These problems have had mathematicians scratching their heads since 2000 Beau Lark/Corbis/VCG
Mathematics is awash with fiendish problems such as that of strong coupling, which crops up in physical systems from boiling water to superconductors where there are too many moving parts to be accurately modelled. Some researchers think they might now be on the way to solving that problem听(see “How magnets and boiling kettles encode the secrets of reality鈥) 鈥 but what other thorns are there still in mathematicians鈥 sides?
In May 2000, the Clay Mathematics Institute in New Hampshire published a list of seven particularly intractable problems, and offered a million-dollar reward for the first correct solution to each. Only one of the Millennium Prizes has so far been claimed 鈥 for the Poincar茅 conjecture, which concerns a problem in four-dimensional geometry. The remaining six are up for grabs.
1. Navier鈥揝tokes existence and smoothness
The Navier-Stokes equations are used to describe the behaviour of fluids as they run out of a tap or flow over the wing of a commercial jet, which makes them incredibly important to solve. But their mathematical soundness is in question: for certain problems, it鈥檚 possible that the equations could malfunction to generate incorrect answers, or give no solutions at all. The existence and smoothness problem aims to sort out once and for all what鈥檚 really going on 鈥 and hopefully establish that the equations are a good fit to reality. Many mathematicians have tried 鈥 and failed 鈥 to find the answer, including recently Mukhtarbay Otelbaev of the Eurasian National University in Astana, Kazakhstan, who in 2014 claimed a solution, but later retracted…
