The Oxford Murders

by Guillermo Martinez

  “Is it a problem that Arthur Seldom has set you?” he asked. “It was from him that I first heard about these symbols, in a lecture he gave at a conference on Fermat’s last theorem. You know, of course, that Fermat’s theorem is simply an extension of the problem of the Pythagorean triples, the sect’s best-kept secret.”

  “When was that?” I asked. “Not recently, surely.”

  “No, no, it was years ago,” he said. “So long ago that, as far as I can tell, Seldom doesn’t remember me. Of course, he was already the great Seldom then, while I was just an obscure graduate student from the small Russian town in which the conference was held. I showed him my work on Fermat’s theorem-it was all I thought about at the time-and I asked him to pass it on to the Number Theory group in Cambridge, but they were apparently too busy to read it. Well, not all of them,” he said. “One of Seldom’s students read my work, corrected my faulty English and published it under his own name. He was awarded the Fields Medal for the most important contribution of the decade to solving the problem. Now Wiles is about to take the final step thanks to those theorems. When I wrote to Seldom, he answered that there was an error in my work and that his student had corrected it.” Podorov laughed drily and exhaled a puff of smoke forcefully upwards. “My only mistake,” he said, “was that I wasn’t English.”

  I wished I had the power to make him stop talking. I felt again, as I had during my walk in the University Parks, that I was on the point of seeing something and that perhaps, if I were alone, the piece of the puzzle that had eluded me once would fall into place. I got up, murmuring a vague excuse, and quickly filled out a card so that I could borrow the book. I wanted to be outside, far away, in the night, away from everything. I rushed downstairs and, as I was heading out the door, I almost collided with a black-clad figure entering from the car park. It was Seldom, now wearing a raincoat over his dinner jacket. I suddenly realised it was raining.

  “You’ll get your book wet,” he said, and held out his hand to see what it was. “So you’ve found it. And I can see from your face that you’ve discovered something else, haven’t you? That’s why I wanted you to try to find it yourself.”

  “I bumped into my room-mate, Podorov. He said he met you once years ago.”

  “Viktor Podorov, yes. I wonder what he told you. I’d forgotten all about him until Inspector Petersen gave me the list of all the mathematicians at the Institute. I wouldn’t have recognised him anyway: I remember him as a rather troubled young man with a pointed beard, who thought he had a proof of Fermat’s theorem. It was only much later that I remembered that I’d given a talk about Pythagorean numbers at that conference. I didn’t want to mention it to Inspector Petersen. I always felt a little guilty about Podorov. I heard that he tried to commit suicide when my student received the Fields Medal.”

  “But it couldn’t have been him, could it?” I asked. “He was here in the library this evening.”

  “No, I never really thought it was him, but I knew he was probably the only person who would see immediately how the series continued.”

  “Yes,” I said, “he remembered your lecture perfectly.”

  We were standing beneath the semicircular awning at the entrance, getting splashed by the rain that was blowing in on gusts of wind.

  “Let’s make our way to the pub,” said Seldom.

  I followed him, shielding the book from the rain. The pub seemed to be the only place open in all of Oxford. It was full of people talking in booming voices and laughing, with the exhilaration and slightly artificial cheerfulness that the English only seemed to achieve after a lot of beer. We sat at a table, the wood marked with wet rings.

  “I’m sorry,” said the landlady from the bar, as if there was nothing she could do for us, “you’ve missed last orders.”

  “We can’t stay here long,” said Seldom. “I just wanted to know what you think, now that you know what the series is.”

  “It’s much simpler than anything a mathematician would have devised, isn’t it? Maybe that’s what’s ingenious about it, but it’s still a little disappointing. After all, it’s just one, two, three, four, like the series of symmetrical figures you showed me the first day. But maybe it isn’t a kind of puzzle, as we thought, but simply his way of enumerating the murders: first, second, third.”

  “Yes,” said Seldom, “that would be the worst-case scenario, because he could go on murdering indefinitely. But I still have hopes that the symbols are the challenge and that he’ll stop if we show him that we know what the series is. Inspector Petersen just called me from his office. He’s got an idea he thinks might be worth trying and apparently he has the psychologist’s approval. He’s changing tack regarding what appears in the papers: he’s going to let the Oxford Times run an article about the third murder on its front page tomorrow, with a picture of the triangle and an interview in which he’ll mention the first two symbols. The interview questions are going to be carefully prepared so as to make Petersen appear baffled by the murders and outwitted by the murderer. According to the psychologist, that’ll provide our man with the sense of triumph he craves.

  “The short note about the tetraktys that I wrote for Petersen will appear, with my name, in Thursday’s edition, in the same section in which they published the chapter on serial murders from my book. That should be enough to show him that I know and can predict the symbol for the next murder. That keeps it on the level of the almost personal challenge that he seemed to lay down at the beginning.”

  “But supposing it works,” I said, slightly taken aback, “supposing, with luck, he reads your note in Thursday’s paper and that, with a lot more luck, it stops him, how is Inspector Petersen going to catch him?”

  “Petersen thinks it’s only a matter of time. I think he’s hoping that eventually a name will emerge from the list of those attending the concert. Anyway, he seems determined to try anything to avoid a fourth murder.”

  “The interesting thing is that we’ve now got everything we need to predict the next step. I mean, we’ve got the three symbols, like in one of Frank Kalman’s series, so we should be able to infer something about the fourth murder, to link the tetraktys…but to what? We still don’t know anything about the link between the deaths and the symbols. But I’ve been thinking about what that doctor, Sanders, said, and I’ve found a recurring theme: in all three cases the victims were, in a way, living on borrowed time, longer than expected.”

  “Yes, that’s true,” said Seldom, “I hadn’t noticed…” His gaze became lost in the distance for a moment, as if he felt suddenly tired, overwhelmed by the constant ramifications of the case. “I’m sorry,” he said, unsure of how long his mind had been elsewhere. “I’ve got a bad feeling about this. I’d thought it a good idea to publicise the series. But perhaps there’s too much time between tomorrow and Thursday.”

  Eighteen

  I still have that Monday’s copy of the Oxford Times, with the careful mise en scene for the benefit of a single phantom reader. As I now look at the slightly faded picture of the dead percussionist and the symbols, and reread the questions prepared for Inspector Petersen, I again sense, as if I were being touched by icy fingers, the shudder in Seldom’s voice when he said perhaps there was too much time until Thursday. Above all, I understand, seeing them still clinging to the page, the horror he felt at the way conjectures in the real world acquired a mysterious life of their own. But on that particular bright morning I was free of premonitions and read about the case enthusiastically, and not without a little pride and no doubt some foolish vanity, knowing almost all of it already.

  Lorna phoned me early. She sounded very excited-she too had just seen the article in the paper and she wanted us to have lunch together so that I could tell her absolutely everything. She couldn’t forgive herself, or me, for having let her stay at home the previous evening while I was there at the concert. She hated me for it, but she’d escape from the hospital at lunchtime and meet me at the French café in Little Clarendon Str
eet, so I shouldn’t even think of planning anything with Emily for lunch. We met at the Cafe de Paris and laughed and chatted about the murders and ate crepes with ham in the slightly irresponsible, invulnerable way of happy young lovers. I told Lorna what Inspector Petersen had said: the percussionist had had a very serious lung operation and his doctor was surprised that he hadn’t died sooner.

  “The same as with Ernest Clarck and Mrs Eagleton,” I said and waited for her reaction to my little theory. She thought for a moment.

  “But that wasn’t really Mrs Eagleton’s case,” she said. “I saw her at the hospital a couple of days before she died and she was delighted because tests had shown that her cancer was in remission. The doctor had told her she might live quite a few more years.”

  “Well,” I said, as if that were a minor objection, “that must have been a private conversation between her and her doctor, there was no way the murderer could have known.”

  “So he chooses people who are living longer than expected? Is that what you mean?”

  Her face darkened for a moment and she pointed to the television behind the bar, which she was facing. I turned and saw the smiling face of a little girl with curly hair on the screen and, beneath it, a telephone number and a request for all of the UK to call.

  “Is that the little girl I saw at the hospital?” I asked Lorna. She nodded.

  “She’s top of the national transplant list now. She’s got forty-eight hours at the most.”

  “How’s the father?” I asked. I still vividly remembered the frantic look in his eyes.

  “I haven’t seen him for a few days. I think he’s had to go back to work.”

  She put out her hand and intertwined her fingers in mine, as if to dispel the sudden dark cloud, and ordered another coffee. I drew a diagram on a napkin to show her the percussionist’s location on the stage and asked if she knew of any way of inducing a respiratory arrest.

  Lorna thought for a moment, stirring her coffee.

  “I can only think of one way that would leave no trace: someone with sufficient strength could have climbed up the back and blocked the percussionist’s mouth and nose with his hand. It’s known as Burke’s Death, after William Burke. Maybe you’ve seen his wax figure at Madame Tussaud’s. He kept a lodging house in Edinburgh in the 1820s. He killed sixteen people and sold the bodies for dissection. It wouldn’t take more than a few seconds to suffocate a person with very reduced lung capacity. I’d say that’s how the murderer was killing the percussionist, when the spotlight swung back to him. He let go immediately, but the man was already in pulmonary and probably cardiac arrest too. What you all saw-the man holding his throat, as if he were being strangled by a ghost-was the typical reflex reaction of someone who can’t breathe.”

  “Another thing,” I said. “Have you spoken to your friend the forensic pathologist again about Mr Clarck’s postmortem? Inspector Petersen believes he has a different explanation.”

  “No,” said Lorna, “but he’s asked me out to dinner several times. Do you think I should say yes and try to find out more?”

  “No, no,” I said, laughing. “I can live with the mystery.”

  Lorna glanced at her watch.

  “I’ve got to get back to the hospital,” she said, “but you still haven’t told me about the series. I hope it’s nothing too difficult, I’ve forgotten all my maths.”

  “No, the surprising thing is precisely how simple the solution is. The series is just one, two, three, four…in the notation used by the Pythagoreans.”

  “The Pythagorean Brotherhood?” asked Lorna, as if this stirred a vague memory.

  I nodded.

  “I studied them briefly as part of my course, in History of Medicine. They believed in the transmigration of souls, didn’t they? As far as I can remember they had a very cruel theory on the mentally retarded, which the Spartans and the doctors of Croton later put into practice. They valued intelligence highly and believed that the retarded were the reincarnation of people who had committed terrible sins in previous lives. They waited until they were fourteen, a critical age for those with Down’s Syndrome, and they used the ones that survived as guinea pigs in their medical experiments. They were the first to try organ transplants. Pythagoras himself had a gold thigh. They were also the first vegetarians, but they weren’t allowed to eat beans,” she said with a smile. “And now I really must go.”

  We said goodbye outside the café. I had to get back to the Institute to write up the first report for my grant and I spent the next two hours going over papers and transcribing references. At a quarter to four I went downstairs, as I did every afternoon, to the Common Room, where the mathematicians gathered for coffee. The room was fuller than usual, as if nobody had stayed in their office that day, and I immediately heard the excited murmurs. Seeing them all together-shy, untidy, polite-I remembered Seldom’s words. Yes, here they were, two and a half millennia later, queuing for their coffee in an orderly fashion, coins in hand, the ardent disciples of Pythagoras. There was a newspaper lying open on one of the tables and I assumed they were discussing the series of symbols. But I was wrong.

  Emily joined me in the queue and said, with shining eyes, as if letting me in on a secret that still only few people knew: “He’s done it, apparently.” She said it as if she still couldn’t believe it herself. When she saw my puzzled look, she added: “Andrew Wiles! Haven’t you heard? He’s asked for two extra hours tomorrow at the Number Theory conference in Cambridge. He’s proving the Shimura-Taniyama conjecture. If he gets to the end, he’ll have proved Fermat’s last theorem. A group of mathematicians are planning to go to Cambridge to be there tomorrow. It may be the most important day in the history of mathematics.”

  Podorov arrived, looking sullen as usual. When he saw the queue he decided to sit and read the newspaper. I approached him, balancing a brimming cup of coffee and a muffin. Podorov looked up from the paper and glanced around contemptuously.

  “So, have you signed up for the outing tomorrow? I can lend you my camera,” he said. “They all want a little photo of Wiles’s blackboard with the QED.”

  “I’m not sure I’ll be going,” I said.

  “Why not? There’s a free bus and Cambridge is a beautiful place too, in a very English way. Have you been?”

  As he turned the page absently, his eyes alighted upon the long article about the murders and the series of symbols. He read the first two or three lines and, alarmed, wary, looked at me.

  “You knew all about it yesterday, didn’t you? How long have these murders been going on?” he asked.

  I said that the first one occurred almost a month ago, but that the police had only now decided to reveal the symbols.

  “And what is Seldom’s part in all this?”

  “The notes after each murder are addressed to him. The second message, with the symbol of the fish, appeared here, stuck to the revolving door at the entrance.”

  “Ah, yes, I remember a small disturbance that morning. I saw the police, but I thought someone had broken a window.”

  He went back to the newspaper and finished reading the article.

  “But Seldom’s name doesn’t appear anywhere here.”

  “The police don’t want to reveal that the three messages have been addressed to him.”

  He looked at me again but his expression had changed: he now seemed amused.

  “So someone is playing cat and mouse with the great Seldom. Perhaps there is divine justice after all. Dispensed by a mathematician god, of course,” he said mysteriously. “What do you imagine the fourth murder will be like?” he asked. “A death in keeping with the ancient solemnity of the tetraktys?” He looked around as if searching for inspiration. “I seem to remember that Seldom liked bowling, at least at one time,” he said. “The game wasn’t very well known in Russia then. In his lecture, he compared the points of the tetraktys to the layout of the pins at the start of a game. And there’s a shot where you knock down all ten pins on the first ball.” />
  “Strike,” I said.

  “Yes, exactly. Isn’t that a magnificent word?” And he repeated it in his strong Russian accent, smiling strangely, as if he was picturing an implacable ball and heads rolling. “Strike!”

  Nineteen

  By five o’clock I’d finished the first draft of my report. Before leaving the office I checked my e-mail again. There was a short message from Seldom asking me to meet him at Merton after his seminar, if I was free. I’d have to hurry to get there on time. I climbed the small staircase that led to the classrooms and, peering through the glass door, saw him discussing a problem on the blackboard with two students who had stayed behind.

  The students left and he motioned for me to enter. While he put away his notes, he pointed to a circle drawn on the board and said:

  “We were discussing Nicholas of Cusa’s geometrical metaphor-the truth as a circumference and human attempts to approach it as a series of inscribed polygons, with more and more sides, coming close in the end to a circular form. It’s an optimistic metaphor, because successive stages enable one to sense the final figure. There is, however, another possibility, one that my students still aren’t aware of and which is much more discouraging.” Beside the circle he quickly drew an irregular figure with numerous points and clefts. “Suppose for a moment that the truth was the shape, say, of an island like Britain, with a very irregular coastline, with endless projections and inlets. This time, when you try to approximate the figure by means of polygons, you encounter Mandelbrot’s paradox. The edge remains elusive, breaking up at each new attempt into ever more projections and inlets, and human efforts to determine it simply never arrive at a final figure. Similarly, the truth may not yield to the series of human approximations. What does this remind you of?”