# The Riemann Hypothesis: The Greates Unsolved Problem in Mathematics.

18 May 2015

Works Cited

The Greatest Unsolved Problem of Mathematics

$1,000,000 reward for successful proof offered by the Clay Mathematics Institute

Bernard Riemann

Riemann's Hypothesis: What is it?

The calculations used in the Riemann Zeta Function rely heavily on summation and limits.

However…

Relation to this Class**The Riemann Hypothesis****Ashton Hammond and Jonathan Haroldsen**

Remains unsolved for over 156 years

Riemann was born on September 17, 1826 in Breselenz in the Kingdom on Hanover.

## "A Friendly Introduction to the Riemann Hypothesis." (n.d.): n.

### And so the Riemann Hypothesis was born!

Riemann came up with a new function called ζ(s) that equaled Z(s), but with the important difference that s could equal any number except 1.

History of the Hypothesis

Attempts to Prove/Disprove

Implications

"Riemann Hypothesis."

Riemann Hypothesis

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### Thus Riemann did not succeed in proving his famous Hypothesis.

Lived 1826-1866

He was a German National

He studied at The University of Göttingen and the University of Berlin

His mother died when he was young

Although he was brilliant, he often suffered from anxiety, shyness, and timidity and was also prone to mental breakdowns and was afraid to speak in public Notable achievements: Riemann Sums and Riemann Integrals

He was the inspiration for "Alice's Adventures in Wonderland" and "Through the Looking Glass This function was first recognized by Euler, but Riemann studied it further and used it as the foundation for his hypothesis

Some values of the function have been found; for values of s that are even, pi is involved in the output, but it has not been shown what the output is for values of s that are odd Why Should We Care?

## The Riemann Hypothesis | Mathematical Association of …

[6]The significance of this is that the (with which the Riemann Hypothesis is intimately linked) employs complex dimensions and generates many results that have no strict meaning in quantitative terms.

## Riemann Hypothesis in a Nutshell - Vancouver Island …

So a major philosophical dilemma - which is central to difficulties in unravelling the Riemann Hypothesis - is that Conventional Mathematics still attempts to interpret complex numbers through a qualitative approach that is solely real.

## Numbers of the World | Understanding the Riemann Hypothesis

So the Riemann Zeta Function thereby represents the sum of terms - that first appeared in the harmonic series - when raised to powers (dimensions) that have complex values.