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November 18, 2009

Unsolved math problem turns 150

Posted: 12:14 PM ET

Happy 150th anniversary to the Riemann Hypothesis, one of the most important math problems ever!

Proposed by Bernhard Riemann in 1859, the Riemann Hypothesis deals with prime numbers. You may recall that a prime number is a positive whole number that has only two positive whole number divisors: one and itself. The first of them are 2, 3, 5, 7, 11, 13, in order.

This hypothesis would be able to provide a better estimate than ever before of a special function denoted as Pi(x). Pi(x) represents the number of prime numbers that are no bigger than x, where x is a positive number. For example, Pi(14) would be 6, because there are six prime numbers (2, 3, 5, 7, 11, 13) no bigger than 14. That's probably the most understandable explanation you're going to get that doesn't involve "zeta functions" and other technical terms.

Given that many of the best mathematicians have tried and failed to provide a solution, the proof is probably not easy or obvious, says Peter Sarnak, professor of mathematics at Princeton University and an authority on the subject. “Most experts expect that a proof will require a major new insight into the structure of whole numbers and the prime numbers,” he said.

But if you can solve it, the Clay Mathematics Institute will give you $1 million.

A proof would have implications not only for mathematics, but also for cryptography and computer science, says Ramin Takloo-Bighash, associate professor at the University of Illinois at Chicago. Internet security protocols, after all, are largely based on prime numbers. Experimental and theoretical evidence has supported the truth of the Riemann Hypothesis, although there are a small number of naysayers who say it can’t be proven, Takloo-Bighash said.

Still, there’s enough confidence in the truth of the Riemann Hypothesis that mathematicians have established “conditional” theorems, which can never be validated until someone proves the 150-year-old problem, says Kenneth Ribet, professor of mathematics at the University of California, Berkeley.

Riemann's paper on the subject was first published in November 1859, but no one knows the day. So, the American Institute of Mathematics picked a Wednesday in the middle of November to celebrate the 150th anniversary, said Brian Conrey, executive director.

Intrigued? Stop by one of these lectures today.

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Filed under: Mathematics

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Fun with numbers   November 18th, 2009 6:44 pm ET

Dear Mom, if you don't understand what the problem is any further explination will fly completely over your head. As for Michael Harris, the reason there is no information on how to follow up with winning the prize is simple. No one has solved it in 150 years, therefore the chances that a blog on CNN will draw out the solution are effectivly zero.

DMR   November 19th, 2009 9:54 am ET

Jason, it's very typical for CNN–I can usually find one grammatical error a week with minimal effort–they are only a touch better than fox, and far, far behind bbc...

Mark C   November 29th, 2009 8:29 pm ET

**** The same thing applies to math, it was invented, people began to follow it and as you get into things like imaginary numbers it just becomes stupid. Stop the madness, admit that this problems have no real application on anything useful and use math just enough to balance your check book, because lets face it, it has to be done. ****

Wow, could you possibly be a bigger moron?

Kindly explain how you get a spaceship to Saturn using "basic math" that you use to balance your checkbook. Or how you do the fluid dynamics necessary to design an airplane. Or understand semiconductors (which involve quantum mechanics) well enough to build the computer you posted this drivel from.

Louise   November 30th, 2009 1:08 pm ET

If you think this is hard; just try explaining the federal tax code.

Jessica*   December 2nd, 2009 1:05 am ET

It cracks me up to see how many people post on the CNN blog that they have the answer – and even funnier that people are quoting Wikipedia – since when is Wikipedia a reliable source of information?

ebrown2112   December 11th, 2009 1:53 am ET

The answer is 42, duh.

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