Two mathematicians fiddling around with an extension of the fundamental theorem of algebra had no idea of the significant implications their work held for gravitational lensing, a prediction of Einstein’s general theory of relativity.

Turns out Dmitry Khavinson and Genevra Neumann proved physicist Sun Hong Rhie’s theory on gravitational lensing. Gravitational lensing explains the deceptive behavior of light traveling at extremely far distances.

A gravitational lens forms when distant light from a particularly bright source, like a star, “bends” in both directions around a massive object. This cosmic optical illusion misleads the observer (usually here on earth), into thinking the light originates from 2 sources, when in fact there is only one. What looks like 2 different stars is actually the same star.

The light-tricks depend on where the massive object lies and how many massive objects there are. A star looks like a circle when the massive object is directly between the star and the observer. A multitude of objects means the observer will view what appears to be a multitude of stars.

Rhie had been trying to determine how many mirages of stars could be created by the bending of light. She calculated that four massive objects lead to 15 ostensible stars, coming up with the formula 5n-5 stars, where n is the number of massive objects. Unfortunately, being “pretty sure” of something doesn’t cut it in science: she needed cold proof.

Over on the west coast, mathematican Jefferey Rabin stumbled across Rhie’s work and took a stab at it. He spent months on the problem with little success. In a simple twist of fate, someone in Rabin’s department had left an article on the printer. Passing by, Rabin read it and realized someone had solved the problem, but with purely mathematical aims; they were completely unaware of gravitational lensing.

That article was Khavinson and Neumann’s, and their work with rational harmonic functions had unknowingly proved Rhie’s assertion. Another example of how important the dissemination of scientific knowledge is! Accidental discoveries make for great stories.