Thomae's formula is a theorem about the properties of Riemann theta functions corresponding to hyperelliptic surfaces. In a paper, Fermionic fields on ${\mathbb Z}_N$ curves by Bershadsky and Radul, this formula is rederived and generalised from hyperelliptic surfaces to $N$-fold covers of the sphere. Their argument works by computing the "partition function" for a quantum field theory describing fermions on the surface. The generalised result can also be derived without reference to QFT (that was part of my PhD thesis) but the result might not have been discovered without intuition coming from physics. There were a number of papers in a similar vein published at that time.