As Dashiell Hammett once pointed out, murders, even in fiction, are not like mathematical problems. This hasn’t, however, prevented plenty of other crime writers from treating them as if they were. In the equation are a few constants – the corpse, perhaps the time and cause of death – and a few unknown quantities. The detective isolates y and z by means of some rigorous and attentive sleuthing, and is then able, with a little lateral thinking, to deduce x: the identity of the murderer.
Take, by way of concrete illustration, Michael Innes’s Death at the President’s Lodging (1936). The president in question is Dr Josiah Umpleby, head of St Anthony’s College, Oxbridge (not to be confused with St Antony’s, Oxford, which wasn’t founded till 1950; Innes’s setting is a fictional composite of the two university towns), who has been shot dead in his study. The list of suspects is reduced by a process of elimination to four dons, all of whom have been behaving suspiciously, each apparently convinced that one of the other three is the murderer. Our hero, Inspector Appleby, is cunning enough to work out which of them is in fact responsible, and the culprit is obliging enough to confirm his guilt in a suitably dramatic manner.
The disobliging reader, however, may not be as satisfied with Appleby’s explanation as the surviving characters in the novel seem to be. With only a few minor adjustments, Innes could have turned any – or all – of the innocent three into the guilty party. It’s almost always possible for a reader to work out a solution to the crime that fits all the facts apart from the final confession. And even that needn’t be trusted: the false confession is a staple of detective fiction – and not unheard of in real life. In Qui a tué Roger Ackroyd? (1998), Pierre Bayard proposed an alternative solution to Agatha Christie’s most notoriously ingenious plot, which fits the evidence better than Hercule Poirot’s (making, in the process, a larger point about the ways in which texts are co-constructed by writers and readers). In this respect, the most satisfying of Christie’s novels has to be Murder on the Orient Express, in which all possible solutions turn out to be simultaneously true.
Guillermo Martínez is a mathematician as well as a writer of fiction. In 2003 he published a book of essays, Borges y la matemática, and his third novel, Crímenes imperceptibles, now translated into English as The Oxford Murders. It features a serial killer who believes that murders are like mathematical problems. The narrator is a 22-year-old Argentinian postgraduate student, in Oxford on a scholarship, who gets involved because the first of the victims is his landlady. We never learn his name; only that English people invariably mispronounce it. Going to pay his second month’s rent, he meets on Mrs Eagleton’s doorstep Arthur Seldom, ‘one of the four leading minds in the field of logic’.
Entering the house, Seldom and the narrator discover Mrs Eagleton’s corpse: having fallen asleep while playing a game of Scrabble against herself, she has been smothered with a pillow. Had her nose not been broken by the pressure, soaking the murder weapon in blood, it might have seemed as if the old woman had died of natural causes. There is further evidence of foul play, however. Seldom reveals that he has received an anonymous note consisting of Mrs Eagleton’s address, her time of death, a ‘neatly drawn circle’, and the announcement that this is ‘the first of the series’: the killer is apparently challenging him to a battle of wits.
Brought together at the scene of the crime, Seldom and the narrator begin an unofficial partnership as amateur sleuths, and the narrator is delighted to be getting so much attention from this ‘legend among mathematicians’. Seldom’s ‘most famous work’ is an ‘extension of Gödel’s theorem’. As he explains to the narrator in one of their impromptu and slightly improbable tutorials, which take place as the two of them are walking down St Giles or, in this instance, finishing lunch at Merton, ‘Gödel showed that even at the most elementary levels of arithmetic there are propositions that can neither be proved nor refuted starting from axioms.’ In other words, he demonstrated that some mathematical problems are, in this respect, like murders. ‘Think of any crime with two possible suspects,’ Seldom says. ‘All too often there isn’t enough evidence to prove either one suspect’s guilt or the other suspect’s innocence. Basically, what Gödel showed in 1930 with his incompleteness theorem is that exactly the same occurs in mathematics.’
Anyone who worries this may not be ‘exactly’ what Gödel showed would do well to remember that Seldom is trying to think his way into the mindset of a deranged murderer. His most recent book, a surprise bestseller, contains a chapter on serial killers, which was extracted – serialised, even – in the Oxford Times. ‘In it I maintain,’ he tells Inspector Petersen, the diligent representative of the local constabulary, ‘that, except in crime novels and films, the logic behind serial murders – at least those that have been documented historically – is generally very rudimentary, and relates to pathological mental states . . . they’re cases that should be subjected to psychoanalysis rather than being true logical enigmas.’ The killer of Mrs Eagleton, Seldom believes, is determined to prove him wrong, committing murders according to an underlying mathematical logic. Either Seldom is mistaken now, therefore, or he was mistaken in his book. It isn’t long before the next victim is claimed, heralded by a note pinned to the door of the Mathematical Institute. The symbol for ‘the second in the series’ is a ‘diagram of a fish, placed vertically, drawn in black ink, that looked like two overlapping parentheses’.
Seldom hopes that if and when he is able to solve the problem set by the killer and predict the next symbol in the series, the murders will cease. There is a difficulty here, however, illustrated by the story of Frank Kalman, a friend of Seldom’s who has for some time now been in a coma in hospital. It used to be Kalman’s job to set questions for school IQ tests: ‘He spent his whole life preparing logical series, of the most basic kind . . . given three symbols in sequence, please fill in the fourth symbol.’ He also had to mark students’ papers, and in the process discovered a curious thing: there were always a very few exam scripts in which all but one of the answers were right, and the one mistake was never an error he’d have expected. Asking the candidates to justify their answers, Kalman found that each ‘incorrect’ solution was rather ‘another possible and perfectly valid way of continuing the series, only with a much more complicated justification’.
As Seldom observes, ‘Frank had rediscovered in practice, in a real experiment, what Wittgenstein had already proved theoretically decades earlier: the impossibility of establishing an unambiguous rule . . . You can always find a justification, a rule, that lets you use any number as the fourth term in the series’ – or one that lets you finger any character in a whodunnit as the criminal. ‘Do you really believe he’ll stop if we find the solution?’ Inspector Petersen asks. ‘He’ll stop,’ Seldom replies, ‘if it’s the solution that he has in mind’ – suggesting an intriguing affinity between the killer and writers of detective fiction.
There is the usual line-up of unusual suspects. Top of the list as far as the police are concerned, before the cryptic messages and further deaths rule her out, is Mrs Eagleton’s beautiful granddaughter, Beth, a cellist who hates playing the cello. Then there’s the postgraduate who shares a room with the narrator at the Mathematical Institute, a surly Russian chainsmoker called Podorov, who accuses Seldom of having taken his work on Fermat’s last theorem and passed it on to a group of English mathematicians without acknowledging him. Or what about the narrator’s new girlfriend, Lorna, a fiery redhead he met on the tennis court? A nurse at the Radcliffe, she has an extensive library of crime fiction, and a copy of Seldom’s latest book on her bedside table. Then again, it would be naive simply to rule out Seldom himself; or even, for that matter, our mysteriously unnamed narrator, as flattered by Seldom’s attention as Podorov is frustrated by his neglect. Or could there be two murderers at work, the original killer and a copycat?
The Oxford Murders is comfortably short enough to be read in a single evening, and the plot rattles along at an efficient pace, pausing occasionally to fill the reader in with a bit of necessary theoretical background, but never for too long, and always ready with a chilling revelation or another death to get things back up to speed. The prose is straightforward but has some nice touches, which I assume are present in the Spanish original as well as in Sonia Soto’s translation. On entering Mrs Eagleton’s house, Seldom and the narrator can ‘hear, like a muffled heartbeat, the stealthy to and fro of a clock’s pendulum’. When the plane bringing the narrator to Britain begins its descent into Heathrow, ‘the green hills of England appeared, undeniably true to life, in a light that had suddenly faded, or perhaps I should say deteriorated, because that was my impression: that, as the plane went down, the light was becoming increasingly tenuous, as if it were weakening and languishing, having passed through a filter.’
It’s refreshing to see such a familiarly English setting for a murder mystery as Oxford – most of the life having been wrung out of it in recent decades by Colin Dexter’s Inspector Morse stories – re-exoticised through the eyes of a visitor from the other side of the world. When Beth tells the narrator she sometimes feels as if she’d ‘give anything to get away from here’, he is surprised, replying that he ‘can’t imagine a more beautiful place’.
Yet, though he finds it beautiful, there is also a sense of anticlimax or disappointment in that description of arriving in England, expecting fabled green hills but finding them doused in thin grey light. And it’s canny of Martínez to introduce the idea of anticlimax so early in the story. ‘The aim of detective fiction, which makes it unique among literary forms’, is, as Bayard neatly puts it, ‘to prevent an idea from taking shape’. But if much of the excitement of reading a mystery story derives from being kept in the dark, the revelations at the end must always in some sense come as a disappointment. One way round this problem, the Raymond Chandler way, is to make the solution to the original mystery almost a side issue. Another way is to do what Martínez does, and incorporate that sense of disappointment into the solution, to make it to some extent the point. The narrator and the reader have together been seduced into the thrill of trying to solve an abstract logical puzzle. The unmasking of the culprit reveals that, however much they’ve been dressed up with intellectual fun and games, the motives behind the killings are at once intellectually simpler and emotionally more complex – but not less rational – than was previously supposed. Murders, even in fiction, are not like mathematical problems.