Millennium Prize: the Birch and Swinnerton-Dyer Conjecture

If this doesn’t bake your hippy noodle, nothing will. stuartpilbrow

MILLENNIUM PRIZE SERIES: The Millennium Prize Problems are seven mathematics problems laid out by the Clay Mathematics Institute in 2000. They’re not easya correct solution to any one results in a US$1,000,000 prize being awarded by the institute.

Russian mathematician Grigori Perelman was awarded the Prize on March 18 last year for solving one of the problems, the Poincaré conjecture – as yet the only problem that’s been solved. Famously, he turned down the $1,000,000 Millennium Prize.

Over the coming weeks, each of these problems will be illuminated by experts from the Australian Mathematical Sciences Institute (AMSI) member institutions.

Here, Daniel Delbourgo explains the Birch and Swinnerton-Dyer Conjecture. Enjoy.

Elliptic curves have a long and distinguished history that can be traced back to antiquity. They are prevalent in many branches of modern mathematics, foremost of which is number theory.

In simplest terms, one can describe these curves by using a cubic equation of the form