The Jacobi triple product formula is

$$\prod_{m=1}^\infty \left( 1 - x^{2m}\right) \left( 1 + x^{2m-1} y^2\right) \left( 1 +\frac{x^{2m-1}}{y^2}\right) = \sum_{n=-\infty}^\infty x^{n^2} y^{2n} $$

Borcherds found an elegant combinatorial argument for this formula based on counting the number of ways it is possible for a certain physical system to achieve particular energy levels. The physical model was based on the Dirac sea model of the vacuum.

Many combinatorial formulae find interpretations this way. For example the appearance of $n-\frac{1}{24}$ in Rademacher's formula for the partition function is less of a surprise for physicists familiar with vacuum energies.