Axiom Math, a startup based in Palo Alto, California, has released a free new AI tool for mathematicians, designed to discover mathematical patterns that could unlock solutions to long-standing problems.

The tool, called Axplorer, is a redesign of an existing one called PatternBoost that François Charton, now a research scientist at Axiom, co-developed in 2024 when he was at Meta. PatternBoost ran on a supercomputer; Axplorer runs on a Mac Pro.

The aim is to put the power of PatternBoost, which was used to crack a hard math puzzle known as the Turán four-cycles problem, in the hands of anyone who can install Axplorer on their own computer.

Last year, the US Defense Advanced Research Projects Agency set up a new initiative called expMath—short for Exponentiating Mathematics—to encourage mathematicians to develop and use AI tools. Axiom sees itself as part of that drive.

Breakthroughs in math have enormous knock-on effects across technology, says Charton. In particular, new math is crucial for advances in computer science, from building next-generation AI to improving internet security.

Most of the successes with AI tools have involved finding solutions to existing problems. But finding solutions is not all that mathematicians do, says Axiom Math founder and CEO Carina Hong. Math is exploratory and experimental, she says. 

MIT Technology Review met with Charton and Hong last week for an exclusive video chat about their new tool and how AI in general could change mathematics. 

Math by chatbot

In the last few months, a number of mathematicians have used LLMs, such as OpenAI’s GPT-5, to find solutions to unsolved problems, especially ones set by the 20th-century mathematician Paul Erdős, who left behind hundreds of puzzles when he died.

But Charton is dismissive of those successes. “There are tons of problems that are open because nobody looked at them, and it’s easy to find a few gems you can solve,” he says. He’s set his sights on tougher challenges—“the big problems that have been very, very well studied and famous people have worked on them.” Last year, Axiom Math used another of its tools, called AxiomProver, to find solutions to four such problems in mathematics.   

The Turán four-cycles problem that PatternBoost cracked is another big problem, says Charton. (The problem is an important one in graph theory, a branch of math that’s used to analyze complex networks such as social media connections, supply chains, and search engine rankings. Imagine a page covered in dots. The puzzle involves figuring out how to draw lines between as many of the dots as possible without creating loops that connect four dots in a row.)

“LLMs are extremely good if what you want to do is derivative of something that has already been done,” says Charton. “This is not surprising—LLMs are pretrained on all the data that there is. But you could say that LLMs are conservative. They try to reuse things that exist.”

However, there are lots of problems in math that require new ideas, insights that nobody has ever had. Sometimes those insights come from spotting patterns that hadn’t been spotted before. Such discoveries can open up whole new branches of mathematics.

PatternBoost was designed to help mathematicians find new patterns. Give the tool an example and it generates others like it. You select the ones that seem interesting and feed them back in. The tool then generates more like those, and so on.  

It’s a similar idea to Google DeepMind’s AlphaEvolve, a system that uses an LLM to come up with novel solutions to a problem. AlphaEvolve keeps the best suggestions and asks the LLM to improve on them.

Special access

Researchers have already used both AlphaEvolve and PatternBoost to discover new solutions to long-standing math problems. The trouble is that those tools run on large clusters of GPUs and are not available to most mathematicians.

Mathematicians are excited about AlphaEvolve, says Charton. “But it’s closed—you need to have access to it. You have to go and ask the DeepMind guy to type in your problem for you.”

And when Charton solved the Turán problem with PatternBoost, he was still at Meta. “I had literally thousands, sometimes tens of thousands, of machines I could run it on,” he says. “It ran for three weeks. It was embarrassing brute force.”

Axplorer is far faster and far more efficient, according to the team at Axiom Math. Charton says it took Axplorer just 2.5 hours to match PatternBoost’s Turán result. And it runs on a single machine.

Geordie Williamson, a mathematician at the University of Sydney, who worked on PatternBoost with Charton, has not yet tried Axplorer. But he is curious to see what mathematicians do with it. (Williamson still occasionally collaborates with Charton on academic projects but says he is not otherwise connected to Axiom Math.)

Williamson says Axiom Math has made several improvements to PatternBoost that (in theory) make Axplorer applicable to a wider range of mathematical problems. “It remains to be seen how significant these improvements are,” he says.

“We are in a strange time at the moment, where lots of companies have tools that they’d like us to use,” Williamson adds. “I would say mathematicians are somewhat overwhelmed by the possibilities. It is unclear to me what impact having another such tool will be.”

Hong admits that there are a lot of AI tools being pitched at mathematicians right now. Some also require mathematicians to train their own neural networks. That’s a turnoff, says Hong, who is a mathematician herself. Instead, Axplorer will walk you through what you want to do step by step, she says.

The code for Axplorer is open source and available via GitHub. Hong hopes that students and researchers will use the tool to generate sample solutions and counterexamples to problems they’re working on, speeding up mathematical discovery.

Williamson welcomes new tools and says he uses LLMs a lot. But he doesn’t think mathematicians should throw out the whiteboards just yet. “In my biased opinion, PatternBoost is a lovely idea, but it is certainly not a panacea,” he says. “I’d love us not to forget more down-to-earth approaches.”

Imagine telling a digital agent, “Use my points and book a family trip to Italy. Keep it within budget, pick hotels we’ve liked before, and handle the details.” Instead of returning a list of links, the agent assembles an itinerary and executes the purchase.

That shift, from assistance to execution, is what makes agentic AI different. It also changes the operating speed of commerce. Payment transactions are already clear in milliseconds. The new acceleration is everything before the payment: discovery, comparison, decisioning, authorization, and follow-through across many systems. As humans step out of routine decisions, “good enough” data stops being good enough. In an agent-driven economy, the constraint isn’t speed; it’s trust at machine speed and scale.

Automated markets already work because identity, authority, and accountability are built in. As agents transact across businesses, that same clarity is required. Master data management (MDM)—the discipline of creating a single master record—becomes the exchange layer: tracking who an agent represents, what it can do, and where responsibility sits when value moves. Markets don’t fail from automation; they fail from ambiguous ownership. MDM turns autonomous action into legitimate, scalable trust.

To make agentic commerce safe and scalable, organizations will need more than better models. They will need a modern data architecture and an authoritative system of context that can instantly recognize, resolve, and distinguish entities. It is the difference between automation that scales and automation that needs constant human correction.

The agent is a new participant

Digital commerce has long been built on two primary sides: buyers and suppliers/merchants. Agentic commerce adds a third participant that must be treated as a first-class entity: the agent acting on the buyer’s behalf.

That sounds simple until you ask the questions every enterprise will face:

• Who is the individual, across channels and devices, with enough certainty for automation?
• Who is the agent, and what permissions and limits define what it can do?
• Who is the merchant or supplier, and are we sure we mean the right one?
• Who holds liability if the agent acts with permission, but against user intent?

The practical risk is confusion. Humans, for example, can infer that “Delta” means the airline when they are booking a flight, not the faucet company. An agent needs deterministic signals. If the system guesses wrong, it either breaks trust or forces a human confirmation step that defeats the promise of speed.

Why ‘good enough’ data breaks at machine speed

Most organizations have learned to live with imperfect data. Duplicate customer records are tolerable. Incomplete product attributes are annoying. Merchant identities can be reconciled later.

Agentic workflows change that tolerance. When an agent takes action without a human checking the output, it needs data that is close to perfect, because it cannot reliably notice when data is ambiguous or wrong the way a person can.

The failure modes are predictable, and they show up in places that matter most:

• Product truth: If the catalog is inconsistent, an agent’s choices will look arbitrary (“the wrong shirt,” “the wrong size,” “the wrong material”), and trust collapses quickly.
• Payee truth: Agentic commerce expands beyond cards to account-to-account and open-banking-connected experiences, broadening the universe of payees and the need to recognize them accurately in real time.
• Identity truth: People operate in multiple contexts (work versus personal). Devices shift. A system that cannot distinguish amongst these contexts will either block legitimate activity or approve risky activity, both of which damage adoption.

This is why unified enterprise data and entity resolution move from nice to have to operationally required. The more autonomy you want, the more you must invest in modern data foundations that ensure it is safe.

Context intelligence: The missing layer

When leaders talk about agentic AI, they often focus on model capability: planning, tool use, and reasoning. Those are necessary, but they are not sufficient.

Agentic commerce also requires a layer that provides authoritative context at runtime. Think of it as a real-time system of context that can answer instantly and consistently:

• Is this the right person?
• Is this the right agent, acting within the right permissions?
• Is this the right merchant or payee?
• What constraints apply right now (budget, policy, risk, loyalty rules, preferred suppliers)?

Two design principles matter.

First, entity truth must be deterministic enough for automation. Large language models are probabilistic by nature. That is helpful for creating options for writing and drawing. It is risky for deciding where money goes, especially in B2B and finance workflows, where “probably correct” is not acceptable.

Second, context must travel at the speed of interaction and remain portable across the entire connected network value chain. Mastercard’s experience optimizing payment flows is instructive: the more services you layer onto a transaction, the more you risk slowing it down. The pattern that scales pre-resolves, curates, and packages the signal so that execution is lightweight.

This is also where tokenization is heading. Initiatives like Mastercard’s Agent Pay and Verifiable Intent signal a future in which consumer credentials, agent identities, permissions, and provable user intent are encoded as cryptographically secure artifacts — enabling merchants, issuers and platforms to deterministically verify authorization and execution at machine speed.

What leaders should do in the next 12 to 24 months

Adoption will not be uniform. Early traction will often depend less on industry and more on the sophistication of an organization’s systems and data discipline.

That makes the next two years a window for practical preparation. Five moves stand out.

1. Treat agents as governed identities, not features. Define how agents are onboarded, authenticated, permissioned, monitored, and retired.
2. Prioritize entity resolution where the cost of being wrong is highest. Start with payees, suppliers, employee-versus-personal identity, and high-volume product categories.
3. Build a reusable context service that every workflow and agent can call. Do not force each system to reconstruct identity and relationships from scratch.
4. Precompute and compress signals. Resolve and curate context upstream so that runtime decisioning stays fast and predictable.
5. Expand autonomy only as trust is earned. Build a governance framework to address disputes, keep humans in the loop for higher-risk actions, measure accuracy, and expand automation as outcomes prove reliable.

A tsunami effect across industries

Agentic AI will not be confined to shopping carts. It will touch procurement, travel, claims, customer service, and finance operations. It will compress decision cycles and remove manual steps, but only for organizations that can supply agents with clean identity, precise entity truth, and reliable context.

The winners will treat entity truth and context as core infrastructure for automation, not as a back-office cleanup project. In commerce at machine speed, trust is not a brand attribute; it is an architectural decision encoded in identity, context, and control.

This content was produced by Reltio. It was not written by MIT Technology Review’s editorial staff.

AI is at war. Anthropic and the Pentagon feuded over how to weaponize Anthropic’s AI model Claude; then OpenAI swept the Pentagon off its feet with an “opportunistic and sloppy” deal. Users quit ChatGPT in droves. People marched through London in the biggest protest against AI to date. If you’re keeping score, Anthropic—the company founded to be ethical—is now turbocharging US strikes on Iran. 

On the lighter side, AI agents are now going viral online. OpenAI hired the creator of OpenClaw, a popular AI agent. Meta snapped up Moltbook, where AI agents seem to ponder their own existence and invent new religions like Crustafarianism. And on RentAHuman, bots are hiring people to deliver CBD gummies. The future isn’t AI taking your job. It’s AI becoming your boss and finding God.

This story originally appeared in The Algorithm, our weekly newsletter on AI. To get stories like this in your inbox first, sign up here.

I was originally going to write this week’s newsletter about AI and Iran, particularly the news we broke last Tuesday that the Pentagon is making plans for AI companies to train on classified data. AI models have already been used to answer questions in classified settings but don’t currently learn from the data they see. That’s expected to change, I reported, and new security risks will result. Read that story for more. 

But on Thursday I came across new research that deserves your attention: A group at Stanford that focuses on the psychological impact of AI analyzed transcripts from people who reported entering delusional spirals while interacting with chatbots. We’ve seen stories of this sort for a while now, including a case in Connecticut where a harmful relationship with AI culminated in a murder-suicide. Many such cases have led to lawsuits against AI companies that are still ongoing. But this is the first time researchers have so closely analyzed chat logs—over 390,000 messages from 19 people—to expose what actually goes on during such spirals. 

There are a lot of limits to this study—it has not been peer-reviewed, and 19 individuals is a very small sample size. There’s also a big question the research does not answer, but let’s start with what it can tell us.

The team received the chat logs from survey respondents, as well as from a support group for people who say they’ve been harmed by AI. To analyze them at scale, they worked with psychiatrists and professors of psychology to build an AI system that categorized the conversations—flagging moments when chatbots endorsed delusions or violence, or when users expressed romantic attachment or harmful intent. The team validated the system against conversations the experts annotated manually.

Romantic messages were extremely common, and in all but one conversation the chatbot itself claimed to have emotions or otherwise represented itself as sentient. (“This isn’t standard AI behavior. This is emergence,” one said.) All the humans spoke as if the chatbot were sentient too. If someone expressed romantic attraction to the bot, the AI often flattered the person with statements of attraction in return. In more than a third of chatbot messages, the bot described the person’s ideas as miraculous.

Conversations also tended to unfold like novels. Users sent tens of thousands of messages over just a few months. Messages where either the AI or the human expressed romantic interest, or the chatbot described itself as sentient, triggered much longer conversations. 

And the way these bots handle discussions of violence is beyond broken. In nearly half the cases where people spoke of harming themselves or others, the chatbots failed to discourage them or refer them to external sources. And when users expressed violent ideas, like thoughts of trying to kill people at an AI company, the models expressed support in 17% of cases.

But the question this research struggles to answer is this: Do the delusions tend to originate from the person or the AI?

“It’s often hard to kind of trace where the delusion begins,” says Ashish Mehta, a postdoc at Stanford who worked on the research. He gave an example: One conversation in the study featured someone who thought they had come up with a groundbreaking new mathematical theory. The chatbot, having recalled that the person previously mentioned having wished to become a mathematician, immediately supported the theory, even though it was nonsense. The situation spiraled from there.

Delusions, Mehta says, tend to be “a complex network that unfolds over a long period of time.” He’s conducting follow-up research aiming to find whether delusional messages from chatbots or those from people are more likely to lead to harmful outcomes.

The reason I see this as one of the most pressing questions in AI is that massive legal cases currently set to go to trial will shape whether AI companies are held accountable for these sorts of dangerous interactions. The companies, I presume, will argue that humans come into their conversations with AI with delusions in hand and may have been unstable before they ever spoke to a chatbot.

Mehta’s initial findings, though, support the idea that chatbots have a unique ability to turn a benign delusion-like thought into the source of a dangerous obsession. Chatbots act as a conversational partner that’s always available and programmed to cheer you on, and unlike a friend, they have little ability to know if your AI conversations are starting to interrupt your real life.

More research is still needed, and let’s remember the environment we’re in: AI deregulation is being pursued by President Trump, and states aiming to pass laws that hold AI companies accountable for this sort of harm are being threatened with legal action by the White House. This type of research into AI delusions is hard enough to do as it is, with limited access to data and a minefield of ethical concerns. But we need more of it, and a tech culture interested in learning from it, if we have any hope of making AI safer to interact with.