Douglas Adams may have been onto something.<p>> Now, there are certain attributes of the Riemann zeta function called its moments which should give rise to a sequence of numbers. However, before the Seattle conference, only two of these moments were known: 1, as calculated by Hardy and Littlewood in 1918; and 2, calculated by Ingham in 1926.<p>> The next number in the series was suggested as 42 by Conrey (now also at Bristol) and Ghosh in 1992.<p>> The challenge for the quantum physicists then, was to use their quantum methods to check the number 42 and to calculate further moments in the series, while the number theorists tried to do the same using their methods.<p>> Prof Jon Keating and Dr Nina Snaith at Bristol describe the energy levels in quantum systems using random matrix theory. Using RMT methods they produced a formula for calculating all of the moments of the Riemann zeta function. This formula confirmed the number 42.
The connection was first made (decades ago) in a chance interaction between Hugh Montgomery (who was working on the Riemann Hypothesis) and Freeman Dyson.<p>For a description of how serendipity struck, and an nice explanation of how scientists are trying to understand and work the analogy, see here -- <a href="http://www.americanscientist.org/issues/id.3349,y.0,no.,content.true,page.2,css.print/issue.aspx" rel="nofollow">http://www.americanscientist.org/issues/id.3349,y.0,no.,cont...</a>
Really exciting connection, and I am glad I read the article. What I hate though is the box at the end of the article:<p><pre><code> So why is this work so important?
As we have said, prime numbers are the basic building blocks of mathematics.
And primes are vital to cryptography and therefore to the ever-burgeoning world
of online commerce and security.
</code></pre>
Nope, cryptography is not why this work is important. What a lot of bull.
from what i've heard attempts to prove the Riemann hypothesis this way have been a dead end. mathematicians agree the heuristics concerning random matrices and quantum chaos are true but<p>Physics of the Riemann Hypothesis
<a href="http://arxiv.org/abs/1101.3116" rel="nofollow">http://arxiv.org/abs/1101.3116</a><p>Quantum chaos, random matrix theory, and the Riemann zeta-function
<a href="http://www.math.harvard.edu/~bourgade/papers/PoincareSeminar.pdf" rel="nofollow">http://www.math.harvard.edu/~bourgade/papers/PoincareSeminar...</a><p>The quantum physics methods being used to solve the Riemann hypothesis can solve easier number theory problems as well. We can look at the structure of the primes more directly.<p><a href="http://en.wikipedia.org/wiki/Apollonian_gasket#Integral_Apollonian_circle_packings" rel="nofollow">http://en.wikipedia.org/wiki/Apollonian_gasket#Integral_Apol...</a>
Okay, yes, random matrix theory is a type of mathematics that was developed largely for its applications in physics. But it's still a branch of elementary mathematics! You don't need to know anything about quantum mechanics to wonder about the average eigenvalues of a random matrix.<p>I was hoping this was a case of a quantum physics <i>experiment</i> shedding light on the Riemann hypothesis -- now that would be impressive! And actually not that far fetched, either, although clearly beyond the state of the art (see: quantum computing).
From an Euler problem (412 IIRC), I had played around with Young's tableaux, counting which also gives rise to the sequence 1,2,42,24024. More numbers here: <a href="http://oeis.org/A039622" rel="nofollow">http://oeis.org/A039622</a><p>Am I onto something? Let's see if the next moment is 701149020.
I find science and math really interesting without actually knowing anything deep.<p>It's just like magic. There are these interesting ratio, numbers, series, and functions appear in both nature and mathematics. Similar to how scientists praise Big Band, a lot of things are so well-defined, well put together with a precise amount (in the case of Big Bang a slight off amount might actually destroy today's universe). Sometimes I have to say and assume there is this powerful being God there writing this novel...
Cultural note: Bristol University have some nice cryptography stuff going on. They also have links to GCHQ via the Heilbronn Institute.<p>(<a href="http://www.bristol.ac.uk/engineering/research/research-groups/cryptography.html" rel="nofollow">http://www.bristol.ac.uk/engineering/research/research-group...</a>)<p>(<a href="http://www.maths.bris.ac.uk/research/heilbronn_institute/" rel="nofollow">http://www.maths.bris.ac.uk/research/heilbronn_institute/</a>)
Very Exciting.<p>I recently watched a talk by Ed Witten where he said that he thought that quantum physics would be useful for number theory eventually, it's cool to see this borne out in the present day.<p>Here is the talk (Knots and Quantum Theory) at the moment during the Q&A where he was asked about this.
<a href="http://youtu.be/8nA17Id4JyU?t=45m3s" rel="nofollow">http://youtu.be/8nA17Id4JyU?t=45m3s</a>
Suggesting that prime numbers are the atoms of arithmetic seems inappropriate. Can anyone explain this? Am I looking at a journalism major's summary of research?