Math and Machine Learning

Machine learning makes it possible to generate more data than mathematician can in a lifetime

For the first time, mathematicians have partnered with artificial intelligence to suggest and prove new mathematical theorems. While computers have long been used to generate data for mathematicians, the task of identifying interesting patterns has relied mainly on the intuition of the mathematicians themselves. However, it’s now possible to generate more data than any mathematician can reasonably expect to study in a lifetime. Which is where machine learning comes in.

Two separate groups of mathematicians worked alongside DeepMind, a branch of Alphabet, Google’s parent company, dedicated to the development of advanced artificial intelligence systems. András Juhász and Marc Lackenby of the University of Oxford taught DeepMind’s machine learning models to look for patterns in geometric objects called knots. The models detected connections that Juhász and Lackenby elaborated to bridge two areas of knot theory that mathematicians had long speculated should be related. In separate work, Williamson used machine learning to refine an old conjecture that connects graphs and polynomials.

András Juhász and Marc Lackenby of the University of Oxford taught DeepMind’s machine learning models to look for patterns in geometric objects called knots. The models detected connections that Juhász and Lackenby elaborated to bridge two areas of knot theory that mathematicians had long speculated should be related. In separate work, Williamson used machine learning to refine an old conjecture that connects graphs and polynomials.

“The most amazing thing about this work and it really is a big breakthrough is the fact that all the pieces came together and that these people worked as a team,” said Radmila Sazdanovic of North Carolina State University.

Some observers, however, view the collaboration as less of a sea change in the way mathematical research is conducted. While the computers pointed the mathematicians toward a range of possible relationships, the mathematicians themselves needed to identify the ones worth exploring.

Synchronous Fireflies

Great Smoky Mountains National Park has had the market cornered on synchronous fireflies for years. But thanks to a relatively recent discovery, the Blue Ridge Mountains just might give it a run for its money.


The Photinus carolinus is a species of firefly that each year, typically in the spring, put on a synchronous light display in order to find a mate. They are the only species in America whose individuals can synchronize their flashing light patterns.

CREDIT: JIM MAGRUDER

For decades, it was believed that the Smokies had the only population of synchronous fireflies in U.S. And while synchronous fireflies were eventually identified in Pennsylvania, South Carolina, and in two other parts of Tennessee, the Smokies have always gotten the glory. In fact, the annual viewing event at the Elkmont Campground in Gatlinburg, Tennessee, is so popular that the National Park Service instituted a lottery system for tickets.

So, you can imagine how surprised Dr. Clyde Sorenson, a professor of entomology at N.C. State University, was by what he saw when he spent the night on Grandfather Mountain in June 2019.

"I noticed them immediately by their flash pattern—they were synchronous. By 10 p.m. there were hundreds of them. I walked up and down the roads and they were all through the woods. It thrilled me to death," Sorenson told the Asheville Citizen-Times.  TO READ MORE ABOUT THESE FIREFLIES, CLICK HERE...