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[Fabien @Fabien_Mikol]

Hugo Duminil-Copin (médaille Fields 2022) : la résolution de 350 problèmes majeurs par OpenAI, c'est comme si des camions m'avaient écrasé ; tous les problèmes (et donc pistes de recherche) que je mentionnais dans mes exposés, articles et demandes de financement, ont été résolus.

[Ole Lehmann @itsolelehmann]

“okay, so what? it’s just math.”

no, you don't get it.

here’s what OpenAI’s math breakthroughs could eventually help make possible in the real world:

Vlasov–Maxwell → stronger foundations for fusion research, whose ultimate prize is virtually limitless clean energy to power civilization

Calderón’s Problem → portable body scanners using electrical signals, making medical imaging cheaper and easier to access

Maximum-Cardinality Matching → faster searches for compatible kidney swaps across large donor pools, helping hospitals coordinate lifesaving transplants

Inverse Elasticity Problem → scans that map tissue stiffness, helping doctors locate suspicious growths inside the body

Mumford–Shah Conjecture → better tools for spotting tissue changes in brain scans, helping doctors identify signs of disease

Bose–Einstein Condensation → stronger foundations for quantum sensors that could help vehicles navigate without GPS

Simple Stochastic Games → better safety checks for self-driving cars and robots before dangerous mistakes reach the real world

Matrix Multiplication → cheaper AI and bigger scientific simulations using the same computers

Edit Distance → faster DNA comparisons, helping researchers study genetic changes linked to disease

The k-Server Problem → robots that waste less movement and energy, making warehouses more efficient and goods cheaper to move

a reminder that math is the foundation of science.

so accelerating mathematical discovery could compress centuries of scientific progress into years.

insane timeline to be alive for!

[Konsti Wohlwend @konstiwohlwend]

i visualized the top 500 unsolved math problems by who solved them. no bingo yet!

how many can humans solve before AI takes over?

[Fabien @Fabien_Mikol]

Cédric Villani au micro de @s_jourdain pour évoquer les ~400 résultats annoncés par OpenAI : "il y a matière à une douzaine de médailles Fields", c'est "une montée en puissance d'une ampleur considérable, il y a encore quelques mois je n'aurais jamais pensé vivre une telle nuit".

[Joshua Gans @joshgans]

I wanted to screenshot this for those historians of AI and technology in the future. The day after OpenAI's mathplosion, it was nowhere to be found on the front page of the New York Times.

[Maxime Fournes⏸️ @FournesMaxime]

I saw the current progress of AI coming a while ago. What I did not see coming was the total disinterest of the media in the face of the entire field of mathematics being made obsolete. How is that not front page news of every newspaper on this planet? That's insane.

[Eli Lifland @eli_lifland]

Important work and terrifying result

[AI Notkilleveryoneism Memes ⏸️ @AISafetyMemes]

Suddenly, AI has solved 90 of the 500 most important open problems in mathematics

Highest ranked problems:

#2 Riemann Hypothesis — PARTIAL
#4 Hodge Conjecture — PARTIAL
#5 Birch and Swinnerton-Dyer Conjecture — PARTIAL
#10 Extended Riemann hypothesis for Dedekind zeta functions — PARTIAL
#12 Generalized Riemann Hypothesis for Dirichlet L-functions — PARTIAL
#15 Tate Conjecture for Algebraic Cycles — PARTIAL
#22 Hilbert's Tenth Problem over the Rationals — FULL CLAIM
#24 Grothendiecks Generalized Hodge Conjecture — PARTIAL
#28 Matrix-Multiplication Exponent Equals Two — PARTIAL
#29 Unique Games Conjecture — FULL CLAIM
#31 Anderson Model Extended States in Dimension at Least Three — FULL CLAIM
#37 Prove the Penrose inequality or present a counterexample — FULL CLAIM
#38 Higher-dimensional Euclidean Kakeya conjecture — PARTIAL
#39 Modularity of Elliptic Curves over Number Fields (End_K(E)=Z) — PARTIAL
#40 Hilbert's Sixteenth Problem, Second Part — PARTIAL
#46 Fourier restriction conjecture — PARTIAL
#47 The Fontaine-Mazur Conjecture on Geometric Galois Representations — PARTIAL
#48 Nonexistence of Landau–Siegel zeros for quadratic Dirichlet L-functions — FULL CLAIM
#52 The Baum-Connes Conjecture for the K-Theory of Reduced Group C*-Algebras — FULL CLAIM
#62 Permanent versus Determinant over C — PARTIAL
#69 Finiteness of the Tate-Shafarevich Group for Elliptic Curves — PARTIAL
#72 Termination of Flips Conjecture in the Minimal Model Program — PARTIAL
#77 Chowla conjecture on correlations of the Liouville function — PARTIAL
#78 Abundance Conjecture for the minimal model program — FULL CLAIM
#80 Hadwiger Conjecture — FULL CLAIM
#83 Zilber-Pink Conjecture on Unlikely Intersections — PARTIAL
#87 Bose-Einstein Condensation in Interacting Continuous Bose Gases — FULL CLAIM
#92 Entanglement Area Law for 2D Gapped Quantum Systems — FULL CLAIM
#94 Grothendieck Standard Conjecture of Hodge Type — PARTIAL
#95 Kannan-Lovasz-Simonovits conjecture on isoperimetry of log-concave measures — PARTIAL
#99 Grothendiecks Section Conjecture in Anabelian Geometry — PARTIAL
#112 The Haldane Conjecture on Spectral Gaps of Antiferromagnetic Quantum Spin Chains — PARTIAL
#114 Iitaka conjecture C_{n,m} on subadditivity of Kodaira dimension — FULL CLAIM
#119 The Borel Conjecture on Topological Rigidity of Aspherical Manifolds — FULL CLAIM
#124 Aspherical Manifolds Admit No Metric of Positive Scalar Curvature — FULL CLAIM
#130 Polynomial Bound for Limit Cycles of Planar Polynomial Vector Fields — PARTIAL
#136 Erdős problem 3: divergent harmonic series and long arithmetic progressions — FULL CLAIM
#139 Cannon's conjecture — FULL CLAIM
#145 Residual Finiteness of Hyperbolic Groups — FULL CLAIM
#153 Congruent Number Problem — PARTIAL
#161 BPL = L (Derandomizing Bounded-Error Logspace) — FULL CLAIM
#163 NP versus the Existential Theory of the Reals — PARTIAL
#169 The Free Group Factor Isomorphism Problem — FULL CLAIM
#172 Conformal Invariance of the Critical Random-Cluster Model with q <= 4 — FULL CLAIM
#179 Arnold Conjecture on Hamiltonian Fixed Points — FULL CLAIM
#181 Polyakov Conjecture: Absence of a Phase Transition for Planar O(n) Models with n >= 3 — FULL CLAIM
#183 Smooth anisotropic Calderón uniqueness from full boundary data — FULL CLAIM
#193 Nonvanishing conjecture for projective log canonical pairs — FULL CLAIM
#195 Parity conjecture for elliptic curves — PARTIAL
#198 Long-Range Order in the Quantum Heisenberg Ferromagnet — FULL CLAIM
#203 Bochner-Riesz conjecture — PARTIAL
#205 Local Smoothing Conjecture for Wave Equations — PARTIAL
#206 Kaplansky's Zero-Divisor Conjecture for Torsion-Free Groups — FULL CLAIM
#210 Artin's primitive root conjecture — PARTIAL
#211 Hilbert-Smith Conjecture — FULL CLAIM
#213 Falconer distance set conjecture — FULL CLAIM
#222 Virasoro Conjecture for Gromov–Witten Invariants — PARTIAL
#224 Wall's Poincare Duality Group Conjecture — FULL CLAIM
#225 K(pi,1) conjecture for Artin groups — FULL CLAIM
#234 Unconditional 2−epsilon Inapproximability of Minimum Vertex Cover — FULL CLAIM
#235 Chromatic Number of the Plane (Hadwiger--Nelson Problem) — PARTIAL
#237 Global Existence of Classical Solutions to the Relativistic Vlasov-Maxwell System — PARTIAL
#239 Universal Optimality of the Hexagonal Lattice in Dimension Two — FULL CLAIM
#246 De Giorgi Conjecture for the Allen-Cahn Equation in Dimensions 4 to 8 — FULL CLAIM
#254 Exact satisfiability threshold for random k-SAT for small k (k = 3) — PARTIAL
#256 Polynomial-Time Decidability of Semidefinite Programming Feasibility — PARTIAL
#260 RL versus L — FULL CLAIM
#261 Kadison Similarity Problem for C*-Algebras — FULL CLAIM
#267 Sidorenko Conjecture on Bipartite Homomorphism Densities — FULL CLAIM
#268 Shafarevich Holomorphic-Convexity Conjecture — FULL CLAIM
#270 Kuznetsov Rationality Conjecture for Cubic Fourfolds — FULL CLAIM
#271 All groups are good: the four-dimensional disc-embedding conjecture — FULL CLAIM
#278 Planar homogeneous Mumford–Shah local-structure conjecture — PARTIAL
#284 Nearby Lagrangian Conjecture — FULL CLAIM
#285 Cartan-Hadamard isoperimetric conjecture — FULL CLAIM
#289 Sharp Upper Bound in Yau's Conjecture on Nodal Sets of Laplace Eigenfunctions — FULL CLAIM
#290 Kaplansky's Idempotent Conjecture — FULL CLAIM
#291 Calderón uniqueness for bounded measurable real isotropic conductivities — FULL CLAIM
#292 Global Attractor Conjecture for Complex-Balanced Mass-Action Systems — FULL CLAIM
#295 Zariski Multiplicity Conjecture for Hypersurface Singularities — FULL CLAIM
#297 Amenability of Thompson's Group F — FULL CLAIM
#298 Griffiths Positivity Conjecture for Ample Vector Bundles — FULL CLAIM
#300 The Singer Conjecture on Vanishing of L2-Cohomology of Aspherical Manifolds — PARTIAL
#305 Birkhoff Conjecture (Near-Boundary Continuous Invariant Foliation) — FULL CLAIM
#306 Secret key from all entangled states — FULL CLAIM
#311 Mahler Conjecture on the Volume Product of a Convex Body — FULL CLAIM
#321 Finiteness of Finitely Presented Periodic Groups — FULL CLAIM
#328 Sinai's Positive Metric Entropy Conjecture for the Chirikov Standard Map — FULL CLAIM
#334 Unrestricted Linear-Circuit Lower Bound for the Discrete Fourier Transform — FULL CLAIM
#343 Koebe circle-domain uniformization conjecture — FULL CLAIM
#351 Kobayashi Conjecture: Hyperbolic Compact Kähler Manifolds Have Ample Canonical Bundle — FULL CLAIM
#356 Bott Conjecture: nonnegatively curved simply connected manifolds are rationally elliptic — PARTIAL
#357 Strong Hyperplane Conjecture for Isotropic Constants — FULL CLAIM
#358 CAT(0) Models for All Word-Hyperbolic Groups — FULL CLAIM
#359 Hopf Conjecture: no metric of positive sectional curvature on S^2 x S^2 — PARTIAL
#361 Alperins Weight Conjecture for Modular Representations of Finite Groups — FULL CLAIM
#364 Log-Brunn-Minkowski Inequality for Symmetric Convex Bodies — FULL CLAIM
#366 Hyperkähler SYZ (Lagrangian Fibration) Conjecture — FULL CLAIM
#368 Benjamini-Schramm conjecture p_c<p_u for non-amenable Cayley graphs — FULL CLAIM
#369 Dixmier unitarisability problem for discrete groups — FULL CLAIM
#374 Fujita Freeness Conjecture — FULL CLAIM
#375 Nagata Conjecture on Plane Curve Linear Systems — FULL CLAIM
#378 Toms–Winter: Strict Comparison Implies Z-Stability — FULL CLAIM
#379 Margulis–Platonov normal-subgroup conjecture — FULL CLAIM
#388 Shelah's Categoricity Conjecture for L_omega1,omega — PARTIAL
#392 Measure-zero singular set of stationary integral varifolds — FULL CLAIM
#401 Serres Positivity Conjecture for Intersection Multiplicities over Regular Local Rings — FULL CLAIM
#403 Rokhlin problem on multiple mixing — FULL CLAIM
#419 Lück's Determinant Conjecture for Discrete Groups — FULL CLAIM
#420 Absolute continuity of Bernoulli convolutions outside reciprocal Pisot parameters — FULL CLAIM
#421 GNRS Conjecture — PARTIAL
#424 Irrationality of Catalan's Constant — FULL CLAIM
#425 Separable Quotient Problem for Banach Spaces — FULL CLAIM
#430 Long-Time Existence of the Calabi Flow on Compact Kaehler Manifolds — FULL CLAIM
#432 Combinatorial Invariance of Kazhdan-Lusztig Polynomials — FULL CLAIM
#434 Realizable Limit Shapes in Two-Dimensional First-Passage Percolation — PARTIAL
#438 Zariski Cancellation Problem (characteristic zero, dimension ≥ 3) — FULL CLAIM
#440 Stein's Conjecture on the Hilbert Transform along Lipschitz Vector Fields — FULL CLAIM
#448 Smooth Realization of Finite-Entropy Ergodic Transformations — FULL CLAIM
#450 Deligne–Drinfeld Freeness Conjecture for grt_1 — FULL CLAIM
#453 Shub entropy conjecture — FULL CLAIM
#456 Maximal Number of Mutually Unbiased Bases in Composite Dimensions — PARTIAL
#458 LeBrun-Salamon Conjecture: positive quaternion-Kahler manifolds are symmetric spaces — FULL CLAIM
#461 Kaplansky's Direct Finiteness Conjecture — FULL CLAIM
#465 David–Semmes Riesz-transform problem in intermediate dimensions — FULL CLAIM
#467 Small Cohen-Macaulay Conjecture — FULL CLAIM
#468 Ergodicity of Irrational Triangular Billiards — FULL CLAIM
#472 CAT(0) Conjecture for All Artin Groups — FULL CLAIM
#475 Katok entropy rigidity conjecture — FULL CLAIM
#476 Polynomial-Time Solvability of Condon's Simple Stochastic Games — PARTIAL
#480 Furstenberg No-Bigeodesics (Planar FPP, Standard Minimum Moment) — FULL CLAIM
#483 Gaboriau's Fixed Price Problem for Countable Groups — FULL CLAIM
#484 Persistence Conjecture for Weakly Reversible Mass-Action Systems — FULL CLAIM
#486 Campana-Peternell Conjecture — PARTIAL
#497 Maximum Number of k-sets and Complexity of k-levels — PARTIAL

[Fabien @Fabien_Mikol]

➡️ @StanDehaene évoque les différents travaux qui ont mis en valeur des éléments pointant vers une forme de conscience dans les LLM : "ces machines ne sont pas très différentes de nous et c'est fascinant, même si au départ elles n'ont pas la même architecture".
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[Haider. @haider1]

intelligence explosion

arXiv hit a record 40,363 submissions in september, nearly double what it received two years ago, and now it's limiting submitters to 2 papers a month because moderators can't keep up

science is about to look very different

[Annie Jacobsen @AnnieJacobsen]

🚨Breaking. There's been a pneumonic plague outbreak at a BSL-3 lab in Siberia, Russia.🚨

"Nearly 200 People Under Observation After Irkutsk Lab Worker Dies From Plague" - Moscow Times

This is fact, and also the inciting incident in my book BIOLOGICAL WAR: A SCENARIO, which is unnerving.

Will post more as I learn more, including from Russian speaking sources🧵
https://t.co/zd4u0iVhHK

[AI Notkilleveryoneism Memes ⏸️ @AISafetyMemes]

This is not good.

It appears OpenAI just purged 3 AI safety whistleblowers.

Hours later, a key OpenAI Safety Systems leader quit. (The previous leader quit just 3 months ago.)

3 weeks ago, all 3 publicly tweeted how concerned they were about AI.

OpenAI claims they shared unauthorized info with an independent AI safety org... which certainly sounds like they were whistleblowing, and OpenAI, like most corporations, didn't like that.

This is a reminder of why we badly need governments to step in and provide whistleblower protection.

Reminder to AI company workers: you will soon be replaced by the AIs you're building, then you will have no power. If you're going to quit, the time is NOW - and when you do, do it loudly, and be blunt.

[orph @orphcorp]

please stop saying that airplanes can "fly". they are only exploiting aerodynamic regularities to produce flight-like behavior

[ARC Prize @arcprize]

GPT-6.1 Sol from @OpenAI on ARC-AGI (Verified):

- ARC-AGI-3: 52.7%, $7.6K (standard harness), 96.4%, $4.4K (provider adapter harness)
- ARC-AGI-2: 94.2%, $0.25/task
- ARC-AGI-1: 98.5%, $0.06/task

Its 96.4% on v3 was comparable to GPT-6 Astra's 99.9% but at a 77% lower cost.

[Andrew Curran @AndrewCurran_]

When I posted this in March, many people pointed out that it did not include the labor impact of robotic systems combined with language models. Anthropic updated the chart in a report released this morning.

[Demis Hassabis @demishassabis]

Biosecurity is one of the most urgent challenges for the AI era. Bringing SynthID to biology so AI-generated proteins can be watermarked is a critical step - and we’re open sourcing SynthID Bio tools so the research community can build on this work. Published in @Nature today, congrats to the team! https://t.co/Y4sv8bnGQY

[Sundar Pichai @sundarpichai]

Lots of discussion out there about our next model(!), so I wanted to give an early look as soon as possible. Introducing Gemini 4 Argon!

It shows frontier performance in complex workflows, cyber defense and software engineering. Teams are using it extensively at Google, from coding to quantum computing, great feedback.

Here’s a look at the benchmarks:

[sdmat @sdmat123]

I'm convinced Anthropic made some kind of technical breakthrough for diversity and creativity with Opus 5.5. It's far ahead of the competition and previous Anthropic models.

Left: Opus max, Right: Sol 6.1 max

[Bill Gates @BillGates]

I appreciated the opportunity to speak with @ezraklein at length about the state of AI. I believe the world isn't awake to the dangers of this technology and the choices humanity has to make. AI will either be the greatest tool for opportunity and equality we've ever seen—or the cause of immense, unprecedented harm. Which way things go is up to us. https://t.co/ZW69yCnW2L

[josh :) @jfonsecarivera]

you're not crazy

between anthropic and openai, a new model used to come out every ~10 weeks

now it's every ~11 days