What is the most important problem in mathematics?
David Hilbert thought he knew. On August 8, 1900, at the International Congress of Mathematicians in Paris, he announced his definitive 23 problems that would come to dominate mathematical research for the next century.
One hundred years later, paying homage to Hilbert in the best mathematical tradition, the Clay Mathematical Insitute announced the Millennium Prize Problems: seven of the most difficult problems still eluding mathematicians at the turn of the millennium. These problems were so important that solving any one would win a mathematician $1 million, yet even with this incentive, only one has been cracked so far.
A good candidate for the most important problem in math, then, might be something that made both of these landmark lists. And it just so happens there's one that fits the bill: the Riemann hypothesis.
"Ask any professional mathematician what the single most important open problem in the entire field is," wrote mathematician Keith Devlin in 1998, "and you are almost certain to receive the answer 'the Riemann Hypothesis'".
And now, there's a rumor circulating that this 160-year-old mega-problem might finally be solved – by British-Lebanese geometer Sir Michael Atiyah.
First conjectured by Bernhard Riemann in 1859, the Riemann hypothesis is an attempt to answer an age-old question about primes – numbers that divide only by themselves and one. Primes are one of the most fundamental concepts in mathematics – the "atoms" of numbers – but they are also mysterious and inexplicable, turning up seemingly randomly along the number line. That's why it's such big news when mathematicians find new, enormous primes. Even if we find one prime number, there's no way to predict what the next one is or how many there are below it.