New research has used machine learning to identify properties of atomic parts of geometry in a paper that could spur the development of new results in mathematics. Mathematicians from the University of Nottingham and Imperial College London have used machine learning for the first time to expand and accelerate work to identify the “atomic shapes” that form the fundamental elements of geometry in higher dimensions. Their findings were published at: Nature Communication.

A research group began working several years ago to create a table of periodic form. Atomic parts are called Fano types. The team associates a sequence of numbers called quantum periods with each shape, providing a “barcode” or “imprint” that identifies the shape. Their latest invention uses a new machine learning methodology to very quickly examine these barcodes, identifying their shapes and characteristics such as the dimensions of each shape.

“The most important step for mathematicians is to identify regularities in a particular problem. “It can be very difficult, and it can take years to discover some mathematical theories,” says Oleksandr Kasprzyk.

“This is where AI can truly revolutionize mathematics, as we have shown that machine learning is a powerful tool for discovering patterns in complex fields such as algebra and geometry,” says Professor Tom Coates.

Sarah Veneziale, co-author and Ph.D. The student in the team continues: “We are very excited about the fact that machine learning can be used in pure mathematics. This will accelerate new understanding in the field.” Source