Professor Pythagoras Vavasor lies face up on the floor of his study in the house that he shares with his twin brother Archimedes, trying to comprehend what is happening to him. When the police toxicologist runs her tests on his body over the next few days, she will discover that he has been drugged. This, however, is not the primary reason for Professor Vavasor’s present terminal condition. Rather, this condition is almost exclusively due to the metal set-square that has been inserted, sharp angle first, into his aorta.
Suspicion will immediately fall upon his missing brother, although the motive will (for the moment) remain elusive. While the police deliberate, the twins’ housekeeper, Mrs Deirdre Snopes (47), will be interviewed by the tabloids, and a picture will emerge of a curious ménage which is so far beyond the comprehension of their readership that it will quickly acquire the status of a freak show. The “reclusive mathematical geniuses” who until very recently shared this domicile will be revealed to be confirmed bachelors, almost certainly onanistic virgins at the age of 54 – although this judgement will later be overturned when a rent boy emerges from the shadows to sell his somewhat exotic and scarcely believable story concerning his relationship with the deceased. It will soon be common knowledge that the two mathematicians were in the habit of eating the same meal every day (lamb cutlets reform, with spinach and boiled potatoes), and that between them they possessed only a single suit, along with a dozen pairs of corduroy trousers. Underpants were habitually only changed on Fridays, and neither of them considered it worth their while to bathe more than once a month. Despite these lapses, Mrs Snopes will be seen to have held “her boys” Pye and Archie in some considerable affection.
It will also turn out that the twins owned a mangy cat called µ (mu/mew), whose fate will be of much concern to the papers’ readership. µ will eventually be taken in by a neighbour following the departure of Mrs Snopes.
When the quality papers get hold of the story, however, it will take on a more intellectual aspect. In The Guardian, a correspondent with a passing grasp of mathematics will suggest that the twins’ relationship was similar to that of the two transcendental numbers e and π, given by Euler’s equation, thus: eiπ = -1 where i is the square root of minus one. It is a complicated and flawed analogy – the idea of two ineffable constants linked by an imaginary one – which will be somewhat spoilt by a sub-editor’s insistence on replacing the word “transcendental” with “irrational”, applying a new and almost entirely incorrect spin on the story. The twins were, after all, anything but irrational beings. Inevitably, the letters page of the paper will be clogged for several weeks with the fallout from this, until the exasperated editor declares the correspondence closed.
As Professor Pythagoras Vavasor’s life ebbs away from him, his weak eyes (missing his spectacles which got knocked off during the course of the brief and half-hearted tussle that preceded his stabbing) attempt to focus on the back of his assailant, who is now busy at his desk.
“You?” he gasps. “Why?” But he is ignored.
Once the initial flurry of excitement has died down (and the missing Archimedes has still failed to materialise, although – Elvis-like – he has been sighted in numerous places, including the British Museum, Edinburgh Castle and the Hemel Hempstead branch of Claire’s Accessories), a leading feature-writer called Conrad Murk (who has several novels under his belt, none of which has been published apart from a truly terrible pot-boiler, written under an assumed name, that has achieved notable success in the airport branches of W H Smith) will attempt a more in-depth analysis. Based on the papers found on the desks of both the Vavasor twins, he will propose a truly fascinating theory, which – if true – will provide his readers with a rare and illuminating insight into the brains of these two extraordinary people. He will win an award for this piece of journalism, and it will ultimately be made into a disappointing film, called – in an egregious misappropriation from a different branch of mathematics altogether – “The Twins Paradox”. The film will star Jude Law, Ben Affleck and Gwyneth Paltrow, and it will last a week in the cinemas before disappearing from sight. The DVD will later be available for £3 in the HMV sale, and even then it will sell badly.
Murk’s theory is that both men, at the time of Pythagoras’ untimely demise, were working on a definitive proof of the Riemann hypothesis, a notoriously intractable problem in complex analysis, which has remained unsolved for almost 150 years. This obsession was well-known in mathematical circles – it was after all what sent the twins' own father babbling first to a mental institution and then to an early grave. His last words were, incidentally, “I have a truly marvellous proof of this proposition which this margerine is too narrow to contain.” Sadly, the only proof that this statement in fact offered was that Vavasor père was indeed completely insane.
After a brief description of the hypothesis (largely borrowed from Wikipedia, with the addition of a few telling mistakes), Murk goes on to say that the twins were working on a radical method of proof which involved solving two interlinked lesser hypotheses simultaneously. This enabled a problem that was too big for one mind to cope with to be broken down into two parallel problems that were more manageable. This approach turned out to be perfect for a team of two people working together – particularly two people who shared the same neural chemistry.
However, shortly before Pythagoras’ death, his papers suggest that he had abandoned this approach without telling Archimedes. Instead, he was working on a whole new line of attack – one that didn’t need a twin. Exactly why he decided to do this isn’t clear, although he seems to have found it inspirational – his notes become more and more frenzied in his last few hours. Murk even holds out to his readers the possibility that somewhere amongst the tortuous final scribblings a proof of Riemann’s hypothesis may yet be found. This possibility will be summarily dismissed as a sensationalist fabrication by the mathematical community, although when the hypothesis is finally proved a decade later, and the author of the proof collects his million dollar prize, some aspects of his work will seem curiously familiar.
Not long after the publication of Murk’s piece, Archimedes’ body will be found, his wrists slashed, in the mathematics section of an academic bookshop in Cambridge, and the tragic circle will appear to be complete.
“Just tell me why …” says Pythagoras Vavasor again. But he gets no reply. Or if he does, it is immaterial; for it turns out that he has posed the question with his dying breath.
One evening, six months after Archimedes’ apparent suicide, a mousy middle-aged woman sits in a bar in downtown Havana, sipping at a Mojito. The trio in the corner are playing “Guantanamera”. She hasn’t been keeping count, but she reckons that it’s probably at least the tenth time that she has heard “Guantanamera” so far today. Then again, she hasn’t been keeping count of the Mojitos either, so she isn’t really that bothered.
Oh Archie, she says to herself, you would have enjoyed this so much. Why did you have to get so remorseful? I showed you his notes, didn’t I? You saw what he was up to. It was never going to end well with you two.
I think I might have loved you in a way, Archie. And I suppose I might have loved Pye too. But I had to choose in the end, didn’t I, and I chose you. You were so alike, though – and wasn’t it funny when we found out that he’d stashed his money in the same place as you? You never did trust banks, did you? And there was even more than I’d expected – but I suppose neither of you spent it on anything. There would have been enough for two of us, you know, if you hadn’t gone and lost your nerve.
But then again, did I really love you, Archie? The more I think about it, the more I wonder if I did. You smelt funny, you had revolting manners and you were unbelievably boring to talk to. You paid me a pittance to clean up after you and you never once said thank you. I got on better with that revolting cat with the stupid name than either of you pair of freaks. Do you know something? When I stuck that set-square into Pye, I felt so liberated! It was the best moment of my wretched life, bar none.
I don’t suppose you realised, did you? It was me who re-wrote Pye’s notes to show that change of direction. I was the one who came up with all that pseudo-mathematical mumbo-jumbo that was scrawled over the final few pages – but it took you all in, didn’t it? Well, I suppose you’d never imagine in a million years that a mere woman could come up with anything like that. But I’ve been following your work for a long time. And not just with a duster and polish.
Deirdre Snopes takes another sip of her drink, picks up her copy of “Topics in Advanced Complex Analysis” and starts to read at page 326. Every now and then, she makes a brief note on a pad of paper, humming quietly to herself and tapping her foot in time to the music.
© Jonathan Pinnock, 2008
Mathematical puzzels and diversions was read by Sabina Cameron at the Liars' League Crime & Punishment event on Tuesday 9 September, 2008.