• Question: what does the Riemann zeta function shows when its in complex numbers?

    Asked by to Naomi, Edward on 24 Jun 2014. This question was also asked by .
    • Photo: Edward Hughes

      Edward Hughes answered on 24 Jun 2014:


      Wow – super question. The Riemann zeta function actually crops up all over maths and physics. Nobody knows for sure why it’s so important.

      One of the most famous ideas is the Riemann zeta function in complex numbers tells you about a pattern in the prime numbers. This is called the Riemann hypothesis and it says that the points where the Riemann zeta function is zero all lie on a particular (complex) line. This would reveal a mysterious secret pattern behind prime numbers!

      The Riemann hypothesis has been checked up to an enormous number! But just checking it for bigger numbers won’t prove it completely. So far nobody has come up with an argument for why it’s right. If you did then you would win a million dollars from the Clay Foundation in America!

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