Mathematics is full of weird number systems that most people have never heard of and would have trouble even conceptualizing. But rational numbers are familiar. They’re the counting numbers and the fractions—all the numbers you’ve known since elementary school. But in mathematics, the simplest things are often the hardest to understand. They’re simple like a sheer wall, without crannies or ledges or obvious properties you can grab ahold of.

Minhyong Kim, a mathematician at the University of Oxford, is especially interested in figuring out which rational numbers solve particular kinds of equations. It’s a problem that has provoked number theorists for millennia. They’ve made minimal progress toward solving it. When a question has been studied for that long without resolution, it’s fair to conclude that the only way forward is for someone to come up with a dramatically new idea. Which is what Kim has done.

“There are not many techniques, even though we’ve been working on this for 3,000 years. So whenever anyone comes up with an authentically new way to do things it’s a big deal, and Minhyong did that,” said Jordan Ellenberg, a mathematician at the University of Wisconsin, Madison.

Over the past decade Kim has described a very new way of looking for patterns in the seemingly patternless world of rational numbers. He’s described this method in papers and conference talks and passed it along to students who now carry on the work themselves. Yet he has always held something back. He has a vision that animates his ideas, one based not in the pure world of numbers, but in concepts borrowed from physics. To Kim, rational solutions are somehow like the trajectory of light.

If the connection sounds fantastical it’s because it is, even to mathematicians. And for that reason, Kim long kept it to himself. “I was hiding it because for many years I was somewhat embarrassed by the physics connection,” he said. “Number theorists are a pretty tough-minded group of people, and influences from physics sometimes make them more skeptical of the mathematics.”