An unreleased Anthropic model helped push two textbook computing problems slightly below speed limits that had stood for decades. A preprint dated October 5, 2026, by Josh Alman and Virginia Vassilevska Williams, reports "truly subquadratic" time for a problem called 3SUM and "truly subcubic" time for finding all shortest paths in a weighted network. The authors credit an internal Claude model with the seed algorithm.
The result came up on Moonshots with Peter Diamandis, recorded October 6 and published October 7. In the discussion it was used as evidence for a claim the panel kept returning to: the best AI is being kept inside the labs, and open models will struggle to catch up.
What the paper found
3SUM is a simple question. Alexander Wissner-Gross, a computer scientist and founder of Reified, explained it on the show: given a set of numbers, what is the most efficient way to find three that add up to zero, and how does the work grow as the set grows? The obvious methods take roughly n² steps for n numbers, which is called quadratic time. All-pairs shortest paths (APSP), which finds the shortest route between every pair of points in a network, has a similar barrier at roughly n³, or cubic time.
According to the preprint, the new deterministic algorithms run in O(n^1.9992) time for 3SUM on integers of polynomial size, and O(n^2.9995) for APSP on directed graphs with polynomially bounded integer weights. "Truly" subquadratic means the exponent sits a fixed amount below 2, not merely that smaller factors were trimmed. The gain is tiny: 0.0008 in the 3SUM exponent. Its importance is theoretical. Researchers in fine-grained complexity, the study of exactly how fast specific problems can be solved, use hypotheses about problems like 3SUM and APSP to argue that many other problems cannot be sped up. The paper's improvements concern particular versions of those hypotheses. Its authors list stronger or practical improvements, and balanced cases of the underlying triangle problem, as further work.
The central technique computes selected entries of thin matrix products. It reaches 3SUM and APSP by recasting them as problems of finding triangles in sparse, lopsided graphs, where the groups being connected differ greatly in size.
The paper also says who did what. An internal Claude model produced a seed algorithm during a long session of about 16 million output tokens, the units of text a model generates. The human authors then changed the reductions, derived further results and wrote the paper. A model-assisted formalization in Lean, a proof assistant that checks each logical step mechanically, certified the main results.
How it was told on the show
Diamandis, the host and founder of XPRIZE, asked whether open-source models were also being built a couple of generations ahead. The answer in the discussion was that it was difficult because open models lack the "density of knowledge" of the labs' systems, and it pointed to a fresh discovery of "truly sub-quadratic" 3SUM and shortest-path algorithms. Diamandis called it "math porn."
The discussion then described an internal Anthropic model being shown to a couple of professors from Columbia and MIT, who adjusted and analyzed it and got it to 1.9995. The paper's 3SUM exponent is 1.9992; 2.9995 is its figure for shortest paths. The account of the division of labor, a model pointed at a set of complexity problems and humans writing up the results, broadly fits the paper's split between a model-generated seed and human follow-up work. The discussion also held that humanity had never managed to break quadratic time on this problem, or even thought it possible.
Wissner-Gross linked the moment to science fiction. He cited Charles Stross's short story "Antibodies," whose premise, he said, is that AI or progress causes a collapse of the complexity hierarchy. In 3SUM, he suggested, you might hear that hierarchy start to creep a little.
The conversation also touched on a report that OpenAI might release solutions to 400 top math problems. Dave Blundin, founder and general partner of Link Ventures, said he had seen it too. No source was given on the show, so it remains an unverified rumor.
"They're all just marketing"
The 3SUM news landed in the middle of an argument about where labs' best models go. Diamandis opened it by relaying remarks he attributed to Boris Power, OpenAI's head of applied research, at a Fellows Forum at the end of September. He said Power described 80 to 90 percent of the company's research as aimed at training GPT-7 and GPT-8, because "that's where the most value will be," with incremental updates such as 5.1 and 5.2 seen as short-term and "extremely short-sighted" bets. Those figures come only from Diamandis's account.
Diamandis asked when the next models would stop being released and be used for vertical applications inside the labs. "We're already past that point," Wissner-Gross said, probably by several months. In his view, the most valuable use of a frontier lab's tokens, at least on a future discounted basis, is recursive self-improvement: using today's models to build stronger ones. Other uses, such as curing the top 5,000 diseases, are in that world "all just marketing." A lab like Anthropic or the OpenAI Foundation, he said, might spend 10 to 20 percent of its token budget on alignment and a few percent on curing disease, to keep the social permission to focus on self-improvement.
Blundin carried the idea into drug development. He asked listeners to imagine being the CEO of Moderna with no AI team, planning to license models from Anthropic for a few years. Anthropic, he said, has already opened wet labs, where biological experiments are physically run. "They're never going to release those to you," he said of models two generations ahead. "They're going to use those to develop drugs, and then they're going to sell drugs." CEOs, he added, are only starting to realize that "five years of compute has been reserved," and companies would need to get aggressive within months to have any chance of getting back on the map.
Salim Ismail, founder of Open ExO, said most executives are further behind than that. They are still working out how to absorb today's models, he said, without seeing that models "10x better" may arrive in three months. "They're literally looking at how do I employ chatbots."
Wissner-Gross described "an enormous amount of denial in the pharma industry." On a recent panel, he said, a major pharma venture capitalist asked the audience how many would take a drug designed by Claude, as if that were a steel-man argument for business as usual. Blundin compared talking to pharma or insurance companies to telling a T. rex that has roamed unchallenged for 10 million years that a meteor will end it in two weeks.
Open models "can only get you so far"
The discussion described the open side's limits concretely. A harness, the software loop that lets a model work through tasks, called Zenith was said to lift the open model DeepSeek V4.1 to what was called "Astra levels," but "it kind of hits a limit."
The 3SUM result, the discussion held, did not come from a model the public can use. Small models with coordination tricks and new harnesses were said to have replicated some closed findings, but "there is a big difference between a model that's trained on 2,000 chips and one that's trained on a hundred thousand chips internally," along with techniques the labs have worked out privately. The paper documents what one unreleased model contributed; it does not compare that model with public or open ones.
Another example was a game. Using a current frontier model, a complete video game was generated end to end, with 21 bosses and 15 biomes, and QA tester agents judged it a really good game. The argument drawn from it was that open models can only get you so far, and that there is going to be a divergence because they lack that internal knowledge organization.