Using Astronomy to Study Math

Dn140641_2501 Stephen Battersby in New Scientist:

A gravitational lens can do more than reveal details of the distant universe. In an unexpected collision of astrophysics and algebra, it seems that this cosmic mirage can also be used to peer into the heart of pure mathematics.

In a gravitational lens, the gravity of stars and other matter can bend the light of a much more distant star or galaxy, often fracturing it into several separate images (see image at right). Several years ago, Sun Hong Rhie, then at the University of Notre Dame in Indiana, US, was trying to calculate just how many images there can be.

It depends on the shape of the lens – that is, how the intervening matter is scattered. Rhie was looking at a lens consisting of a cluster of small, dense objects such as stars or planets. If the light from a distant galaxy reaches us having passed through a cluster of say, four stars, she wondered, then how many images might we see?

She managed to construct a case where just four stars could split the galaxy into 15 separate images, by arranging three stars in an equilateral triangle and putting a fourth in the middle.

Later, she found that a similar shape works in general for a lens made of n stars (as long as there are more than one), producing 5n – 5 images. She suspected that was the maximum number possible, but she couldn’t prove it.

At about the same time, two mathematicians were working on a seemingly unrelated problem. They were trying to extend one of the foundation stones of mathematics, called the fundamental theorem of algebra.