This is a thread about defining a ring of polynomials. That is, we are not just evaluating a polynomial or looking for its roots, but we want to be able to do something like add two polynomials (to get another polynomial), multiply two polynomials, etc. 1/10

EVs are rapidly taking over the auto market in Europe, with trucks not far behind. Oil-burners are on a fast track to the bin!

This is very cool, and something I was curious about when I first learned about Grothendieck's work on tame topology in Montpellier late in his career: where are the documents and what are the details? https://mathoverflow.net/a/516391/4177 Now people can see! Ideally a write-up of this in a […]

Mathematical introduction: I work on Metamath's iset.mm which formalizes mathematics from the axioms of IZF set theory to https:// us.metamath.org/ileuni/taupi.html (a sentimental favorite) and, at this writing, 27 of the theorems at https:// us.metamath.org/mm_100.html . The classical set.mm […]

New solar-powered clam just dropped, part of a small club that partner with algae in their bodies for food! Geloina expansa lives in mangroves in South Asia and farms algae called zooxanthellae in its gills, the same type that corals partner with in a process […] [Original post on scicomm.xyz]

Big news on irrational numbers! Aabir Fauzan from Aalto University released a preprint on Zenodo before it hit the arXiv, and a formalisation has been posted by Moritz Firsching. Since the statement is so elementary, the repo is set up to be checked by the […] [Original post on mathstodon.xyz]

@dougmerritt @ColinTheMathmo Ooh nice. The part from timestamps 2:42 to 14:15 was nice to listen to, since I just finished a formalization of Bertrand's postulate from IZF axioms in metamath which uses the prime counting function π, the Chebyshev theta function, etc. Seeing them in this talk was […]

@ColinTheMathmo FYI not quite what you said, but of high interest IMHO: Terry Tao gave a 30 min. talk on his current project, and the first half is a very breezy overview of analytic number theory in terms of current state of the art theorems proving/improving constants related to primes, such […]

Yesterday I noticed a swarm of tiny water striders next to a boat dock on the Sacramento River. They move so fast that they are mostly a blur! I had seen them before but never had stopped to ID them. I learned from iNaturalist they are Rhagovelia distincta. I wondered if they are a river-adapted […]

Let's do some performance exploration of the Anthropic FLT proof (https://github.com/anthropics/fermats-last-theorem) To set the scene, we are talking about 60,475 Lean modules in FLT on top of 8,312 already part of Mathlib. However, these two file sets are not of quite the same shape: the […]

Today I successfully used Shamos's catalog of the real numbers! (https://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf) but the number I was looking up was 𝑒 − 2, which I really should have recognised...

Nobody can replace Alitalia

When dealing with how to navigate a software development job (promotions, approaching coworkers to get things done, etc), the topic calls for a combination of serious advice and humor (yes, even snark at times because how else can you cope with some of the absurdity). I say this as a description […]

I'm going to write a mini-thread on finite sets in #constructiveMathematics (mostly to pass along some intuition from a friend who is new to this material shared with me). Classical intuition works poorly on constructive finite sets, but once you adapt your intuition, constructive finite sets […]

The alternative fields medalists have been decided: https://esander1789.github.io/afm/

I asked a long question on MathOverflow about which topos best represents L. E. J. Brouwer's ideas on intuitionism (some of which I have tried to summarize): mathoverflow.net/q/514026/17064

Which topos (or topoi) most accurately reflect Brouwer's ideas on intuitionism?

Let me first clarify that I am not expecting the titular question to have a single well-defined answer (or it would probably have to be a useless one like “the topos freely generated by the followi...

mathoverflow.net

Just stumbled on this delightful exchange from several years ago. @christianp is an excellent human being who does sterling work keeping the nonsense levels around here just right. https://mathstodon.xyz/@christianp/111137629332647555

I'm going to write a mini-thread on finite sets in #constructiveMathematics (mostly to pass along some intuition from a friend who is new to this material shared with me). Classical intuition works poorly on constructive finite sets, but once you adapt your intuition, constructive finite sets […]

RE: https://mastoxiv.page/@arXiv_csLO_bot/116911516892048971 It looks as though one of my favourite problems has been solved! It's related to both Petri nets and linear logic. BVAS are more general than VAS – which are more or less the same as Petri nets. The reachability problem for VAS was […]

I hope you are sitting down… https://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

I was invited to speak at the Summer Conference on Topology 2026and its Applications in Split, Croatia. This is how I tried to explain the topos of countable reals to ordinary topologists: https://www.andrej.com/assets/slides/topology-in-the-topos-of-countable-reals.pdf I did get a bunch of […]

The regular dodecahedron is rigid (but the truncated dodecahedron might not be): https://mathoverflow.net/a/513195/8217

Is the dodecahedron flexible (as a polytope with fixed edge-lengths)?

Consider the (regular) dodecahedron $D\subset\Bbb R^3$. I want to continuously deform it so that throughout the deformation it stays a convex polytope, it stays a combinatorial dodecahedron (i.e. ...

mathoverflow.net

**The first doges — John the Deacon** The elections of the first doges of Venice are shrouded in mystery, both as to who they were, and why, how and by whom they were chosen. The Istoria Veneticorum by _John the Deacon_ is our earliest source for […] [Original post on historywalksvenice.com]

Find a function whose derivative equals its inverse. Solution: https://www.johndcook.com/blog/2026/06/29/derivative-equals-inverse/

Here is one! Traditionally a caltrop is a cluster of four spikes, arranged like the vertices of a regular tetrahedron. It's a defensive weapon. A defending army can litter the ground with these spikes, which will slow down any attacking force. The caltrop […] [Original post on mathstodon.xyz]

Excited at our paper just out in PNAS. We used JWST to detect frozen deuterated water ("heavy water") on the moons of Uranus. There is **much more** on the moons than on Uranus itself, showing that Uranus and the moons formed from separate reservoirs of water. Fun lab work in the supplement, too.🔭🪐

Deuterated water and the formation of the satellites of Uranus | PNAS

The satellites of Uranus orbit in a low-eccentricity, equatorial plane that is tilted by 98° relative to the solar system—a geometry that mirrors U...

pnas.org

RE: https://mathstodon.xyz/@mc/116647599132585695 I have to quote this to add confirming context: (A) there is, and needs to be, an encyclopedia of definitions of the center of triangles, and (B) it has over 71,000 definitions. As Jeremy eloquently puts it, wtf?!

Woah, a geometric topology paper with 31 authors! It's titled "Algorithms in 4-Manifold Topology", and they show that there exists an algorithm that takes as input two closed, simply connected, topological 4-manifolds and decides whether or not the manifolds are homeomorphic […]

@soaproot galleomatids are famously cryptic. For example, one species in Southern CA tidepools, an extremely well-studied setting, was thought to be extinct, only known from fossils until 2022! They are good at hiding, tiny and hard to ID even for experts […]