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@BartoszMilewski@mathstodon.xyz I would pay to watch this sitcom

@mc@mathstodon.xyz is there a follow-up paper that you recommend that talks about multiple variable binding and nested binding contexts? (e.g. local variable shadowing/aliasing whether in an imperative or functional language)

@highergeometer@mathstodon.xyz @wtgowers@mathstodon.xyz @tao@mathstodon.xyz I find it hard for people with little programming experience to understand how to properly use AI, much less comment on it. I might be too close to AI on this since I've personally been keeping abreast of machine learning since the early days of the recommendation systems in 2011.

Do you think these types of posts are more indicative of the state of AI or more the state of the math community's lagging experience with AI?

FWIW, my observations after 2 years of lurking in various non-CS/AI communities like math, medicine, etc:

• most serious AI practitioners hold their techniques like closely guarded secrets while what permeates socials are either people working at AI companies or AI Hype grifters
• a fields introduction to AI follows an eerily predictable pattern and Gowers
• Fields Medalists may be geniuses but they're still human and it took me awhile to realize that programming is a completely foreign field to them

The biggest mistake I see in all these posts is ignorance that the AI harness not the AI model is what makes or breaks AI usage. You have to program your own problem specific harness around one's own domain problems. This keeps being validated time and time again, most recently with the Firefox team (https://hacks.mozilla.org/2026/05/behind-the-scenes-hardening-firefox/)

To use an analogy with cars, it's as if we're at the dawn of invention of automobiles, but everyone is trying to use them as a faster horse-buggy while complaining that cars don't work. The reality is that we need infrastructure and paved roads because of course the car is useless without paved roads, gas stations, etc.

I turned my notes on spectral sequences into an interactive exploration:
https://ikrima.github.io/topos.noether/x/spectral-sequences-guide.html

Source material that finally helped make it click was @tpfto@mathstodon.xyz recommendation of Chow's "You Could Have Invented Spectral Sequences"

I also experimented with making study aid infographics using ChatGPT 5.5 image generator but it's too fickle for me right now to rely on for maintaining detail like subscript indices.

#letsplay #math

Coxeter and Dynkin Diagrams: Part II
https://ikrima.github.io/topos.noether/baez/coxeter-dynkin-02.html

Based on the wonderful tour of Coxeter and Dynkin Diagrams from Baez (https://arxiv.org/abs/2601.02290)

#letsplay #math

Spectral sequences are fascinating but the topic is so dense. Can someone write a Spectral Sequences for Dummies book? :P
#letsplay #math

Exploring Knot Theory Part II
I don't quite understand J-Polynomials or Khovanov homology so I wouldn't trust my Reidemeister move verification logic yet.

That said, it's kinda fun just playing with trefoil knot

#letsplay #math

Time to dive into Coxeter and Dynkin Diagrams: Part I
https://ikrima.github.io/topos.noether/baez/coxeter-dynkin-01.html

Based on the wonderful tour of Coxeter and Dynkin Diagrams from Baez (https://arxiv.org/abs/2601.02290)

#letsplay #math #casuals

Claude/ChatGPT continue to be my 2026 Game Of The Year, transforming learning into a Let's Play Math.

Here's a fun session exploring knot theory.

#letsplay #math

@Alrecenk@peoplemaking.games oooh that's pretty clever! Your math knowledge is way ahead mine. Is that multiplication trick with exp(log(A)+log(B)) coming from tropical geometry, where + is min or max and * is normal addition?

@Alrecenk@peoplemaking.games but to answer your question, imho your intuition is spot on. I think you just rediscovered Lie Groups/algebras. Also they're super useful for spectral based neural nets. If you're curious, you can look into neural operators (e.g. Neural Tangent Kernels/DeepONets/GNNs)

@Alrecenk@peoplemaking.games x1000 to this. I don't have to regulate my autistic infodump when "conversing" with AI. Fwiw, I view it as a self-reflective cognitive mirror, akin to meditating. Small protip: Tell the AI to role-play as your favorite domain experts and pose the question to them. I have a rotating council of luminaries featuring Carmack, Tao, Jonathan Blow, and the Chrono Trigger design dream team. I may have accidentally turned Claude into a MUD based RPG where the dungeons are math problems :P

@highergeometer@mathstodon.xyz I've been building and exploring coding infrastructure/tools around your goal of "bring higher (i.e. categorified) geometry down to earth to the point that physicists can do routine concrete calculations with it"

I obviously don't have the domain knowledge from physics so at best I can only showcase it for computer graphics but I'd love your thoughts of this is along the lines of what your thinking (imagine someone with actual math expertise combined with my programming skills because I can automate my program into tools but can't magically imagine things from a physicists/geometer's perspective):

https://ikrima.github.io/topos.noether/x/descent-part3-gaussian-descent.html

I see this pattern everywhere as I explore higher end math as a #math casual: a category C\mathcal{C}
C (modules, bundles, representations, sheaves, projections in an algebra) decomposes into
atoms (simples, irreducibles, points, primes, factors), and there's a trace-like map from C\mathcal{C}
C to a more linear object (cohomology, class functions, cyclic homology, the modular spectrum) that turns the categorical structure into something computable, and that — in good cases — lets you reconstruct C\mathcal{C}
C from the atoms plus the trace data. The atoms live on a space (Spec, classifying space, moduli space), and that space is the
classifying space in a sense: not a thing but a parameter space for the irreducible building blocks.

The right mirror doesn't distort less. It distorts along the structure, so that the features you need to see are the ones that remain invariant. #math

@cbaberle How do you intuit around polynomial functors? The paper's beyond my current category theory knowledge (evidenced by the wikipedia entry for Polynomial Functors being incomprehensible)

@DavidKButler @soaproot @highergeometer the fwiw tidbit was meant for the non-math experts like me, not you :P

@DavidKButler @soaproot @highergeometer +1 fwiw, all of us computer graphics people literally treat infinity as a point, both from a mathematical sense (an old trick for dynamic shadows in the 2000s relied on projective geometry and parallel lines intersecting at infinity) and from a handwavy sense (we abuse floating point denormals and infinity representations for shader bit tricks)

@highergeometer@mathstodon.xyz Thank you!

@highergeometer@mathstodon.xyz Will there be a video posted somewhere of this?

@BartoszMilewski@mathstodon.xyz like health, it also only works when you participate