To Infinity and beyond

A "set" is a collection of objects, and sometimes as mathematicians we want to count these objects. We uncover some surprising facts about infinite sets, sometimes finding that one set that surely seems much larger than another is actually the same (infinite) size.

As Albert Einstein once said, "Everything that can be counted does not necessarily count; everything that counts cannot necessarily be counted."

Dr Walling is a number theorist in the School of Mathematics at the University of Bristol.

Most stars will end their days as compact ultra dense white dwarfs. Having run out of nuclear fuel, they simply fade as they age and are generally considered fairly boring.

But over the past decade, a significant number of boring white dwarfs have been observed with pollution in their atmospheres - rocky elements and metals that should have long sunk to their centres. It seems that these stars are now eating the solar systems that they once helped to form. I will discuss what we know and why the story is so interesting and yet truly mysterious.