Summary of The Riemann Hypothesis, Explained

00:00:00 - 00:15:00

The Riemann hypothesis is a conjecture in mathematics that states that every non-zero complex number has a real part and an imaginary part. It was first proposed by Bernhard Riemann in 1859 and has since been heavily investigated. Riemann's breakthrough in prime number theory could potentially lead to a deeper understanding of the mysteries of prime numbers. Despite the fact that computers have checked over 10 trillion zeros, the Riemann hypothesis remains an unresolved problem.

• 00:00:00 The Riemann hypothesis is an unsolved problem in mathematics that could solve a mystery as old as math itself: the prime numbers. If the hypothesis is true, it would show that all whole numbers are constructed out of prime numbers. The prime counting function, which shows where prime numbers appear as the numbers get bigger, stays flat until you hit a prime, and then jumps up by one. Gauss's conjecture, that there is another function with a graph that looks similar to the prime counting function, is called the Riemann hypothesis. Riemann proved that the hypothesis is true, and this solved a problem that had been troubling mathematicians for centuries.
• 00:05:00 The Riemann Hypothesis is a conjecture in mathematics that states that every non-zero complex number has a real part and an imaginary part. It was first proposed by Bernhard Riemann in 1859 and has since been heavily investigated. Riemann's breakthrough in prime number theory could potentially lead to a deeper understanding of the mysteries of prime numbers.
• 00:10:00 The Riemann hypothesis states that all the non-trivial zeros of the Zeta function lie on a single vertical line in the middle of the critical strip, where the real part of s is exactly one half. This hypothesis is important for prime number theory, as it allows us to predict the distribution of prime numbers.
• 00:15:00 The Riemann hypothesis is a mathematical theory proposed in 1859 by Bernhard Riemann. It is named after him, and states that every non-trivial zeta zero lies on a line in the complex plane. However, despite the fact that computers have checked over 10 trillion zeros, they have yet to find a single zeta zero that lies on the critical line. This means that the Riemann hypothesis remains an unresolved problem, and can only be proven through rigorous mathematical proof.