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.”

Pokémon Go was the world’s first augmented-reality megahit. Released in 2016 by the Google spinout Niantic, the AR twist on the juggernaut Pokémon franchise fast became a global phenomenon. From Chicago to Oslo to Enoshima, players hit the streets in the urgent hope of catching a Jigglypuff or a Squirtle or (with a huge amount of luck) an ultra-rare Galarian Zapdos hovering just out of reach, superimposed on the everyday world.

In short, we’re talking about a huge number of people pointing their phones at a huge number of buildings. “Five hundred million people installed that app in 60 days,” says Brian McClendon, CTO at Niantic Spatial, an AI company that Niantic spun out in May last year. According to the video-game firm Scopely, which bought Pokémon Go from Niantic at the same time, the game still drew more than 100 million players in 2024, eight years after it launched. 

Now Niantic Spatial is using that vast and unparalleled trove of crowdsourced data—images of urban landmarks tagged with super-accurate location markers taken from the phones of hundreds of millions of Pokémon Go players around the world—to build a kind of world model, a buzzy new technology that grounds the smarts of LLMs in real environments. 

The company’s latest product is a model that it says can pinpoint your location on a map to within a few centimeters, based on a handful of snapshots of the buildings or other landmarks in view. The firm wants to use it to help robots navigate with greater precision in places where GPS is unreliable.

In the first big test of its technology, Niantic Spatial has just teamed up with Coco Robotics, a startup that deploys last-mile delivery robots in a number of cities across the US and Europe. “Everybody thought that AR was the future, that AR glasses were coming,” says McClendon. “And then robots became the audience.”

From Pikachu to pizza delivery

Coco Robotics deploys around 1,000 flight-case-size robots—built to carry up to eight extra-large pizzas or four grocery bags—in Los Angeles, Chicago, Jersey City, Miami, and Helsinki. According to CEO Zach Rash, the robots have made more than half a million deliveries to date, covering a few million miles in all weather conditions.

But to compete with human couriers, Coco’s robots, which trundle along sidewalks at around five miles per hour, must be as reliable as possible. “The best way we can do our job is by arriving exactly when we told you we were going to arrive,” says Rash. And that means not getting lost.

The problem Coco faces is that it cannot rely on GPS, which can be weak in cities because radio signals bounce off buildings and interfere with each other. “We do deliveries in a lot of dense areas with high-rises and underpasses and freeways, and those are the areas where GPS just never really works,” says Rash. 

“The urban canyon is the worst place in the world for GPS,” says McClendon. “If you look at that blue dot on your phone, you’ll often see it drift 50 meters, which puts you on a different block going a different direction on the wrong side of the street.” That’s where Niantic Spatial comes in. 

For the last few years, Niantic Spatial has been taking the data collected from players of Pokémon Go and Ingress (Niantic’s previous phone-based AR game, launched in 2013) and building a visual positioning system, technology that tells you where you are based on what you can see. “It turns out that getting Pikachu to realistically run around and getting Coco’s robot to safely and accurately move through the world is actually the same problem,” says John Hanke, CEO of Niantic Spatial.

“Visual positioning is not a very new technology,” says Konrad Wenzel at ESRI, a company that develops digital mapping and geospatial analysis software. “But it’s obvious that the more cameras we have out there, the better it becomes.” 

Niantic Spatial has trained its model on 30 billion images captured in urban environments. In particular, the images are clustered around hot spots—places that served as important locations in Niantic’s games that players were encouraged to visit, such as Pokémon battle arenas. “We had a million-plus locations around the world where we can locate you precisely,” says McClendon. “We know where you’re standing within several centimeters of accuracy and, most importantly, where you’re looking.”

The upshot is that for each of those million locations, Niantic Spatial has many thousands of images taken in more or less the same place but from different angles, at different times of day, and in different weather conditions. Each of those images comes with detailed metadata that pinpoints where in space the phone was at the time it captured the image, including which way the phone was facing, which way up it was, whether or not it was moving, how fast and in which direction, and more.   

The firm has used this data set to train a model to predict exactly where it is by taking into account what it is looking at—even for locations other than those million hot spots, where good sources of image and location data are scarcer.

In addition to GPS, Coco’s robots, which are fitted with four cameras, will now use this model to try to figure out where they are and where they are headed. The robots’ cameras are hip-height and point in all directions at once, so their viewpoint is a little different from a Pokémon Go player’s, but adapting the data was straightforward, says Rash. 

Rival companies use visual positioning systems too. For example, Starship Technologies, a robot delivery firm founded in Estonia in 2014, says its robots use their sensors to build a 3D map of their surroundings, plotting the edges of buildings and the position of streetlights. 

But Rash is betting that Niantic Spatial’s tech will give Coco an edge. He claims it will allow his robots to position themselves in the correct pickup spots outside restaurants, making sure they don’t get in anybody’s way, and stop just outside the customer’s door instead of a few steps away, which might have happened in the past.  

A Cambrian explosion in robotics 

When Niantic Spatial started work on its visual positioning system, the idea was to apply it to augmented reality, says Hanke. “If you are wearing AR glasses and you want the world to lock in to where you’re looking, then you need some method for doing that,” he says. “But now we’re seeing a Cambrian explosion in robotics.”

Some of those robots may need to share spaces with humans—spaces such as construction sites and sidewalks. “If robots are ever going to assimilate into that environment in a way that’s not disruptive for human beings, they’re going to have to have a similar level of spatial understanding,” says Hanke. “We can help robots find exactly where they are when they’ve been jostled and bumped.”

The Coco Robotics partnership is the start. What Niantic Spatial is putting in place, says Hanke, are the first pieces of what he calls a living map: a hyper-detailed virtual simulation of the world that changes as the world changes. As robots from Coco and other firms move about the world, they will provide new sources of map data, feeding into more and more detailed digital replicas of the world. 

But the way Hanke and McClendon see it, maps are not only becoming more detailed; they are being used more and more by machines. That shifts what maps are for. Maps have long been used to help people locate themselves in the world. As they moved from 2D to 3D to 4D (think of real-time simulations, such as digital twins), the basic principle hasn’t changed: Points on the map correspond to points in space or time.

And yet maps for machines may need to become more like guidebooks, full of information that humans take for granted. Companies like Niantic Spatial and ESRI want to add descriptions that tell machines what they’re actually looking at, with every object tagged with a list of its properties. “This era is about building useful descriptions of the world for machines to comprehend,” says Hanke. “The data that we have is a great starting point in terms of building up an understanding of how the connective tissue of the world works.”

There is a lot of buzz about world models right now—and Niantic Spatial knows it. LLMs may seem like know-it-alls, but they have very little common sense when it comes to interpreting and interacting with everyday environments. World models aim to fix that. Some firms, such as Google DeepMind and World Labs, are developing models that generate virtual fantasy worlds on the fly, which can then be used as training dojos for AI agents. 

Niantic Spatial says it is coming at the problem from a different angle. Push map-making far enough and you’ll end up capturing everything, says McClendon: “I’m very focused on trying to re-create the real world. We’re not there yet, but we want to be there.”