Upon looking at these numbers, one has the feeling of being in the presence of one of the inexplicable secrets of creation. number theory & physics archive mysterious occurrences on the interface of physics and number theory introductory prime number theory resources related curiosities guest book personal a message about the future of this website ...

The Riemann Hypothesis is currently the most famous unsolved problem in mathematics. Like the Goldbach Conjecture (all positive even integers greater than two can be expressed as the sum of two primes), it seems true, but is very hard to prove. I did some playing around with the Riemann Hypothesis, and I'm convinced it is true. My observations follow. The Zeta Function Euler showed that z(2) = ...

Riemann Hypothesis ...

Timothy Gowers Informal discussions of mathematical topics Over the last two or three years I have written several of these, for a variety of related reasons. One is to provide a more thorough discussion of definitions and basic results than I can normally hope to give in a lecture course from the Cambridge Mathematical Tripos . Another is to try to indicate, in the spirit of George Polya , how ...

Dedicated to increasing and disseminating mathematical knowledge The Riemann Hypothesis Some numbers have the special property that they cannot be expressed as the product of two smaller numbers, e.g., 2, 3, 5, 7, etc. Such numbers are called prime numbers, and they play an important role, both in pure mathematics and its applications. The distribution of such prime numbers among all natural ...

Ueber die Anzahl der Primzahlen unter einer gegebenen Gr sse. By Bernhard Riemann The paper Ueber die Anzahl der Primzahlen unter einer gegebenen Gr sse by Bernhard Riemann, first published in Monatsberichte der Berliner Akademie, November 1859, is available here in the following formats: LaTeX DVI PostScript PDF A translation of this paper into English is also available in the following ...

Ivars Peterson's MathTrek June 21, 1999 The Mark of Zeta It is a curious fact about the human mind that people will work harder to do something which captures their imagination than they will for any practical purpose, mathematician Ian Richards of the University of Minnesota once commented. Mathematicians exhibit such a fascination when they delve into the mysteries of prime numbers. A prime ...

Critical Strip Explorer (version 0.67) This applet has been developed by Raymond Manzoni, based on my suggestions. It is still very much under development. New features and improvements will be added in due course, and there may still be bugs to be removed. Clicking and dragging with your mouse on the blue field, you are able to explore the behaviour of the Riemann zeta function in the complex ...

The Riemann Hypothesis Riemann's Hypothesis was one of the 23 problems - milestones that David Hilbert suggested in 1900, at the 2nd International Conference on Mathematics in Paris, that they should define research in mathematics for the new century (and indeed, it is not an exaggeration to say that modern mathematics largely come from the attempts to solve these 23 problems). It is the most ...

Andrew Odlyzko: Papers on Zeros of the Riemann Zeta Function and Related Topics (see also Tables of zeros of the zeta function and Some unpublished materials on the main home page) The 10^22-nd zero of the Riemann zeta function, A. M. Odlyzko. Dynamical, Spectral, and Arithmetic Zeta Functions, M. van Frankenhuysen and M. L. Lapidus, eds., Amer. Math. Soc., Contemporary Math. series, no. 290, ...

The Riemann Hypothesis With Andrew Wiles' recent proof of Fermat's Last Theorem now confirmed, the most notorious unsolved problem in mathematics becomes the Riemann hypothesis. This conjecture states that all the zeros of in the strip lie on the central line Re(z)=1/2. Here is a completely elementary restatement of the Riemann hypothesis . Define a positive squarefree integer to be red if it is ...