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.

We'll discuss the Riemann hypothesis, other Millenium problems, and encryption.

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
.

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?

A meeting on the Riemann Hypothesis, and on the theory of the zeta-function and other L-functions.

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.

Understanding the Riemann Hypothesis | Everything …

Indeed this realisation of the intimate connection, as between prime numbers and the behaviour of quantum particles, has now come to be recognised in a dramatic fashion through the search for a solution to the Riemann Hypothesis.

Can someone please explain the Riemann Hypothesis …

So in a dramatic fashion the Riemann Zeta Function points to the need for incorporation of both systems of logic in the interpretation of results (both quantitatively and qualitatively).

The Riemann Hypothesis - Prime Pages

MAT 806: Advanced Number Theory (3)
Basic concepts from analytic and algebraic number theory including the Prime Number Theorem, Dirichlet’s Theorem, the Riemann Hypothesis, algebraic integers, ideals and factorization in algebraic number fields. Additional topics as time permits. It is strongly recommended that students have completed courses in number theory, abstract algebra, and real analysis or differential equations.