Will the toughest problem in maths ever be solved?

For many, not just mathematicians, the Riemann hypothesis is the very definition of a supremely difficult problem that might be forever beyond our intellect. Most mathematicians had given up on it, being pessimistic about making any headway. But recently, the first progress – although not a solution – in more than 50 years has been made.

The 165-year-old hypothesis was bequeathed to us by German mathematician Berhard Riemann. It deals with prime numbers – numbers that can only be divided by themselves and 1. For example, 2, 3, 5, 7, 13, 17, 19 and so on to infinity.

They first appeared in 300 bc with Euclid. His work Elements is like reading poetry using numbers. Probably compiled from earlier works, it is arguably the greatest work of mathematics. It is thought to be second only to the Bible in the number of editions produced since its first printing in 1482. Of its 13 books, it is number nine that says there are an infinite number of primes.

They look innocent, but they are not. They are the building blocks of all numbers, as atoms are to the physical universe. The scaffolding of a mathematical universe that reaches to infinity – because mathematics is the only thing that can be truly infinite. The nature of the primes is among the greatest of mysteries.

We see that there are patterns in numbers, sometimes complicated, sometimes trivial. Examples are triangular numbers that can make triangles, 1, 3, 6, 10, 15 etc, and Fibonacci numbers – where each one is the sum of the preceding two numbers, for example, 0, 1, 1, 2, 3, 5, 8, 13, 21 etc. The number of petals on a flower is inevitably a Fibonacci sequence, as is the number of spirals in a fir cone, and the pattern in a seashell.