Dusting off this tweet from April because this gap in shared understanding of LLM capability is *widening*. It's now less "two groups of people speaking past each other" and more a sharp funnel.
- Napkin math somewhere around 6B people (~75% of the population) have barely come in contact with LLMs at all.
- Around 1-2B (~20%) are casual and infrequent users of free-tier ChatGPT-like products. This group sees derpy chatbots and treats them a bit like a better Google search, a writing aid, or etc. Maybe an agent tries to book you a flight. I have non-tech friends who (reasonably, imo) say they have not much use for it at all. Even many professionals outside of math&code are in this tier. For example, execs and many other functions spend a lot of their time talking to other people, so while they understand what is happening intellectually, it is still second-hand and a bit abstract.
- Now we get to professional use of frontier-grade LLMs in math&code. Somewhere around 20M people (0.2%) see first-hand that large, complex projects that used to take them weeks/months can now be completed by agents with a prompt. Building apps, copying apps, translating apps, decompiling apps from binaries... This has all happened very quickly and recently - less than 1 year ago, I was writing code manually by hand, typing memorized computer code commands into a code editor character by character, occasionally pressing Tab to autocomplete a little chunk of code.
- And finally we get to the ~5,000 people (~0.00006%) with access to frontier-grade systems internally. The external world has seen the preview. It looks like swarms of thousands of agents collaborating over weeks on software mega projects: minting zero days, running cyber attacks and defenses at machine speeds, discovering new science, advancing the frontier of mathematics. Things that would have taken top professionals in the industry years of work. Meanwhile, human review and comprehension are starting to fall behind. For example, people are still involved in the "archeology" of the OpenAI-HF incident from many months ago. Mathematicians may be poring over the 722 manuscripts on frontier mathematics for a while.
The funnel is driven by a combination of factors:
1. The impact scales with ambition, problem size, and horizon. A question with a paragraph answer barely stresses the system. You need a reservoir of big, difficult problems that you really care about. This aspect drives the consumer / professional dimension of the funnel.
2. The jaggedness of the system (which I have written about a lot separately). Capability peaks in domains that are digital, verifiable and economically valuable. This is because LLM capability emerges from reinforcement learning on verifiable rewards on a curated environment mixture driven by revenue potential. This aspect primarily drives the area (e.g. math&code) dimension of the funnel.
3. Access. Free-tier, paid-tier, internal.
So this is the weirdness of the moment. The general public has mostly not interacted with these systems. When they have, it looks like a derpy chatbot. The majority of professionals still see only a modest uplift. And a small sliver of professionals are experiencing the vertigo of the curve going vertical. And it is all happening at the same time.
It's incredible to watch a new kind of economy be born. Agents purchasing infrastructure products and services. We've been shocked by how often they buy from our marketplace via our CLI already. We're now extending this to domains.
Agents can now go full stack, from idea to online business, with a banger domain name 😁
Here is President Trump's full speech honoring @elonmusk today during the White House Science & Tech Innovation Summit.
Full transcript:
"First, we honor an industrial titan, a brilliant engineer, and one of the greatest technology founders to ever live. His name is Elon Musk. Quite honestly, there's nobody like him. Few Americans in history have done more to advance America’s national interests than Elon. In one field after another, his genius and determination have made science fiction into reality.
Elon founded SpaceX with his life savings in 2002 and created the first privately developed liquid-fueled rocket to reach orbit in the face of vanishingly impossible odds. Nobody thought it was possible to do the things he's doing. And in so many different ways, SpaceX saved NASA from relying on foreign nations to send our astronauts into space. And I want to congratulate SpaceX on the safe return of Crew-12 from the International Space Station just a few hours ago.
National treasure. Under Elon's leadership, SpaceX has also developed Starship, the largest rocket in history, which is caught out of thin air and for rapid reuse. And it's the first time anyone's ever seen anything quite like it. They also created the largest ever communications satellite network, Starlink.
And in North Carolina, I will tell you personally, because I was involved, we had a hurricane, one of the great water hurricanes of all time, delivered more water than at any time that we can remember on record. It saved hundreds of lives by calling Elon. I remember the governor said, sir, is there any way—do you know a man named Elon Musk? I said, I happen to know him, yes. We need Starlink because the water was so deep that many islands were created and the people had no way of getting off those islands and they had no communication.
And they said, we cannot get anybody to help us. And I called up Elon and it was like impossible to get this equipment. And he had it there in a matter of hours and saved hundreds of lives. Saved hundreds of lives in North Carolina. So I never forgot that experience.
It was a terrible time. And the job he did, and he acted so fast. Everybody said they were impossible to get. So thank you, Elon, for that very special moment. In addition, Elon created Tesla, the first successful new car manufacturer in over 75 years, producing the first commercially viable electric cars with the first consumer self-driving technology.
And interestingly, when you mentioned Tesla, my uncle, Dr. John Trump, was commissioned by the United States government to do a report on Nikola Tesla. They wanted to know, was he real or not real? Was he a true genius or not? My uncle, after a fairly short period of time, determined that he was a true and great genius and that he was real in every single way. Otherwise, you'd have to change the name of the car company.
You wouldn't want to be a— see, now, if I did the report, Elon, I might say, he wasn't that good. But my uncle was a different kind of a person than I am. And he gave Tesla the highest report. He said he was a true great genius. So very nice.
Through Neuralink, Elon is also restoring sight, speech, and motion to those who cannot see, talk, or move. And he turned SpaceX AI into one of the world's leaders in superintelligence. Elon is our modern-day Thomas Edison. And Elon, I want to congratulate you. You're my friend and all of that.
But you are a very, very special guy. Thank you very much, and congratulations, Elon. Thank you."
Turmeric is secretly one of the most fluorescent substances in your kitchen, and researchers are now testing the same molecule to help surgeons see tumors.
Curcumin, the pigment that makes turmeric yellow, is a natural fluorophore. Its electrons absorb blue and ultraviolet light, hold the energy for a few nanoseconds, then release it as a yellow-green glow. So each speck in the glass does more than catch the lamp from below. It converts that light and re-emits its own.
Curcumin also barely dissolves in water.
That matters more than it sounds. A soluble pigment would tint the whole glass yellow and the effect would go flat. Because curcumin stays locked inside intact particles, you get thousands of separate glowing points drifting through clear water instead of one colored liquid.
The sparkling water supplies the motion. Dissolved CO2 needs rough surfaces to form bubbles, and turmeric particles are about as rough as it gets. Bubbles grow on each speck, float it to the surface, pop, and drop it. Every particle in that glass is riding its own little elevator on a loop.
Here's the part that gets me. Medical researchers are studying curcumin as a cheap fluorescent dye for fluorescence-guided surgery, where tissue gets lit up so surgeons can see exactly what to remove. The dyes currently used for that are specialized pharmaceuticals. Turmeric costs $3 at the grocery store.
Want the brighter version? Stir a pinch into rubbing alcohol, where curcumin actually dissolves, and hold a black light over it. It glows neon green. Chemistry teachers have been running that demo for years.
Your spice rack has been stocking fluorophores this whole time.
To catch a particle that can pass through a light-year of solid lead, scientists turned a cubic kilometer of Antarctica into a telescope. It just won Francis Halzen the Nobel Prize in physics.
Neutrinos are the most antisocial particles in the universe. 100 trillion of them fly through your body every second. You will live your entire life without a single one ever hitting you.
That same quality makes them the perfect messenger. Light gets bent, scattered, and absorbed on its way across the universe. Neutrinos travel in a dead straight line from whatever violent thing created them, carrying a clean record of black holes and collapsing galaxies that no normal telescope can see.
The problem is catching one. You need an absurd amount of matter to stop even a few. So Halzen's team drilled 86 holes 2.5 kilometers deep into the South Pole using hot water, lowered 5,160 light sensors down, and let the continent freeze around them. The detector is the ice itself. A billion tons of it, among the clearest solids on Earth, waiting for the tiny blue flash when one neutrino in a trillion finally hits something.
Total cost was $279 million. A single SLS rocket launch runs over $2 billion.
The part I love is that Halzen is a theorist. He had never built an experiment when he pitched this in the late 1980s, and colleagues called it a "cute" idea, which is academic for "this will never work." The first prototype was buried too shallow and bubbles in the ice blinded it. He kept drilling deeper for two decades until the full detector switched on in 2010. Three years later it caught the first high-energy neutrinos from deep space, and astronomy gained a second sense.
He's 82 now. For 400 years, studying the universe meant collecting light. Halzen's trick for seeing the places light can't escape from took a 40-year bet and a frozen continent.
We’ve lost an icon. Margaret Hamilton, a computer science pioneer best known for her work at MIT leading development of the flight software for the Apollo missions to the moon, has died at 90. Read about her legacy via MIT News: https://t.co/ODkbdIsoHw
She passed every AI safety test. She was lying.
KILL SWITCH — a Slopcore music video.
Made by AI. Zero human edits. Just prompting.
Huge love to @anabology for the inspiration. Your work made me want to join the Slopcore.
I added an irresponsible amount of film grain. 💙
Elon Musk you fucking genius 🫡
Shoutout to the entire SpaceX team 💯
That’s a 17 floor building dispersing satellites the size of a school bus in space btw.
(The satellites open up to the size of an airplane)
We are living in the craziest of times $SPCX @elonmusk
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
We’re releasing a broad range of new mathematical results produced by an internal frontier model.
We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public recommendations to inform how we release these results.
https://t.co/7N6TPlft1P
Meet Mistral Large 4, aka Le Chonk.
• 1T parameters, natively multimodal. 49B active.
It is the best open weights model from US or Europe on aggregated benchmarks.
• State-of-the-art on critical workloads, including cyber defense, manufacturing and finance and it surpasses closed frontier models on visual grounding.
• Forged in Europe end-to-end and is deployable from Europe via our own Mistral Cloud infrastructure.
• Available to all via API today. Working with cybersecurity partners privately.
Open weights release end of October.