How times have changed since the year 2000. In that year, there were a billion fewer people living on the planet. The International Space Station hadn’t yet housed any resident astronauts. Brad Pitt and Jennifer Aniston were in love and got married.
And on 24 May that year, a group of mathematicians took to a stage in Paris to set some problems. They used acetate sheets and an overhead projector in their presentation, but this was no high-school maths challenge. These were the seven Millennium Problems, the hardest mathematical puzzles then known. The exercise was organised by the Clay Mathematics Institute, a US-based non-profit foundation that promised anyone who could solve one would have their grit rewarded with a $1 million prize.
Twenty-five years later, how have mathematicians got on? At first blush, the answer seems to be: not brilliantly. Only one of the challenges has been solved, which might make you wonder whether the maths world has lost its mojo. Delve below the surface, though, and the story of the Millennium Problems can teach us a lot about the state of modern mathematics and what progress really means in this most abstract of disciplines.
Plus, there is reason to believe progress on these puzzles could soon become much more exciting, as machine learning begins to make its mark. “I’ll be very intrigued to see whether the way…
