The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics by Marcus du Sautoy
My rating: 4 of 5 stars

Natural Religion

If there is advanced technological life elsewhere in the universe, it would unlikely be Christian, or Muslim, or Jewish, or Buddhist. It would however certainly know the same mathematics that we do. And it would understand the phenomenon of the prime numbers and their significance as much as, perhaps more than, we do. Mathematics is the natural religion of the cosmos; and prime numbers are its central mystery.

Prime numbers are those integers which can only be divided without remainder by themselves (or of course by 1). Put another way, as du Sautoy does, prime numbers are the atoms from which all other numbers are composed. 1, 2, 3, and 5 are prime. 4 is merely 2 x 2; and 6 is 2 x 3. 10 is 2 x 5. Prime numbers constitute the periodic table of mathematical elements which can be mixed and matched to form molecules and compounds of enormous size and complexity.

Prime numbers become less frequent as numbers get larger. There are fewer in any interval greater than let’s say 1000, than the same interval less than 1000. This is intuitively obvious since the greater the number the more lesser numbers there that might be divided into it evenly. Interestingly, there is always at least one prime between any number and its double.

The fun arises because although mathematicians know primes occur less and less frequently as we progress up the scale of numbers, no one knows how to predict when the next one will be encountered. They can be, and have been, calculated to very large numbers indeed, but they can’t be anticipated, only recognised once they appear.* Or should the term be ‘revealed’?

Is it any wonder that prime numbers can take on an almost cultic significance? The 18th century philosopher, Denis Diderot, hated both religion and mathematics for the same reason. Both, he felt, provided a veil that obscured reality. Much of today’s popular aversion to mathematics may well be down to this same associative prejudice: if something isn’t immediately obvious or somewhat abstract, it is merely an unverifiable belief or theory and not worthy of respectable thought.

There is a good reason for the religious, even spiritual, interpretation of mathematics - particularly number theory, and especially prime numbers. In the first instance, unlike any other area of human inquiry - even theology - the results obtained in mathematics never change. Euclid’s proofs may be superseded by more general analysis but they are nevertheless entirely correct and need no modification in a world of radically different cosmology and technology.

Mathematics also shares another characteristic with religion: a concern with aesthetics. Religion orders the world. It provides comprehensibility in a world that might appear otherwise chaotic. And order is an essential component of beauty. Mathematicians not only investigate order as beauty, they collectively insist upon it in their evaluation of their work. A proof or a theorem just isn’t acceptable if it is ugly. The liturgy and art of the Roman Church has no advantage over the aesthetic wonder of the Euler Identity, which connects worlds even further apart than Heaven and Earth.

And, it must be said in an era of fake news and rootless factoids, there is nothing quite so practical as a good theory. And mathematics has the best theories - in astronomy, encryption, communications, and logistics to name some of the most obvious areas that are dependent upon them. In fact understanding almost anything at all reported in the press or online demands familiarity with at least the most glaring abuses of mathematical logic.

Not all of us, naturally, have the talent or discipline to become mathematicians. But most of us can appreciate the importance of history without being historians, or of engineering without building bridges. The real value of The Music of the Primes is that it inspires an appreciation of, and therefore interest in, the thought and thinkers that are perhaps the purest examples we have of shared human thought; who knows, perhaps cosmic thought. Mathematics - and its heroes like Euler, Gauss and Reimann, and Cauchy, and Godel - belong to all of humanity not just some sect. I find this inspiring. It is more than music; but music will do.

*The search for ever larger prime numbers continues. Here is the latest discovery: http://www.independent.co.uk/news/sci...

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