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In the early 1900s, German mathematician David Hilbert said that if he awakened after 1,000 years of sleep, the first question he’d ask would be: Has the Riemann hypothesis been proven?
It’s been only 100 years, but the answer so far is no. Put forward by Bernhard Riemann in 1859, the hypothesis would establish the distribution of zeroes on something called the Riemann zeta function. That, in turn, correlates to the intervals between prime numbers.
Prime numbers (numbers that can be divided only by 1 and themselves: 2, 3, 5, et cetera) are the building blocks of mathematics, because all other numbers can be arrived at by multiplying them together (e.g., 150 = 2 x 3 x 5 x 5). Understanding the primes sheds light on the entire landscape of numbers, and the greatest mystery concerning primes is their distribution. Sometimes primes are neighbors (342,047 and 342,049). Other times a prime is followed by desert of nonprimes before the next one pops up (396,733 and 396,833).
Making sense of this bizarre arrangement would offer a base from which to solve numerous other long-standing math problems and could affect related fields, like quantum physics. Until they know whether it’s true, though, mathematicians can’t use Riemann. Princeton mathematician Peter Sarnak put it this way: “Right now, when we tackle problems without knowing the truth of the Riemann hypothesis, it’s as if we have a screwdriver. But when we have it, it’ll be more like a bulldozer.” Which is why the Riemann hypothesis has been named one of the Clay Millennium prize problems: Whoever proves (or disproves) it gets $1 million. - Simon Singh, author of Fermat’s Enigma