from my feed. slate.com/technology/2...

Drowning Doesn’t Look Like Drowning

Drowning is not the violent, splashing call for help that most people expect.

slate.com

The Budapest type theory group is hiring a postdoc to work on higher observational type theory. lists.seas.upenn.edu/pipermail/ty...

19 juin, colloque en l'honneur de feu Gilles Dowek deducteam.gitlabpages.inria.fr/colloque-gil... M. le ministre passera honorer notre ancien collègue.

I promise to keep this account mostly mathematical, but since there is so little to rejoice about in global politics at the moment, let me share some pictures that I took two weeks ago at the parliament in Budapest.

After postponing looking into the numbers for a long time because there is already more to be depressed about in the news these days than I can handle, I finally just started reading about AI's environmental impact and… man. This is obscene. www.wired.com/story/new-ga...

New Gas-Powered Data Centers Could Emit More Greenhouse Gases Than Entire Nations

A WIRED review of permits for data center projects using natural gas and linked to OpenAI, Meta, Microsoft, and xAI shows they could emit more than 129 million tons of greenhouse gases per year.

wired.com

Exciting news from Agda: types.pl/@amy/1165222...

Evan Cavallo, Jonas H\"ofer: Univalence without function extensionality https://arxiv.org/abs/2605.00812 https://arxiv.org/pdf/2605.00812 https://arxiv.org/html/2605.00812

I just created a Wikipedia page about cubical type theory. For now this is a stub with just keyword-dropping and reference-dropping. Help to augment it is very welcome, we really need a readable first introduction to cubical type theory written down somewhere. en.wikipedia.org/wiki/Cubical...

Un billet de blog où j'essaie de raconter de façon pas trop interminable et j'espère pas trop incompréhensible de quoi parle le texte que j'ai écrit récemment avec @jeanas.bsky.social, et ce que sont ces «degrés d'Arthur-Nimué-Merlin». www.madore.org/~david/weblo...

Breaking mathematical news: recent events have formally disproved the claim that adults are adults, refuting a nearly 350 years old conjecture of Leibniz. This is the first fully automated contribution to mathematics by autonomous geopolitical agents.

In French mathematics, families are tied into tribes living on separated spaces.

I asked on MathOverflow whether a certain corollary of the Cayley-Hamilton theorem can be interpreted from the point of view of algebraic geometry. Help appreciated, this would be very useful for a research project. mathoverflow.net/q/510112/