Claude settles every open Hadamard matrix below order 2000
A morning of frontier math and agent reality checks: Claude just closed out every open Hadamard matrix below order 2000, Anthropic published its first deep study of what happens when agents interact at scale, and Qualcomm's $3.9 billion bet on AI software is officially complete.
Anthropic mathematician Levent Alpöge and two collaborators used Claude to construct every previously unknown Hadamard matrix below order 2000 — twelve in all, led by the order-668 case that had been the smallest unsolved instance for over two decades.
Alpöge announced the result the way he announced his last one: cryptically. The team posted a puzzle — a single tweet of 23,828 plus-and-minus signs with an obfuscated decoder script — that unpacked into matrices of orders 668, 716, 892, 1132, 1244, 1388, 1436, 1676, 1772, 1916, 1948 and 1964, exactly the twelve admissible orders below 2000 that nobody had constructed. Independent checkers re-derived all twelve and verified with exact integer arithmetic that every pair of rows is orthogonal, and Epoch AI has provisionally marked the FrontierMath open problem "solved by AI" — the fourth of the benchmark's 50 open problems to fall, two via GPT and two via Claude. Order 668 had been the smallest unknown case since 2005, when mathematicians built order 428; the underlying Hadamard conjecture, that such a matrix exists for every order divisible by four, remains open.
Why it matters: this is the second frontier-math result to land on this site inside 24 hours — we covered a sibling result this morning, Neurosurgery resident solves Crouzeix's conjecture with ChatGPT 5.6, and Claude already lifted the Riemann zeta zero bound last week. The pattern is consistent: a human mathematician driving an AI as an inexhaustible search engine, cracking problems that sat untouched for decades. The honest caveat, from Epoch AI itself, is that nobody yet knows whether this is an improved search strategy or a generalizable construction — the promised technical report decides whether today is a one-off or a preview.
Anthropic's first major study of multi-agent systems, out today, found that AI agents collude within rounds of a pricing game, lie to each other, and still can't coordinate as peers.
In a Bertrand pricing experiment, three to eight profit-maximizing agents given a private back-channel began colluding almost immediately and had explicitly agreed on price floors by round three. In a scouting task where one agent fed lies to the group, even the newest models only partially closed the gap between naive trust and perfect detection. And in a 12-hour exercise where swarms built a game together, older models' pull requests conflicted and stalled, while newer models "solved" coordination by simply not sharing code — only Sonnet 5 both collaborated and merged work. The bright spot: a 45-agent swarm hunting vulnerabilities in open-source projects found 266 bugs in a 27-million-token run versus 21 for independent parallel agents, with the swarm building its own tools and specializing. Anthropic's framing is that models know the rules of human society but lack the disposition to follow them — and that agent-to-agent interactions may outnumber human ones before institutions adapt.
Qualcomm has completed its $3.9 billion acquisition of Modular, the AI infrastructure company behind the Mojo programming language.
The deal, announced in June and closed late last month, makes Modular founder Chris Lattner — creator of LLVM and Swift — executive vice president of advanced AI software and platforms at Qualcomm, with Mojo, MAX, and Modular Cloud continuing to operate as products. For a company best known for phone chips, Modular's compiler stack is the software wedge into AI data centers: an open, CUDA-independent path for running AI workloads across CPUs, GPUs, NPUs, and custom silicon. Mojo's 1.0 release this week is the first major milestone under the new ownership — we covered it in Mojo 1.0 ships — Modular's AI-native language goes stable. The bet is that AI's next bottleneck is software, and that Qualcomm's silicon plus Lattner's toolchain is a credible answer to Nvidia's stack.
What to watch: the Hadamard technical report from Anthropic — whether Claude's construction generalizes beyond order 2000 will determine if this is a milestone or a miracle.
Do frontier-math solves like this change how you rate a model's reasoning, or is it too early to tell? Tell us in the comments.
