Quick Takes

At France's initiative, the Security Council has for the first time treated loss of control over AI as a matter of international peace and security. France called for frontier AI to be governed the way the world governed nuclear technology after 1945, with independent model evaluation, oversight, and legal liability for companies. https://cesia.org/en/publications/france-un-security-council-ai-loss-of-control/

OpenAI releases solutions to many open problems in mathematics. They provide both lean proofs and preprints in a git repo. We knew they were working on this, now it has been released. Some results that I thought were interesting include (numbers from this document): #4: Hilbert's 10th problem was resolved negatively 1970. It asks if there is an algorithm to determine whether a multi-variable polynomial with integer coefficients has an integer root. This is a generalization of that result to rational roots: It shows that no algorithm that can decide whether a polynomial with integer coefficients has a rational root. #5: Catalan's constant is irrational. #17: The irrationality exponent of is 2 (same as most other real numbers). #25: Every rational can be written as an Egyptian fraction of length . #28: The Gaussian moat conjecture is true. Here is what it says: Pretend the Gaussian primes are islands and the rest of is ocean. Suppose we can kayak a distance before we need to stop and rest at an island. Then there is no value of large enough to allow us to make a journey from the origin to infinity. #102: The Unique Games Conjecture is true. #103: L = RL = BPL, i.e. probabilistic algorithms with logarithmic space complexity can be de-randomized to deterministic algorithms with logarithmic space complexity. #107: Matrix multiplication in time. #109: Integer multiplication (slightly) faster than . #130: Fourier transforms (slightly) faster than . As measured by the number of arithmetic operations. #137: One-tape Turing machines that run in time can be simulated in space. #155: There is a tile that forces aperiodic tiling of and under the rule that we're not allowed to rotate the tiles. #158: The chromatic number of (the unit distance graph of) the plane is greater than 5. #241: "Rigidity of Turing Degrees": No non-trivial relabelling of Turing degrees preserves their order. #261: Characterize spectrum of lattice Anderson model in dimension 2 vs 3 or more

I asked Astra to check out OpenAI's math repo containing the 722 preprints of results (from ~4,000 problems attempted) obtained using their internal model at “three hours of ChatGPT Pro thinking compute” each. These preprints are organised into 372 families, i.e. “related papers, which may include a principal result, companion arguments, consequences, or alternative proofs”. Astra thinks/claims there are ~30 (range 20–50) potential Fields medal-scale portfolios' worth of results (“I would defend “several dozen” more readily than either endpoint”), including partial results or related work on every Millennium Prize problem except Yang-Mills Millennium Prize problem Match in this release Riemann hypothesis Partial: fixed zero-free strip Birch–Swinnerton-Dyer Partial: full formula for the stated low-Selmer-corank class; further density-one consequences with Goldfeld Hodge conjecture Partial: CM abelian varieties, K3 products and related results Navier–Stokes Related work here; the earlier forced-breakdown release is separate P versus NP Related complexity breakthroughs, no resolution Yang–Mills existence and mass gap No matching resolution identified The workbook constructs 28 illustrative portfolios using 234 distinct families, without assigning any family twice. This makes the comparison inspectable. It does not eliminate common proof dependencies, and some groupings are deliberately broad. A few could plausibly split into multiple portfolios; others may look less substantial once novelty and methods receive expert scrutiny. This is not a measured median Fields Medal equivalent. There is no established scalar ordering of those 30 historical portfolios from which to calculate such a median. The estimate concerns the possible scale of mathematical outcomes. Lasting influence, reusable ideas, exposition, and the work of collaborators remain separate considerations. The strongest concrete repo comparisons include: Repo cluster Historical reference Wh

Help The Unjournal prioritize AI economics and governance research The Unjournal is prioritizing research on AI economics, governance, social and economic impacts, and risks from increasingly capable AI. (NB: We're not covering technical/CS/ML/AI-safety research.). We want to commission expert public evaluations and help synthesize, disseminate, and curate this work. Much of this research seems 1) important/impactful/influential, (2) involves considerable 'firepower' from prominent researchers and practitioners, (3) not 'obviously true', and (4) time-sensitive: relevant for funding, policy, and research-steering now, but not after the "six months to six years" required for the traditional (economics) journal process Our preliminary shortlist page includes paper summaries, AI-generated audio walkthroughs, and an interface for giving feedback. We also invite suggestions fr other research (please check the broader list/interface to avoid duplication). Especially looking for your input on: * Usefulness and accuracy: Is this useful? How could we improve it? What have we got wrong? * Impact: Which research do you use, or think others use or should use? * Scrutiny: What claims and approaches need careful experts and practitioners critique? What sorts of experts? If you're that expert, please dm and join our pool. * Participation: Who should be part of this discussion (nominate and nudge)? * Gaps: What's missing (research, claims, etc.)? Timing and next steps (our plan) * Finalize an initial shortlist of at least three research outputs before the end of October, with more depending on interest and funding. * Commission rapid, public, impact-focused evaluations/reviews by experts and practitioners, aiming for a first public evaluation within about two weeks of commissioning. * Over the following two to four weeks, invite author and stakeholder responses and follow-ups, and facilitate private and public discussion If it this works well, we hope to scale up a

I was recently subpoenaed by the New York City Council. Here is my opening statement, which includes several new facts about why I left Google DeepMind: [...]

I was pleasantly surprised to see the the Berkeley AI Safety community explicitly mentioned by US Representative Ro Khanna when discussing the creation of a US AI Safety Agency during an interview on Breaking Points. "there are plenty of really, really smart people in AI safety who don't make profits. They're all in this one building at Berkeley. They're the AI safety community. Start to appoint them into an independent agency that can regulate these folks."

Incredibly crude alignment technique. Rot13 all text and training data, except for a small corpus of unusually good data.