What your thoughts are on these equations?
The fact that you can theoretically earn $1-million by solving a maths problem is fantastic! It certainly helped to motivate me when I discovered the Millennium Problems as a teenager. However, as with most things that seem too good to be true, there is a catch. The 7 problems were selected precisely because they were seen as the most difficult of all problems facing mathematicians at the start of the new millennium. They weren’t chosen because of their potential applications or because they might change the world one day (although this is in fact true for many of them), they were chosen because they were hard. So, whilst the $1-million prize is a great motivator, it is also quite possibly one of the hardest ways to become a millionaire!
Do you reckon you’d be able to solve any?
Never in a million years. My research background in fluid dynamics means that I know the most about the Navier-Stokes equations – I even have a tattoo of them on my ribs – but I am still very under-qualified to be able to attempt a solution. Some of the most brilliant mathematical minds over the past 100 years have attempted to solve these problems, with little progress, which shows just how difficult they are. The one that has been solved – the Poincaré Conjecture – by Russian mathematician Gregori Perelman, is estimated to have taken over 20 years of work. If you divide up the $1-million by the estimated number of hours he spent working on the problem it equated to being paid less than minimum wage. The money alone isn’t enough – you really do have to love the maths too!
What makes these so unsolvable?
The problems were selected by a ‘scientific advisory board’ with the criteria for selection being “a classical problem that has resisted solution for many years”. This is why they are proving to be so difficult to solve – they were chosen precisely for that reason. However, this does not mean they cannot be solved. Fermat’s Last Theorem is an example of the same type of problem – first proposed by French mathematician Pierre de Fermat in the margin of a textbook in 1637, it took 358 years for a successful proof to be found by Sir Andrew Wiles. The gauntlet has been thrown down to mathematicians, now it’s up to us to try to solve them!
Watch Tom explain each of the 7 problems in a livestream for the Royal Institution below.
Part 1: Riemann Hypothesis, P vs NP, Navier-Stokes Equations, Poincaré Conjecture.
Part 2: Yang-Mills, Hodge, and Birch & Swinnerton-Dyer.