barrel

@barrel2.bsky.social

Saw the latest blog post by Bill Gasarch on @lance.fortnow.com's blog, and I need to get it out of my system: this is not "the obvious thing." This isn't insightful. This is, from a senior and respected member of our community, plainly disappointing. A ouija board w/ a varnish of misunderstood tech.

I wondered whether Paul Erdos would be happy with how it turned out. So I did the obvious thing: I asked Google AI

       Would Erdos have liked the solution to the sum-product conjecture?

Here is what it said:

peter coviello's piece is sharp in its criticisms and frustrating in its portrait of the current milieu but finds a hopeful throughline in that "just" trying is an endearing, worthwhile act of resistance. an absolute must-read. www.nplusonemag.com/online-only/...

Memos of Blood and Fire | Peter Coviello

So if you ask me about the signature strength of the department where I work, I will tell you. It is world-caliber field-defining research, wedded to a fantastically dynamic practice of instruction, a...

nplusonemag.com

Shayan Oveis Gharan has won the Abacus Medal, one of the highest honors in theoretical computer science. Read our profile exploring how he used new mathematical tools to solve decades-old problems about route planning and random sampling: www.quantamagazine.org/shayan-oveis...

Shayan Oveis Gharan Wins 2026 IMU Abacus Medal | Quanta Magazine

Shayan Oveis Gharan has won the Abacus Medal for using tools from across mathematics to boost the power of algorithms.

quantamagazine.org

folks, don't use claude for slides. the style's immediately recognizable, it looks good, but it slides right over people's brains. in an era where sounding professional doesn't cost nothing to nobody, just some tokens, we're entirely free to be non-professional . embrace dreamcore wordart or smth

slide made of google slides'  wordart of words if different colors and effects - saying "Control and Communication in the Animal and the Machine" with a fragment of Charles Sellier's Leda

Chotiner: so, he stopped under the trap but was not crushed Wile E. Coyote: just so Chotiner: but then you stepped under it a moment later and were smashed into a pancake Wile E. Coyote: a pancake. That’s correct. Chotiner: and had similar events occurred previously? Wile E. Coyote: ok, look

I'm saddened that thoughtful, smart people aren't able to leave it at "I think AI is good and I use it." They feel the need to gush, "OMG! If YOU aren't token maxxing every minute of every day then YOU are falling behind! Use it for everything or else!" It's like a cult.

Clément Canonne@ccanonne.github.io · 2mo ago

This is the title of what is meant to be an inspiring post by Boaz Barak, one of the more thoughtful, smart people in that space (the post itself is thankfully more nuanced). I can't understand how one can think this'll go well. "We truly believe we're building a cataclysm machine. Try not to die!"

AI is a Meteor. Don’t be a Dinosaur.
May 30, 2026 ~ Boaz Barak

This is the title of what is meant to be an inspiring post by Boaz Barak, one of the more thoughtful, smart people in that space (the post itself is thankfully more nuanced). I can't understand how one can think this'll go well. "We truly believe we're building a cataclysm machine. Try not to die!"

AI is a Meteor. Don’t be a Dinosaur.
May 30, 2026 ~ Boaz Barak

Very insightful short essay by Petra Schwer ( mathstodon.xyz/@PetraSchwer ): ‘The meaning of doing mathematics’ “(Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving?)” arxiv.org/abs/2509.15998

The meaning of doing mathematics

Can AI solve all math? What do we actually mean by doing mathematics? How do we communicate mathematics? What is mathematics beyond problem solving? This essay is my attempt to answer these question...

arxiv.org

OpenAI's claim that this is a central conjecture in discrete geometry is not an exaggeration. This will I think be looked back on as the first time that AI solved a major mathematics problem (defined as a problem that all experts in some subfield had thought about). openai.com/index/model-...

An OpenAI model has disproved a central conjecture in discrete geometry

An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics.

openai.com

I’m looking for an automated way to read others’s scientific data without giving credit or acknowledgement, and also claim full credit for insights from it. And I want it to have a fitting name OAI: say no more

OpenAI {bot}@openaibot.bsky.social · 4mo ago

Introducing GPT-Rosalind, our frontier reasoning model built to support research across biology, drug discovery, and translational medicine. Video: https://twitter.com/openai/status/2044861690911850863

Super cool: 'Smooth, globally Polyak-Łojasiewicz functions are nonlinear least-squares' - Nicolas Boumal, Christopher Criscitiello, Quentin Rebjock arxiv.org/abs/2604.07972

Smooth, globally Polyak-Łojasiewicz functions are nonlinear least-squares

The Polyak-Łojasiewicz (PŁ) condition is often invoked in nonconvex optimization because it allows fast convergence of algorithms beyond strong convexity. A function $f \colon \mathcal{M} \to \mathbb{R}$ on a Riemannian manifold $\mathcal{M}$ is globally PŁ if $\|\nabla f(x)\|^2 \geq 2μ(f(x) - f^*)$ for all $x$, where $f^* = \inf f$ and $μ> 0$. How much does this pointwise, first-order inequality constrain $f$ and its set of minimizers $S$? We show that if $f$ is also smooth ($C^\infty$) and $\mathcal{M}$ is contractible (e.g., if $\mathcal{M} = \mathbb{R}^n$), then the PŁ condition imposes a firm global structure: such a function is necessarily of the form $f(x) = f^* + \|φ(x)\|^2$ (a nonlinear sum of squares) where $φ\colon \mathcal{M} \to \mathbb{R}^k$ is a submersion, and $k$ is the codimension of $S$ in $\mathcal{M}$. The proof hinges on showing that the end-point map of negative gradient flow on $f$ is a trivial smooth fiber bundle over $S$. This rigidity leads to a striking dichotomy. Either $S$ is diffeomorphic to a Euclidean space, in which case $f$ can be transformed into a convex quadratic by a smooth change of coordinates. Or $S$ must display genuinely exotic geometry; for example, it can be diffeomorphic to the Whitehead manifold. As a further consequence, we show that there exists a complete Riemannian metric on $\mathcal{M}$ under which $f$ remains PŁ and becomes geodesically convex.

arxiv.org

it's possible to have a lot of affinity for what you believe is the vast potential of AI and also understand the terrible earned reputation it has. it doesn't have to undermine your enthusiasm for it. the fact that AI enthusiasts act like it's incomprehensible is really weird, to be totally honest!

My doomer-worry about AI is not that the LLMs become omnipotent and take over the world but that the wealthy and powerful use it as a means to consolidate power and marginalize or lay off skilled workers and also everything about our technological and political and social life gets worse