Axiom Math, a startup in Palo Alto, California, has released Axplorer, a free tool built to help mathematicians uncover patterns that could lead to solutions for difficult problems. The software is a redesign of PatternBoost, which François Charton co-developed in 2024 while at Meta. PatternBoost ran on a supercomputer; Axplorer runs on a Mac Pro. Axiom’s goal is to make the capabilities behind PatternBoost available to anyone who can install the new system on their own computer.
The company is targeting a side of mathematics that goes beyond solving known tasks. Carina Hong, Axiom Math’s founder and CEO, argues that mathematics is exploratory and experimental, not just about finding answers to existing questions. Charton draws a contrast with large language models, which he describes as effective when the task is close to work that already exists, but less suited to generating genuinely new ideas. Axiom is instead focusing on tools that help researchers notice patterns that had not been recognized before, since those observations can open new directions in mathematics.
PatternBoost was built for that kind of exploratory work. A mathematician gives the system an example, it generates related examples, and the researcher selects the most interesting outputs to guide the next round. The approach resembles systems that keep promising suggestions and iteratively refine them. Researchers have already used PatternBoost and other systems to make progress on long-standing problems, but access has often been limited because the software depends on large GPU clusters. Charton said that when he solved the Turán four-cycles problem with PatternBoost, he had access to literally thousands, sometimes tens of thousands, of machines, and the system ran for three weeks.
Axiom says Axplorer is much more efficient. Charton says it took Axplorer just 2.5 hours to match PatternBoost’s Turán result. And it runs on a single machine. The company has released the code as open source on GitHub, and Hong says the product is designed to guide mathematicians step by step rather than asking them to train their own neural networks.
Outside researchers see promise but remain cautious. Geordie Williamson of the University of Sydney, who worked with Charton on PatternBoost, said the changes made by Axiom could make Axplorer applicable to a wider range of problems, though he said it remains unclear how significant those improvements will be in practice. He also noted that mathematicians are already being presented with many new Artificial Intelligence tools and may be overwhelmed by the options. Even so, he welcomed additional experimentation while warning that systems like PatternBoost are not a panacea and should not replace more traditional methods.
