> 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.
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...
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.
While I agree that its worth it just for its knowledge pushing value alone, academics and researchers do need to take the public with them, especially these days when finances are squeezed and more people are struggling to make ends meet.
So, if this is what you are telling the tax payer, then you are just telling lies to the tax payer.
If we avoid such research out of fear that we might discover something that breaks RSA, we are relying on security by obscurity.
Nice to know we've got our cultural priorities straight!
Physics of the Riemann Hypothesis
Quantum chaos, random matrix theory, and the Riemann zeta-function
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.
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).
Am I onto something? Let's see if the next moment is 701149020.
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...
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).
"Since the principles of certain sciences, such as logic, geometry and arithmetic are taken only from the formal principles of things, on which the essence of the thing depends, it follows that God could not make things contrary to these principles. For example, that a genus was not predicable of the species, or that lines drawn from the centre to the circumference were not equal, or that a triangle did not have three angles equal to two right angles."
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.
"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."
Prime numbers are can only be split (factorized) in one axiomatic way (1 and the prime itself). This is with multiplication(or it's inverse division) as the building (splitting) operation. Primes are tough to deal with,
yet with them you can create (through multiplication) all other numbers. This is the fundamental theory of
The correlation is apparent. Though as explained with atoms we are creating structures that are made up of atoms
but are not classified as atoms themselves (fusion can give you atoms from atoms but it is not easy business),
but with primes numbers we make other numbers that are not primes.