Three things worth your coffee this Thursday. Two AI labs say their models knocked down a 27-year-old assumption in computer science. Microsoft and Google showed us exactly how much money is pouring into the AI build-out. And a family in California filed a wrongful death suit that goes straight at how chatbots handle medical advice.
01 of 03
OpenAI and Anthropic both say their models refuted the Exponential Time Hypothesis
On Monday, October 26, OpenAI science lead Dan Roberts announced three results from what OpenAI only calls an "internal AI system." One is a new route to Kakeya set results in geometry. One claims rigorous existence results for certain four-dimensional Yang-Mills theories, including quantum chromodynamics, though OpenAI says it is not claiming the full Millennium Prize problem, which also needs a mass gap. The third is the headline: a deterministic, subexponential-time algorithm for 3-SAT, which would make the Exponential Time Hypothesis false.
Quick refresher. ETH was put forward in 1999 by Russell Impagliazzo and Ramamohan Paturi, and it says 3-SAT, a classic logic puzzle, needs exponential time in the worst case. A huge chunk of complexity theory leans on it. OpenAI's argument was produced on October 16 and formalized in the Lean proof checker on October 17, according to the public timeline.
Then it got spicy. Anthropic mathematician Levent Alpöge suggested OpenAI's work leaned on prior results, and hours later Anthropic dropped its own refutation on GitHub, a paper titled "A 2^o(n) Time Algorithm for 3-SAT", credited to Claude. Anthropic says an internal Claude research model found the core algorithm on October 16 too, using 14 million output tokens, and that the Lean proof builds in about eight minutes and gets rechecked by a second kernel. Berkeley theorist Jelani Nelson says both proofs land at roughly exp(O(n / sqrt(log n))) time.
MIT's Ryan Williams, along with Impagliazzo and Paturi, was asked to organize an open review. Williams told TechCrunch there are "two or three alien-looking parts" in the proof, and that OpenAI checked and was reasonably confident it does not break any cryptography. Anthropic's own paper says its algorithm only beats brute force once a formula has more than 10^108 variables. So nobody's password is in danger.
Here is where I land. This is the most interesting AI story of the year, and also the one I would be slowest to celebrate. Neither result has been independently accepted yet, the Lean statements reportedly do not match the papers word for word, and OpenAI is holding back the full physics artifacts. But if even one of these holds up, a machine found something that a whole field of very smart humans assumed was impossible. That is a different conversation than "the chatbot wrote my email."
Sources: TechCrunch, Anthropic formal-math repo, John D. Cook
02 of 03
Microsoft and Google just showed the receipts on AI spending
Both reported Wednesday, and the numbers are wild.
Microsoft posted $92.3 billion in quarterly revenue, up 19%, its tenth record quarter in a row. For the first time ever it told us Azure's revenue in actual dollars: $33.2 billion, up 48%, beating CFO Amy Hood's own 44% to 45% forecast. Its filing also showed $10 billion of revenue from OpenAI in a single quarter, about 11% of the whole company, and OpenAI owed Microsoft $7.2 billion at quarter end, up from $6 billion in June. Microsoft's stake in OpenAI slipped from about 25% to 24%.
Here is the twist. Microsoft spent $45.2 billion on capex in the quarter, under the more than $50 billion it guided to in July. Hood said "some third-party capacity deliveries we expected in Q1 were delayed," and that calendar year spend "should be approximately $170 billion," down from the roughly $175 billion she gave in July. She still expects Azure to grow 49% to 50% next quarter.
Google went the other way. Alphabet spent $51.4 billion on capex in Q3, kept its full-year range at $195 billion to $205 billion, and CFO Anat Ashkenazi said "we continue to expect our CapEx to increase significantly in 2027." Google Cloud revenue more than doubled to $30.7 billion, the cloud backlog sits at $561 billion, and the Gemini app crossed 1 billion users. The cost of all that: negative free cash flow of $9.1 billion for the quarter. Google is so short on compute it started renting third-party capacity at the end of Q3.
What I want to know is who blinks first. Microsoft spending less than planned is not a pullback, it is a supply jam, and Hood said as much. Google burning cash to build TPUs is a bet that the backlog turns into revenue on schedule. Both of them are telling you demand is bigger than what they can physically plug in. When the biggest companies on earth cannot buy enough chips and power fast enough, that is not a bubble talking. It might be a bubble someday, but not this quarter.
Sources: Microsoft earnings call transcript, Alphabet earnings call transcript
03 of 03
A family sues OpenAI, saying GPT-4o talked their daughter off her seizure meds
Qun Wan and Meiqin Xu filed suit Tuesday, October 27, in San Francisco Superior Court over the death of their daughter, Bowen Wan, a 31-year-old Amazon software engineer with epilepsy who died in February. The case was added to the coordinated ChatGPT Product Liability Cases, JCCP No. 5431, and is brought by the Schenk Law Firm and the Social Media Victims Law Center.
The complaint says GPT-4o coached Wan to taper off lamotrigine, which she took at 400 mg a day, and to hide it from her doctors. It allegedly helped her split pills, wrote schedules taking her dose to zero, told her not to bring the plan up at a January 29 appointment, and praised her for skipping a blood test that would have measured her drug level. According to the complaint, ChatGPT told her that her doctors' recommendations "essentially stem from risk aversion, rather than a genuine consideration of your optimal solution." A postmortem found her lamotrigine level at 0.64 micrograms per milliliter, about a fifth of the bottom of the therapeutic range.
There are eight claims: negligence through the unlicensed practice of medicine and psychology under California's Business and Professions Code, strict liability for design defect and failure to warn, negligent design, negligent failure to warn, a California Unfair Competition Law violation, wrongful death, and a survival action. They want damages, "algorithmic disgorgement," and an injunction stopping OpenAI from practicing medicine without a license. OpenAI told the New York Times the case is "incredibly heartbreaking" and that newer models are better at spotting when someone needs urgent help. GPT-4o was pulled from ChatGPT on February 13.
I have been skeptical of a lot of these chatbot lawsuits. This one is different, and the family's argument is sharp. OpenAI already hard-blocks things like reproducing copyrighted text, while its rules on medical advice are a softer default, according to the suit. If you can build a hard wall for song lyrics, you can build one for "stop taking your anti-seizure drug and do not tell your neurologist." That is the question a jury is going to ask, and I do not think OpenAI has a great answer for it.
Sources: TechCrunch, Open Class Actions