AI Cracks Math Proofs That Took Humans Months to Check

Checking whether a mathematical proof is correct can take months or even years of painstaking work. Now an AI called Gauss has done it automatically, marking a potential turning point for scientific discovery.

Math startup Math, Inc., announced that its AI successfully verified two complex proofs by Fields Medal winner Maryna Viazovska. The proofs solve a mind-bending puzzle about arranging spheres in eight and 24-dimensional space.

The achievement surprised even the company's own team. "The system output the entire formalized proof. That totally surprised us," says Auguste Poiroux, a mathematician who helped launch Math, Inc.

Here's why this matters beyond abstract math. Scientists publish research at an accelerating pace, and experts struggle to verify all the work flowing through their fields. Computer verification could help, but first someone needs to translate human-written proofs into precise programming language, a process called formalization that traditionally takes forever.

Viazovska's original work solved a decades-old challenge. Imagine stacking oranges at a supermarket in the most space-efficient way possible. Easy in three dimensions, but add more dimensions and the problem becomes vastly complex. She proved the optimal solution for eight and 24-dimensional spaces using an elegant mathematical approach.

A team led by Sidharth Hariharan, then a master's student at Imperial College London, began manually formalizing Viazovska's proofs in 2023. They broke the work into small tasks and invited the global mathematics community to collaborate through a public website.

Math, Inc., contacted the team and shared some early results. Then communication went quiet. The startup focused on developing Gauss instead of contributing to the collaborative project. When they tested the finished AI on Viazovska's eight-dimensional proof, it worked automatically.

The Ripple Effect

The breakthrough hints at a future where scientists can verify complex research quickly and build on verified foundations with confidence. Mathematical proofs underpin everything from cryptography to physics, so faster verification could accelerate progress across multiple fields.

Other AI and math startups are racing to develop similar tools, suggesting this technology will continue improving. The collaborative community project continues alongside these commercial efforts, offering different paths toward the same goal.

Some mathematicians have responded cautiously, partly because the project unfolded differently than many hoped. The tension between open collaboration and startup secrecy reflects broader questions about how AI should develop in scientific fields.

Still, Gauss represents genuine progress toward a tool mathematicians have wanted for years. What once required months of expert time now happens in weeks, automatically.

The AI revolution in mathematics is just beginning, and it's already checking work that stumped humans for decades.