While chairman of Stony Brook's math department at age 30, Simons worked on characteristic classes in topology. He struggled with certain "pesky terms" that kept appearing in his calculations - terms he couldn't eliminate to make his desired formulas work.
Instead of discarding them, he recognized these terms had their own intrinsic interest. He defined what became known as Chern-Simons invariants in three dimensions and showed his work to Chern. Chern immediately saw how to generalize it to all dimensions, and they published their groundbreaking paper together.
Neither knew any physics. Simons mentioned it might have physics applications to C.N. Yang (a Nobel Prize winner at Stony Brook), but Yang didn't pursue it. Ten years later, physicist Ed Witten discovered the theory was fundamental to string theory. Russian physicists applied it to condensed matter. Today, on average, four physics papers reference Chern-Simons Theory daily.
The work exemplifies the "unreasonable effectiveness of mathematics" - pure mathematical exploration with no thought of applications later becoming fundamental to physics.