Adventures in Primetime

November 15th, 2010 by Tommaso De Benetti

In high school, math was my personal bane. Like countless others, I found trigonometry tedious and calculus incomprehensible. In time though, as I became older and (ahem) more mature, I started to cultivate a serious fascination for hard science. My conversion happened when I learned of the crazy characters and mad schemes behind so many groundbreaking discoveries. I might not be able to grasp every detail of quantum physics or number theory, but the writer in me can’t resist a good story.

A few years ago, I had the chance to read two amazing books: Fermat’s Last Theorem and The Music of Primes.

Before you give up and click over to Amazon to get the latest Dan Brown thriller, let me tell you just one incredible fact. If it hadn’t been for the work of mathematicians Pierre de Fermat (1601-1665) and Bernhard Riemann (1826-1866) you wouldn’t be able to buy anything on Amazon (or anywhere else online) at all.

The indivisible truth
To make a long story short, both these men were all about primes. Fermat tried to find a way of testing for prime numbers, while Riemann attempted to predict the distribution of primes from zero to infinity. Primes (for those who were skipping classes) are numbers that can be divided only by 1 or themselves. They have no apparent logical order: 2, 3, 5, 7, 11, 13, 17… the list goes on forever.

So what’s so important about a bunch of random numbers?

Well, primes are the basis of all other numbers or, as Marcus du Sautoy elegantly puts it, the atoms of arithmetic. Over the centuries, mathematicians have been obsessed with finding bigger and bigger primes. In 1996, distributed computing joined the search with GIMPS, a project that allows users to run free, prime-hunting software on their PCs. There are thousands of GIMPS volunteers who together have donated teraflops of processing power.

The very randomness of primes has also proved useful, helping to forge the algorithm that now protects all our credit card numbers and online transactions.

Decoding the future
In 1859, Riemann finally realized that, working in a multi-dimensional space, a logic in the distribution of prime numbers could actually be found (illustrated here by XKCD). Unfortunately, Riemann never produced a full proof of his theory – legend has it his cleaning lady accidentally burned the papers – so the Riemann hypothesis remains unsolved.

Even in the absence of concrete proof, many people have adopted the Riemann hypothesis as a working model. Take the RSA algorithm, which is now used to encrypt all transactions with electronic money (including Amazon’s 32 sales per second). Without going into details, the principles of RSA encryption are built on the insights of Fermat and Riemann, but decryption is only possible using the unproven Riemann hypothesis.

A million dollar question
Since it was formulated, there have been two attempts to crowdsource a solution to the Riemann hypothesis. In 1902 David Hilbert included it in his list of 23 great math problems, inviting anyone who could to provide solutions. A century later, the Clay Institute established seven millennium prize problems, offering $1,000,000 for each correct solution.

So far, I regret to say, crowdsourcing has not brought forth the solution to the world’s most complex mathematical problem. Who ever does find the answer – whether it’s an individual, a group, or even (who knows) a huge, widely distributed, network of collaborators – I’m sure the breakthrough will come with another crazy, unbelievable story. And, given the importance of prime numbers, no doubt security services, corporations and governments will be following developments pretty closely as well.

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