REZcast: Proving the Riemann Hypothesis

It’s a million dollar question: Can the Riemann Zeta Hypothesis be proven?

In this episode of REZcast, Sam Johnson talks with fellow lab mates Luke Hillard and Thomas Hobohm about the challenges involved in proving the Riemann hypothesis. 

Excerpt: Listen to Sam’s Introduction

The challenge is part of the Millennium Prize Problems issued by the Clay Mathematics Institute in 2000 – a list of seven of the most difficult problems facing modern mathematics and physics. Anyone who solves them will earn a $1 million prize from the institute.

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Mathematics is in many ways a house of cards. Solutions often depend on assumptions. The prime number theorem and the Riemann zeta function, explains Thomas Hobohm, are two such basic rules.

“Basically all of the math behind modern encryption and behind modern prime number theory is all based on the Riemann zeta hypothesis. Essentially if the Riemann zeta hypothesis was proved true, then it would immediately give a foundation to thousands of houses mathematicians have sort of built based off assuming it’s true, and if it’s proved false, then it would rip the rug under a lot of modern mathematics.”

Excerpt: Listen to Thomas Hobohm

Luke Hillard tells it like it is when you’re dealing with the Reimann zeta function and infinite numbers: “It’s like trying to find a needle in an infinitely large haystack,” he says.

Excerpt: Listen to Luke Hillard

How can infinite numbers be calculated? Hosts Amelia Jaycen and Lucero Cantu guessed that algorithms and computers are a big help, but they learned that pencil and paper still serves its purpose. Sam Johnson explains that his usual plan of attack involves both:

“Infinite series, which the zeta function normal form falls in, are infinite and you cannot compute them. But the whole trick involved in computing these things is reducing it to a harmonic series, and computers can compute harmonic series. You can also compute harmonic series by hand, but it’s very, very difficult, and it depends on the input to the function. So I’ve actually done this for the several first negative coefficients on the real axis by hand, and I’ve definitely taken up a whole notebook of paper just doing the first four. And it’s really cool when it works.”

Excerpt: Listen to Sam on Infinite Series 

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Excerpt: Listen to Thomas’ Closing Remarks

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