The Riemann Hypothesis

[jazzy_dave]

This morning my cousin asked me if I knew anything about Riemann's Hypothesis. This was the eight problem that David Hilbert posed early on the 20th century.

Bernard Riemann had a very short life, born 1828 and died 1866. He founded the field of Riemann geometry, which enabled Albert Einstein to formulate his theory of general relativity and space-time. He was the first to suggest using higher dimensions (other than that of three and four dimensional space) in order to describe physical reality.

Riemann's published works opened up research areas combining analysis with geometry, as well as number theory specifically to do with primes and how you could predict the next prime in a number sequence.

This area of mathematics is part of the foundation of topology, and is still being applied in novel ways to mathematical physics. Topological spaces are use in everyday life, such as the maps used in the London underground, and why a torus, such as a bagel can be deformed into a cup as they have the same topological properties.

He made some famous contributions to modern analytic number theory. In a single short paper (the only one he published on the subject of number theory), he introduced the Riemann zeta function and established its importance for understanding the distribution of prime numbers. He made a series of conjectures about properties of the zeta function, one of which is the well-known Riemann hypothesis, which is still not proven. Several mathematicians have addressed the Riemann hypothesis, but none of their attempts have yet been accepted as correct solutions

Riemann's idea was to introduce a collection of numbers at every point in space (i.e., a tensor) which would describe how much it was bent or curved. Riemann found that in four spatial dimensions, one needs a collection of ten numbers at each point to describe the properties of a manifold, no matter how distorted it is. This is the famous construction central to his geometry, known now as a Riemannian metric. Manifolds are an important contribution to the membrane theory of cosmology.

The Riemann hypothesis implies results about the distribution of prime numbers that are in some ways as good as possible. Along with suitable generalizations, it is considered by some mathematicians to be the most important unresolved problem in pure mathematics

If the hypothesis is solved and proven, apparently;y it would make any code breakable, including that which credit cards rely on. The film “The Echelon Conspiracy” is based on this notion of the ability to crack any code and why the military, spies and banks would love to bank roll such research with a prize of a million dollars to prove and solve it.

Riemann was the inspiration for mathematician Charles Lutwidge Dodgson (better known by his pen name Lewis Carroll) to write Alice's Adventures in Wonderland and Through the Looking-Glass.