Who wants to be a millionaire? Lots of people do, but first, they’d have to provide an answer to the as-yet-unsolved mystery: proving the Riemann hypothesis.
And it’s certainly not as easy as adding two plus two.
The head-scratcher that has baffled mathematicians for a century and a half is a conjecture about the distribution of the zeros of Riemann’s zeta function.
It was devised in 1859 by German mathematician Bernhard Riemann (1826–1866). Riemann, whose birthday is on September 17, calculated the first few nontrivial zeros of the zeta function and confirmed that their real parts were equal to ½. This calculation supported his hypothesis that all zeros had this property, but he suggested that “it would be desirable to have a rigorous proof of this proposition.”
Since then, many—including prominent mathematicians from around the world—have tried to solve the problem, but so far nobody has cracked it or even claimed to be on the verge of providing the answer. Even after the Clay Mathematics Institute offered a $1 million prize in 2000 to anyone who can provide the elusive proof, the hypothesis remains one of the longest-lasting unsolved problems in mathematics.
The others are:
- P versus NP.
- Hodge conjecture.
- Yang-Mills existence and mass gap.
- Navier–Stokes existence and smoothness.
- Birch and Swinnerton-Dyer conjecture.
Although best known for his unproven hypothesis, Riemann also influenced the fields of analysis, number theory, and differential geometry. In fact, his ideas helped pave the way to Albert Einstein’s work on relativity.
But the proof of his hypothesis remains the holy grail of mathematics.