This startup wants to change how mathematicians do math

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.

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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.”

The Bay Area’s animal welfare movement wants to recruit AI

In early February, animal welfare advocates and AI researchers gathered in stocking feet at Mox, a scrappy, shoes-free coworking space in San Francisco. Yellow and red canopies billowed overhead, Persian rugs blanketed the floor, and mosaic lamps glowed beside potted plants. 

In the common area, a wildlife advocate spoke passionately to a crowd lounging in beanbags about a form of rodent birth control that could manage rat populations without poison. In the “Crustacean Room,” a dozen people sat in a circle, debating whether the sentience of insects could tell us anything about the inner lives of chatbots. In front of the “Bovine Room” stood a bookshelf stacked with copies of Eliezer Yudkowsky’s If Anyone Builds It, Everyone Dies, a manifesto arguing that AI could wipe out humanity. 

The event was hosted by Sentient Futures, an organization that believes the future of animal welfare will depend on AI. Like many Bay Area denizens, the attendees were decidedly “AGI-pilled”—they believe that artificial general intelligence, powerful AI that can compete with humans on most cognitive tasks, is on the horizon. If that’s true, they reason, then AI will likely prove key to solving society’s thorniest problems—including animal suffering.

To be clear, experts still fiercely debate whether today’s AI systems will ever achieve human- or superhuman-level intelligence, and it’s not clear what will happen if they do. But some conference attendees envision a possible future in which it is AI systems, and not humans, who call the shots. Eventually, they think, the welfare of animals could hinge on whether we’ve trained AI systems to value animal lives. 

“AI is going to be very transformative, and it’s going to pretty much flip the game board,” said Constance Li, founder of Sentient Futures. “If you think that AI will make the majority of decisions, then it matters how they value animals and other sentient beings”—those that can feel and, therefore, suffer.

Like Li, many summit attendees have been committed to animal welfare since long before AI came into the picture. But they’re not the types to donate a hundred bucks to an animal shelter. Instead of focusing on local actions, they prioritize larger-scale solutions, such as reducing factory farming by promoting cultivated meat, which is grown in a lab from animal cells. 

The Bay Area animal welfare movement is closely linked to effective altruism, a philanthropic movement committed to maximizing the amount of good one does in the world—indeed, many conference attendees work for organizations funded by effective altruists. That philosophy might sound great on paper, but “maximizing good” is a tricky puzzle that might not admit a clear solution. The movement has been widely criticized for some of its conclusions, such as promoting working in exploitative industries to maximize charitable donations and ignoring present-day harms in favor of  issues that could cause suffering for a large number of people who haven’t been born yet. Critics also argue that effective altruists neglect the importance of systemic issues such as racism and economic exploitation and overlook the insights that marginalized communities might have into the best ways to improve their own lives.

When it comes to animal welfare, this exactingly utilitarian approach can lead to some strange conclusions. For example, some effective altruists say it makes sense to commit significant resources to improving the welfare of insects and shrimp because they exist in such staggering numbers, even though they may not have much individual capacity for suffering. 

Now the movement is sorting out how AI fits in. At the summit, Jasmine Brazilek, cofounder of a nonprofit called Compassion in Machine Learning, opened her sticker-stamped laptop to pull up a benchmark she devised to measure how LLMs reason about animal welfare. A cloud security engineer turned animal advocate, she’d flown in from La Paz, Mexico, where she runs her nonprofit with a handful of volunteers and a shoestring budget. 

Brazilek urged the AI researchers in the room to train their models with synthetic documents that reflect concern for animal welfare. “Hopefully, future superintelligent systems consider nonhuman interest, and there is a world where AI amplifies the best of human values and not the worst,” she said. 

The power of the purse 

The technologically inclined side of the animal welfare movement has faced some major setbacks in recent years. Dreams of transitioning people away from a diet dependent on factory farming have been dampened by developments such as the decimation of the plant-based-meat company Beyond Meat’s stock price and the passage of laws banning cultivated meat in several US states.

AI has injected a shot of optimism. Like much of Silicon Valley, many attendees at the summit subscribe to the idea that AI might dramatically increase their productivity—though their goal is not to maximize their seed round but, rather, to prevent as much animal suffering as possible. Some brainstormed how to use Claude Code and custom agents to handle the coding and administrative tasks in their advocacy work. Others pitched the idea of developing new, cheaper methods for cultivating meat using scientific AI tools such as AlphaFold, which aids in molecular biology research by predicting the three-dimensional structures of proteins.

But the real talk of the event was a flood of funding that advocates expect will soon be committed to animal welfare charities—not by individual megadonors, but by AI lab employees. 

Much of the funding for the farm animal welfare movement, which includes nonprofits advocating for improved conditions on farms, promoting veganism, and endorsing cultivated meat, comes from people in the tech industry, says Lewis Bollard, the managing director of the farm animal welfare fund at Coefficient Giving, a philanthropic funder that used to be called Open Philanthropy. Coefficient Giving is backed by Facebook cofounder Dustin Moskovitz and his wife, Cari Tuna, who are among a handful of Silicon Valley billionaires who embrace effective altruism

“This has just been an area that was completely neglected by traditional philanthropies,” such as the Gates Foundation and the Ford Foundation, Bollard says. “It’s primarily been people in tech who have been open to [it].”

The next generation of big donors, Bollard expects, will be AI researchers—particularly those who work at Anthropic, the AI lab behind the chatbot Claude. Anthropic’s founding team also has connections to the effective altruism movement, and the company has a generous donation matching program. In February, Anthropic’s valuation reached $380 billion and it gave employees the option to cash in on their equity, so some of that money could soon be flowing into charitable coffers.

The prospect of new funding sustained a constant buzz of conversation at the summit. Animal welfare advocates huddled in the “Arthropod Room” and scrawled big dollar figures and catchy acronyms for projects on a whiteboard. One person pitched a $100 million animal super PAC that would place staffers with Congress members and lobby for animal welfare legislation. Some wanted to start a media company that creates AI-generated content on TikTok promoting veganism. Others spoke about placing animal advocates inside AI labs.

“The amount of new funding does give us more confidence to be bolder about things,” said Aaron Boddy, cofounder of the Shrimp Welfare Project, an organization that aims to reduce the suffering of farmed shrimp through humane slaughter, among other initiatives. 

The question of AI welfare

But animal welfare was only half the focus of the Sentient Futures summit. Some attendees probed far headier territory. They took seriously the controversial idea that AI systems might one day develop the capacity to feel and therefore suffer, and they worry that this future AI suffering, if ignored, could constitute a moral catastrophe.

AI suffering is a tricky research problem, not least because scientists don’t yet have a solid grip on why humans and other animals are sentient. But at the summit, a niche cadre of philosophers, largely funded by the effective altruism movement, and a handful of freewheeling academics grappled with the question. Some presented their research on using LLMs to evaluate whether other LLMs might be sentient. On Debate Night, attendees argued about whether we should ironically call sentient AI systems “clankers,” a derogatory term for robots from the film Star Wars, asking if the robot slur could shape how we treat a new kind of mind. 

“It doesn’t matter if it’s a cow or a pig or an AI, as long as they have the capacity to feel happiness or suffering,” says Li. 

In some ways, bringing AI sentience into an animal welfare conference isn’t as strange a move as it might seem. Researchers who work on machine sentience often draw on theories and approaches pioneered in the study of animal sentience, and if you accept that invertebrates likely feel pain and believe that AI systems might soon achieve superhuman intelligence, entertaining the possibility that those systems might also suffer may not be much of a leap.

“Animal welfare advocates are used to going against the grain,” says Derek Shiller, an AI consciousness researcher at the think tank Rethink Priorities, who was once a web developer at the animal advocacy nonprofit Humane League. “They’re more open to being concerned about AI welfare, even though other people think it’s silly.”

But outside the niche Bay Area circle, caring about the possibility of AI sentience is a harder sell. Li says she faced pushback from other animal welfare advocates when, inspired by a conference on AI sentience she attended in 2023, she rebranded her farm animal welfare advocacy organization as Sentient Futures last year. “Many people were extremely confident that AIs would never become sentient and [argued that] by investing any energy or money into AI welfare, we’re just burning money and throwing it away,” she says.

Matt Dominguez, executive director of Compassion in World Farming, echoed the concern. “I would hate to see people pulling money out of farm animal welfare or animal welfare and moving it into something that is hypothetical at this particular moment,” he says.

Still, Dominguez, who started partnering with the Shrimp Welfare Project after learning about invertebrate suffering, believes compassion is expansive. “When we get someone to care about one of those things, it creates capacity for their circle of compassion to grow to include others,” he says.

The Pentagon is planning for AI companies to train on classified data, defense official says

The Pentagon is discussing plans to set up secure environments for generative AI companies to train military-specific versions of their models on classified data, MIT Technology Review has learned. 

AI models like Anthropic’s Claude are already used to answer questions in classified settings; applications include analyzing targets in Iran. But allowing models to train on and learn from classified data would be a new development that presents unique security risks. It would mean sensitive intelligence like surveillance reports or battlefield assessments could become embedded into the models themselves, and it would bring AI firms into closer contact with classified data than before. 

Training versions of AI models on classified data is expected to make them more accurate and effective in certain tasks, according to a US defense official who spoke on background with MIT Technology Review. The news comes as demand for more powerful models is high: The Pentagon has reached agreements with OpenAI and Elon Musk’s xAI to operate their models in classified settings and is implementing a new agenda to become an “an ‘AI-first’ warfighting force” as the conflict with Iran escalates. (The Pentagon did not comment on its AI training plans as of publication time.)

Training would be done in a secure data center that’s accredited to host classified government projects, and where a copy of an AI model is paired with classified data, according to two people familiar with how such operations work. Though the Department of Defense would remain the owner of the data, personnel from AI companies might in rare cases access the data if they have appropriate security clearance, the official said. 

Before allowing this new training, though, the official said, the Pentagon intends to evaluate how accurate and effective models are when trained on nonclassified data, like commercially available satellite imagery. 

The military has long used computer vision models, an older form of AI, to identify objects in images and footage it collects from drones and airplanes, and federal agencies have awarded contracts to companies to train AI models on such content. And AI companies building large language models (LLMs) and chatbots have created versions of their models fine-tuned for government work, like Anthropic’s Claude Gov, which are designed to operate across more languages and in secure environments. But the official’s comments are the first indication that AI companies building LLMs, like OpenAI and xAI, could train government-specific versions of their models directly on classified data.

Aalok Mehta, who directs the Wadhwani AI Center at the Center for Strategic and International Studies and previously led AI policy efforts at Google and OpenAI, says training on classified data, as opposed to just answering questions about it, would present new risks. 

The biggest of these, he says, is that classified information these models train on could be resurfaced to anyone using the model. That would be a problem if lots of different military departments, all with different classification levels and needs for information, were to share the same AI. 

“You can imagine, for example, a model that has access to some sort of sensitive human intelligence—like the name of an operative—leaking that information to a part of the Defense Department that isn’t supposed to have access to that information,” Mehta says. That could create a security risk for the operative, one that’s difficult to perfectly mitigate if a particular model is used by more than one group within the military.

However, Mehta says, it’s not as hard to keep information contained from the broader world: “If you set this up right, you will have very little risk of that data being surfaced on the general internet or back to OpenAI.” The government has some of the infrastructure for this already; the security giant Palantir has won sizable contracts for building a secure environment through which officials can ask AI models about classified topics without sending the information back to AI companies. But using these systems for training is still a new challenge. 

The Pentagon, spurred by a memo from Defense Secretary Pete Hegseth in January, has been racing to incorporate more AI. It has been used in combat, where generative AI has ranked lists of targets and recommended which to strike first, and in more administrative roles, like drafting contracts and reports.

There are lots of tasks currently handled by human analysts that the military might want to train leading AI models to perform and would require access to classified data, Mehta says. That could include learning to identify subtle clues in an image the way an analyst does, or connecting new information with historical context. The classified data could be pulled from the unfathomable amounts of text, audio, images, and video, in many languages, that intelligence services collect. 

It’s really hard to say which specific military tasks would require AI models to train on such data, Mehta cautions, “because obviously the Defense Department has lots of incentives to keep that information confidential, and they don’t want other countries to know what kind of capabilities we have exactly in that space.”

If you have information about the military’s use of AI, you can share it securely via Signal (username jamesodonnell.22).