The Humans. Matt Haig

opened it up and saw it was twenty-six pages of mathematical symbols. Or most of it was. At the beginning there was a little introduction written in words, which said:

      PROOF OF THE RIEMANN HYPOTHESIS

      As you will know the proof of the Riemann hypothesis is the most important unsolved problem in mathematics. To solve it would revolutionise applications of mathematical analysis in a myriad of unknowable ways that would transform our lives and those of future generations. Indeed, it is mathematics itself which is the bedrock of civilisation, at first evidenced by architectural achievements such as the Egyptian pyramids, and by astronomical observations essential to architecture. Since then our mathematical understanding has advanced, but never at a constant rate.

      Like evolution itself, there have been rapid advances and crippling setbacks along the way. If the Library of Alexandria had never been burned to the ground it is possible to imagine that we would have built upon the achievements of the ancient Greeks to greater and earlier effect, and therefore it could have been in the time of a Cardano or a Newton or a Pascal that we first put a man on the moon. And we can only wonder where we would be. And at the planets we would have terraformed and colonised by the twenty-first century. Which medical advances we would have made. Maybe if there had been no dark ages, no switching off of the light, we would have found a way never to grow old, to never die.

      People joke, in our field, about Pythagoras and his religious cult based on perfect geometry and other abstract mathematical forms, but if we are going to have religion at all then a religion of mathematics seems ideal, because if God exists then what is He but a mathematician?

      And so today we may be able to say, we have risen a little closer towards our deity. Indeed, potentially we have a chance to turn back the clock and rebuild that ancient library so we can stand on the shoulders of giants that never were.

Primes

      The document carried on in this excited way for a bit longer. I learned a little bit more about Bernhard Riemann, a painfully shy, nineteenth-century German child prodigy who displayed exceptional skill with numbers from an early age, before succumbing to a mathematical career and a series of nervous breakdowns which plagued his adulthood. I would later discover this was one of the key problems humans had with numerical understanding – their nervous systems simply weren’t up to it.

      Primes, quite literally, sent people insane, particularly as so many puzzles remained. They knew a prime was a whole number that could only be divided by one or itself, but after that they hit all kinds of problems.

      For instance, they knew that the total of all primes was precisely the same as the total of all numbers, as both were infinite. This was, for a human, a very puzzling fact, as surely there must be more numbers than prime numbers. So impossible was this to come to terms with, some people, on contemplating it, placed a gun into their mouth, pulled the trigger, and blew their brains out.

      Humans also understood that primes were very much like the Earth’s air. The higher you went, the fewer of them there were. For instance, there were 25 primes below 100, but only 21 between 100 and 200, and only 16 between 1000 and 1100. However, unlike with the Earth’s air it didn’t matter how high you went with prime numbers as there were always some around. For instance, 2097593 was a prime, and there were millions between it and, say, 4314398832739895727932419750374600193. So, the atmosphere of prime numbers covered the numerical universe.

      However, people had struggled to explain the apparently random pattern of primes. They thinned out, but not in any way that humans could fathom. This frustrated the humans very much. They knew that if they could solve this they could advance in all kinds of ways, because prime numbers were the heart of mathematics and mathematics was the heart of knowledge.

      Humans understood other things. Atoms, for instance. They had a machine called a spectrometer which allowed them to see the atoms a molecule was made from. But they didn’t understand primes the way they understood atoms, sensing that they would do so only if they could work out why prime numbers were spread out the way they were.

      And then in 1859, at the Berlin Academy, the increasingly ill Bernhard Riemann announced what would become the most studied and celebrated hypothesis in all mathematics. It stated that there was a pattern, or at least there was one for the first hundred thousand or so primes. And it was beautiful, and clean, and it involved something called a ‘zeta function’ – a kind of mental machine in itself, a complex-looking curve that was useful for investigating properties of primes. You put numbers into it and they would form an order that no one had noticed before. A pattern. The distribution of prime numbers was not random.

      There were gasps when Riemann – mid panic attack – announced this to his smartly dressed and bearded peers. They truly believed the end was in sight, and that in their lifetimes there would be a proof that worked for all prime numbers. But Riemann had only located the lock, he hadn’t actually found the key, and shortly afterwards he died of tuberculosis.

      And as time went on, the quest became more desperate. Other mathematical riddles were solved in due course – things like Fermat’s Last Theorem and the Poincaré Conjecture – which left proof of the long-buried German’s hypothesis as the last and largest problem to solve. The one that would be the equivalent of seeing atoms in molecules, or identifying the chemical elements of the periodic table. The one that would ultimately give humans supercomputers, explanations of quantum physics and interstellar transportation.

      After getting to grips with all this I then trawled through all the pages full of numbers, graphs and mathematical symbols. This was another language for me to learn, but it was an easier and more truthful one than the one I had learnt with the help of Cosmopolitan.

      And by the end of it, after a few moments of sheer terror, I was in quite a state. After that very last and conclusive ∞, I was left in no doubt that the proof had been found, and the key had turned that all-important lock.

      So, without so much as a second’s thought, I deleted the document, feeling a small rush of pride as I did so.

      ‘There,’ I told myself, ‘you may have just managed to save the universe.’ But of course, things are never that simple, not even on Earth.

A moment of sheer terror

      ξ(1/2+it)=[e^Ŗlog(r(s/2))π^-1/4(–t²–1/4)/2]x[e^iJlog(r(s/2))π^-it/2ζ(1/2+it)]

The distribution of prime numbers

      I looked at Andrew Martin’s emails, specifically the very last one in his sent folder. It had the subject heading, ‘153 years later . . .’, and it had a little red exclamation mark beside it. The message itself was a simple one: ‘I have proved the Riemann hypothesis, haven’t I? Need to tell you first. Please, Daniel, cast your eyes over this. Oh, and needless to say, this is for those eyes only at the moment. Until it goes public. What do you reckon? Humans will never be the same again? Biggest news anywhere since 1905? See attachment.’

      The attachment was the document I had deleted elsewhere, and had just been reading, so I didn’t waste much time on that. Instead, I looked at the recipient: [email protected].