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

I really recommend you savor the renaissance-flavored part of this transformation. Even if you’re not a mathematician, try to sit with one or two of these results and understand them conceptually. It is a beautiful day.

Jacob Coxon says Anthropic employees call themselves “ants” and sacrifice their careers for the company’s singular pursuit of superintelligence, while calling OpenAI "distracted and messy" “At Anthropic, it felt a lot more like—well, for starters, the employees call themselves ants. They’re ants in the anthill. Everyone is like a worker ant trying to make Anthropic’s mission go well. “People are very willing to sacrifice themselves for the good of the mission. They’ll take on work that’s less interesting, less big, bold and exciting, and less flashy. They’ll do it at a hit to their own interests for the good of the company. “That’s because every decision comes back down to, ‘Is this going to get us to superintelligence faster?’ “You’ve seen Sora, the video platform OpenAI made. Anthropic would never make Sora because it’s not on the core path to artificial superintelligence. OpenAI is distracted and messy. One guy says, ‘I want to do Sora,’ or, ‘I want to build a little device,’ and they let them do it because it doesn’t have the same focus. At Anthropic, that would never happen.” Patrick Bet-David: “Who would shut it down? The seven co-founders?” Jacob Coxon: “They’d all agree. It would be like, ‘This video isn’t the right direction for heading straight to superintelligence.’”

In this interview I tried to argue that a post-scarcity society will benefit working people. It was largely a rhetorical failure. People don’t trust that the benefits will be distributed, and tech optimists have to fix this communications issue.

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

New post: alignment.openai.com/metagam…

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

Universal HIGH INCOME via checks issued by the Federal government is the best way to deal with unemployment caused by AI. AI/robotics will produce goods & services far in excess of the increase in the money supply, so there will not be inflation.

“We believe the world should accept some bad things happening for the benefits of this technology.” In a conversation for the first edition of Decoded, a new daily newsletter and podcast, OpenAI CEO Sam Altman talked with POLITICO’s @BrendanBordelon about trade-offs, AI safety, and how his company is different from Anthropic. Subscribe to Decoded for the full conversation with Sam Altman: politi.co/4yxilIS

“We believe the world should accept some bad things happening for the benefits of this technology.” In a conversation for the first edition of Decoded, a new daily newsletter and podcast, OpenAI CEO Sam Altman talked with POLITICO’s @BrendanBordelon about trade-offs, AI safety, and how his company is different from Anthropic. Subscribe to Decoded for the full conversation with Sam Altman: politi.co/4yxilIS