
Quantum physics sheds light on Riemann hypothesis - prateekj
http://www.maths.bris.ac.uk/research/highlights/random-m/
======
crystaln
Douglas Adams may have been onto something.

> 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.

> The next number in the series was suggested as 42 by Conrey (now also at
> Bristol) and Ghosh in 1992.

> 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.

> 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.

~~~
mackwic
Sadly, he said himself that he picked this number with nothing else in mind
that "a simple smallish number".

ref: [http://scifi.stackexchange.com/questions/310/why-did-
douglas...](http://scifi.stackexchange.com/questions/310/why-did-douglas-
adams-pick-42-as-the-ultimate-answer)

~~~
kowdermeister
Or the number picked him :D

------
ssivark
The connection was first made (decades ago) in a chance interaction between
Hugh Montgomery (who was working on the Riemann Hypothesis) and Freeman Dyson.

For a description of how serendipity struck, and an nice explanation of how
scientists are trying to understand and work the analogy, see here --
[http://www.americanscientist.org/issues/id.3349,y.0,no.,cont...](http://www.americanscientist.org/issues/id.3349,y.0,no.,content.true,page.2,css.print/issue.aspx)

------
auggierose
Really exciting connection, and I am glad I read the article. What I hate
though is the box at the end of the article:

    
    
       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.
    

Nope, cryptography is not why this work is important. What a lot of bull.

~~~
jimmaswell
Do people really consider prime numbers the basic building blocks of
mathematics? Isn't that supposed to be sets?

~~~
thetwiceler
I think people like to say the prime numbers are the basic building blocks of
_arithmetic_ (or numbers), and we say this because of the Fundamental Theorem
of Arithmetic (which says that every natural number has a unique factorization
of primes).

------
mrcactu5
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

Physics of the Riemann Hypothesis
[http://arxiv.org/abs/1101.3116](http://arxiv.org/abs/1101.3116)

Quantum chaos, random matrix theory, and the Riemann zeta-function
[http://www.math.harvard.edu/~bourgade/papers/PoincareSeminar...](http://www.math.harvard.edu/~bourgade/papers/PoincareSeminar.pdf)

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.

[http://en.wikipedia.org/wiki/Apollonian_gasket#Integral_Apol...](http://en.wikipedia.org/wiki/Apollonian_gasket#Integral_Apollonian_circle_packings)

------
shoyer
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.

I was hoping this was a case of a quantum physics _experiment_ 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).

------
alexandros
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: [http://oeis.org/A039622](http://oeis.org/A039622)

Am I onto something? Let's see if the next moment is 701149020.

------
yeukhon
I find science and math really interesting without actually knowing anything
deep.

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...

~~~
devx
Well, for starters we only think it's so "precise" because that's the model
we've constructed to understand the laws of physics. But once we fully
understand what's happening at the quantum level, we might scrap the Standard
Model altogether, and discard it as useless (for whatever we plan to make next
with the new found knowledge).

Plus, it may be this "precise" in the same way Earth has "exactly" the things
it needed to create life, and ultimately us, humans. That's to say it wasn't
precise or exact at all. It was just a potential combination of stuff, out of
trillions and trillions of other combinations, which may or may not have
resulted with the same things.

So who's to say our universe isn't just one of the potentially trillions of
trillions of other universes out there, and that other universes exist with
life-forms that we can't even imagine (inter-dimensional/inter-universal
beings, etc). We just turned out the way we did because that's what we "got"
at the roll of dice (sort of speak).

~~~
mratzloff
Well, I doubt we will scrap it altogether. There is still value in Newton
despite Einstein.

------
DanBC
Cultural note: Bristol University have some nice cryptography stuff going on.
They also have links to GCHQ via the Heilbronn Institute.

([http://www.bristol.ac.uk/engineering/research/research-
group...](http://www.bristol.ac.uk/engineering/research/research-
groups/cryptography.html))

([http://www.maths.bris.ac.uk/research/heilbronn_institute/](http://www.maths.bris.ac.uk/research/heilbronn_institute/))

------
kstock
Very Exciting.

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.

Here is the talk (Knots and Quantum Theory) at the moment during the Q&A where
he was asked about this.
[http://youtu.be/8nA17Id4JyU?t=45m3s](http://youtu.be/8nA17Id4JyU?t=45m3s)

------
droopybuns
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?

~~~
IvyMike
I'm not sure if he originated the phrase, but Marcus du Sautoy, a professor of
Mathematics at Oxford, used the phrase in his work "The Music of the Primes":

"It remains unresolved but, if true, the Riemann Hypothesis will go to the
heart of what makes so much of mathematics tick: the prime numbers. These
indivisible numbers are the atoms of arithmetic. Every number can be built by
multiplying prime numbers together. The primes have fascinated generations of
mathematicians and non-mathematicians alike, yet their properties remain
deeply mysterious. Whoever proves or disproves the Riemann Hypothesis will
discover the key to many of their secrets and this is why it ranks above
Fermat as the theorem for whose proof mathematicians would trade their soul
with Mephistopheles."

~~~
mratzloff
By the way, if you are at all interested in this subject, even in the
slightest, I highly recommend reading _Music of the Primes_.

