OpenAI and Anthropic claim the same math result, plus Genie 4 and Microsoft's buyouts

Tuesday, October 27, was a day when the most talked-about AI story was also the hardest to explain. OpenAI released proofs, worked out with its AI, for three problems that have stumped researchers for years, and within hours Anthropic posted its own claimed solution to one of them.

Elsewhere, Google DeepMind showed a new version of its world-building AI, Apple announced AI assistants for its creative apps that run partly on OpenAI's models, Microsoft offered buyouts to around 60,000 employees, and Amazon told its engineers to stop judging AI by how much of it they use.

OpenAI and Anthropic claim the same big result

On Tuesday, OpenAI published solutions to three long-standing problems in math, physics and computer science, produced with the help of its AI models. A proof, for anyone who hasn't touched one since school, is a step-by-step argument that shows something is true. It only counts once experts have checked every step, which is why most of Tuesday's coverage was careful to call these claims.

The first problem is about geometry and is known as the Kakeya problem. Picture a needle, and ask how little space you need to turn it so that it points in every direction. Mathematicians Hong Wang and Joshua Zahl proved the three-dimensional version last year, according to Scientific American. OpenAI's model had previously handled four dimensions, and the company now says it has a proof for every dimension.

The second touches the Yang-Mills problem, one of the Clay Mathematics Institute's Millennium Prize Problems, each of which carries a $1 million prize. In plain terms, it asks whether the math behind the Standard Model of particle physics holds together. The problem has two parts. OpenAI claims the first, known as "existence", which is about whether the theory is mathematically consistent. The second part, the "mass gap", is still open. Scientific American reports that OpenAI's Yang-Mills paper has not been made public yet, and that an advisory group on math and AI that OpenAI itself organized has called for its immediate release.

The third result is the one computer scientists are talking about, and it is where the story took a turn. According to TechCrunch, Anthropic mathematician Levent Alpöge suggested that OpenAI's solutions leaned on earlier work. Hours later, Anthropic, the company behind Claude, released its own claimed refutation of the same hypothesis on GitHub, based on an internal model. Scientific American's headline summed up the day: "Dueling proofs from OpenAI and Anthropic astound scientists."

OpenAI also handed each field its result in a different way. Mathematicians got the work on GitHub. Computer scientists formed a working group, asked for the proofs to be released publicly and asked OpenAI to fund a conference. Physicists formed their own group to decide how their result should come out. Scientific American notes that the model is proprietary and that the prompts, computing time and the model's step-by-step reasoning haven't been published.

What the Exponential Time Hypothesis is, and why it matters

The computer science problem is called the Exponential Time Hypothesis, usually shortened to ETH. It was first published in 1999 by Russell Impagliazzo and Ramamohan Paturi of UC San Diego.

Here's the idea. Imagine a really tricky logic puzzle made of lots of yes-or-no switches that all have to be set in a way that satisfies a list of rules. ETH says that as the puzzle grows, even the fastest possible method needs exponentially more time. Add a few more switches and the work doesn't just grow, it explodes. Both labs say their AI found a method that is slightly faster than that, which would mean the hypothesis is wrong.

ETH is closely tied to one of the most famous open questions in computing, called P versus NP. The simple version: if an answer is easy to check, is it always easy to find? TechCrunch uses Sudoku as the example. Checking a finished grid is quick, but finding the solution takes much longer. Most experts believe the answer is no, and ETH has been treated as evidence for that. Scientific American points out that refuting ETH doesn't necessarily lead to a breakthrough on P versus NP.

Ryan Williams, a computer scientist at MIT, is organizing the field's response. He had sharply criticized an earlier OpenAI proof release for swamping mathematicians, but agreed to work with the company on this one, together with Impagliazzo and Paturi. He told TechCrunch that some parts of the proof are routine, but that there are "two or three alien-looking parts". He also said every computer scientist should now give a little more weight to the idea that P could equal NP, even though, in his view, it still seems too good to be true. And he doubts that OpenAI's method is the best one possible.

Why should anyone outside a university care? A lot of online security depends on certain problems staying hard to solve. Williams said that, with a better method, cryptographic systems that rely on certain key sizes could be considered broken. He asked OpenAI's science lead, Dan Roberts, whether the work affected any of them. According to TechCrunch, Roberts said the company had checked and was reasonably confident it didn't break any.

The working group has also published an open letter asking scientists for feedback and discussing how AI contributions to research should be handled. Williams noted that ETH is assumed in many papers that may now need a second look. For now, though, the important caveat stands: these are claims, and experts are still checking them.

Google's Genie 4 builds worlds you can explore

Google DeepMind launched Genie 4, the latest version of what it calls a world model. A world model is an AI that generates an interactive world you can move around in, a bit like a video game, except nobody built it by hand. It is generated on the fly as you explore.

The biggest change is sound. Google says Genie 4 is its first real-time world model to generate audio natively, which means it makes music, background noise and even dialogue from characters as you go. It is also more realistic, with better physics and more humanlike characters, and you can change a world mid-session just by typing, for example switching the weather, moving the camera or adding people and objects. Google's Gemini model works alongside it as a planner that breaks requests into steps and checks the results.

According to TechCrunch, Genie 4 can keep a scene consistent for up to 2 minutes, double the limit of Genie 3, which launched a little over a year ago. Google also tried it in a research experiment that simulated robot tasks in real time, which could help test robots before they are used in the real world.

Google is upfront about the limits. It says visual details and objects can still drift over time, especially in longer sessions or after several edits, and that real-time audio accuracy, readable text inside the world and long-term consistency are still being worked on. Everything Genie 4 makes carries SynthID, Google's invisible watermark for AI-generated content.

For now, Genie 4 is a research preview for trusted testers. Google says it will reach Google AI Ultra subscribers through its Project Genie tool in the coming weeks, along with early-access partners using the Gemini API and Google AI Studio.

Apple's creative apps get AI assistants built partly on OpenAI

Apple announced a major update to Apple Creator Studio, its subscription for creative apps such as Final Cut Pro and Logic Pro, alongside new Macs. 9to5Mac summarized the details from Apple's announcement.

Keynote, Pages and Numbers are getting AI assistants, in beta, that understand what is in your document. In Keynote, the assistant helps design and animate slides. In Pages, it drafts and restructures text. In Numbers, it analyzes data, recommends charts and builds tables. Logic Pro, Apple's music app, gets an assistant of its own, and Pixelmator Pro gains a feature that changes a selected part of an image from a written prompt. Final Cut Pro gets a library of effects, transitions and templates.

The notable part is what powers the assistants. Apple describes them as built on a mix of its own models and OpenAI's, without saying which features use which. Keynote, Pages and Numbers also add support for the Model Context Protocol, or MCP. MCP is a common standard that lets outside AI tools plug into an app, read what is inside and take actions, so another AI agent could, for example, edit a document for you.

The update is free for existing subscribers, and Apple says it will arrive in November, without giving an exact date.

Microsoft offers buyouts to around 60,000 employees

Microsoft is offering voluntary buyouts to about 60,000 employees, roughly a quarter of its workforce, according to CBS News. A buyout is when a company offers staff a payment to leave on their own, instead of laying people off. Eligible employees were notified by email on Monday, October 26.

The offer is open to employees at the vice president level and below in the US, Canada, India and the UK. Bloomberg reported that people working in data centers and in sales and marketing are excluded. TechCrunch reports that the terms are similar to Microsoft's standard severance.

In a memo to employees, Microsoft's chief people officer, Amy Coleman, said the offer gives eligible employees who may be considering a future outside the company "a new choice to make that transition now with support". TechCrunch describes the move as part of Microsoft's effort to cut costs and rework its workforce for the AI age.

It also comes as Microsoft spends heavily on AI. CBS notes that the company expects to spend $175 billion on AI infrastructure, including data centers, in 2026 alone. This is Microsoft's second buyout offer this year: earlier, it offered buyouts to about 8,750 retirement-age employees in the US. Its headcount stood at about 223,000 at the end of June.

Amazon tells engineers to stop tokenmaxxing

Amazon published a memo from its engineering leadership on how its software engineers should use AI. It was written by Terk Terkowitz, a vice president and distinguished engineer for Amazon's worldwide stores business, and updates the guidelines for software engineers and their managers.

It takes aim at a habit with a very internet name: tokenmaxxing. Tokens are the small chunks of text that AI models read and write, and companies pay for every one of them. Tokenmaxxing is when people burn through huge numbers of tokens just to look like heavy AI users, often because their employer tracks usage. Amazon itself had an internal leaderboard that ranked employees by token use, which it shut down earlier this year.

The memo acknowledges that Amazon looks at numbers like token usage, AI tool adoption and the volume of code changes. But it says the company is "aware of how deeply flawed these metrics are", because they are disconnected from what matters, and warns that treating them as targets drives up costs. In its words, "tokenmaxxing is at odds with frugality", one of the values Amazon is known for. Quartz notes that the memo stops short of telling staff to ignore those numbers altogether.

Instead, the memo asks engineers to judge AI by results for customers, the business and their teams, and still urges them to learn and use AI in their daily work now. It also gives people room to push back. If AI doesn't help with a particular job, engineers should document why and share it, because, as the memo puts it, "that is a finding, not a failing."

The big picture

The common thread on Tuesday was AI being asked to prove itself. The math results are only worth something once experts have checked them line by line, and both labs' claims are now going through exactly that. Google was careful to list what Genie 4 still can't do. And Amazon, one of the companies pushing hardest on AI, told its own engineers that using more AI is not the same as getting more done.

At the same time, the money and the reshuffling keep going. Apple is building OpenAI's models into its everyday apps, and Microsoft is offering tens of thousands of people a way out while it plans to spend $175 billion on AI infrastructure this year. Whether the proofs hold up will take a while to know. The other changes are already here.