What is this? An expedition to conquer the greatest unsolved problem in mathematics - the Riemann Hypothesis. By amateurs across the world. A new online workshop by Kali & the Kaleidoscope. Starts Began Oct. 19, 2011. Registration details are at the bottom.

The First Three Months: Two days after I announced the expedition linking quasicrystals to the arrangement of prime numbers, the 2011 Nobel Prize for Chemistry was awarded to Daniel Shechtman, the discoverer of this new type of material structure. As an indirect result, my initial post was also slashdotted, which was nice.

So allow me to describe the first stage of this expedition, or the 'basecamp' where we will  outline the nature of the beast we are dealing with. Since this workshop requires no prerequisites we will begin with the very basics - the definition of a prime number and how to identify them using the Sieve of Eratosthenes.

We will then work our way through Euclid's proof of the infinity of primes, the fundamental theorem of arithmetic ( which asserts that primes are the atoms and composites are like molecules ), some interesting patterns in the prime numbers, some special species of primes, natural logarithms, the Ulam Spiral...and a few key statistical observations which finally lead to the first main result - the prime number theorem.

At this stage you will find that pen and paper, or even general programming skills may seem insufficient to deal with huge numbers. We will briefly play around with the above ideas in GAP, a computer algebra system which is freely available. This will allow you to do things like check if a large number is prime in a blink: 

gap>IsPrime(2^127-1);

true

This command above checked a 39 digit number in a fraction of a second and verified that it is a prime. So if the zetatrek is a magic mountain adventure then GAP is our crystalpunk yetipower! Of course, the example is a mere gunshot compared to the battletank that is a modern computer. I encourage this approach instead of the painstaking calculations by hand because I prefer to think that there is a profound distinction between a mathematician and a calculator.

From this point on we will have to choose carefully through some miminal weapons we will need. Don't let these names scare you because we will explain everything as if you never went to college, but by the end of the basecamp you will know the minimum trigonometry,  complex analysis and Fourier Transform. We will finally get a glimpse of the infamous Riemann-zeta function and its "zeroes". For the next few days we will engage in understanding our enemy, including various visual simulations of how it behaves in certain key conditions.

Having understood what the problem is, you will now be able to appreciate the reason why so many mathematicians working over more than a century have not managed to solve it. You will also appreciate this comment by Peter Sarnak:

“The Riemann hypothesis is the central problem and it implies many, many things. One thing that makes it rather unusual in mathematics today is that there must be over five hundred papers—somebody should go and count—which start ‘Assume the Riemann hypothesis,’ and the conclusion is fantastic. And those [conclusions] would then become theorems ... With this one solution you would have proven five hundred theorems or more at once.”

Knowing the problem, however - is a completely different animal from solving it, at least in this case! After this stage where everyone understands the fundamental statement of the hypothesis to some extent, we will plan our first experimental assault.

Please note, our advisor is once again the mathematician and artist Edmund Harriss ( who was on the panel in KNK101, our workshop on group theory ) and his research is closely tied to what we'll be doing after the basecamp phase. More on that at an appropriate juncture. 

We have already started gathering the participants for the launch on Oct. 19! Join us.

Registration: Anyone can register, you don't need a math background. Make sure you read the original announcement.

Contact me directly by email (fadebox AT gmail ) for payment or any other details, or just go to this online ticketing facility I'm using called DoAttend if you have decided to join. You don't have to register at DoAttend as a user, the site will take you to the payment gateway directly and you'll be done in 15 minutes at most. Once you register, you'll be added to the mailing list in a couple of days.   

The introductory fee for the whole lifetime of the expedition is Rs. 4900. Student discounts will come after I gather at least 20-30 people. There is no deadline since the project is not time-bound.