'Mum's the word,' I said.
He had started to close the door. Convinced now that his situation was extremely serious and that the time had come for emergency action, I grasped the knob and started to push. As he felt my force, he tensed up, gritted his teeth and struggled to prevent me from entering, his face contorted to a grimace of desperation. Fearing the effort might be too much for him (he was nearing eighty, after all) I reduced the pressure a bit for a final attempt at reason.
Of all the possible stupid things I could have said to him, I chose this: 'Remember Kurt Gödel, Uncle Petros! Remember the Incompleteness Theorem – Goldbach's Conjecture is unprovable!'
Instantly, his expression changed from despair to wrath. 'Fuck Kurt Gödel,' he barked, 'and fuck his Incompleteness Theorem!' With an unexpected upsurge of strength, he overcame my resistance and slammed the door shut in my face.
I rang the bell again and again, banged the door with my fist and shouted. I tried threats, reasoning and pleading, but nothing worked. When a torrential October rain began to fall I hoped that, mad or not, Uncle Petros might be moved by mercy and let me in. But he wasn't. I left, soaking wet and very worried.
From Ekali I drove straight to our family doctor and explained the Situation. Without altogether ruling out serious mental disturbance (possibly triggered by my unwarranted interference in his defence mechanisms) he suggested two or three organic problems as likelier causes of my uncle's transformation. We decided to go to his house first thing the next morning, force our way in if necessary, and submit him to a thorough medical examination.
That night I couldn't sleep. The rain was getting stronger, it was past two o'clock and I was sitting at home hunched in front of the chessboard, just as Uncle Petros must have been on innumerable sleepless nights, studying a game from the recent world championship. Yet my concern kept interfering and I couldn't concentrate.
When I heard the ringing I knew it was he, even though he'd never yet initiated a call on his newly installed telephone.
I jumped up and answered.
'Is that you, Nephew?' He was obviously all worked up about something.
'Of course it's me, Uncle. What's wrong?'
'You must send me someone. Now!'
I was alarmed. '"Someone"? A doctor you mean?'
'What use would a doctor be? A mathematician, of course!'
I humoured him: 'I'm a mathematician, Uncle; I’ll come right away! Just promise to open the door, so I won't catch pneumonia and -'
He obviously didn't have time for irrelevancies. 'Oh hell!' he grunted and then: 'All right, all right, you come, but bring another one as well!'
'Another mathematician?'
'Yes! I must have two witnesses! Hurry!'
'But why do the witnesses have to be mathematicians?'
Naively, I had thought at first he wanted to write his will.
'To understand my proof!'
‘Proof of what?’
'Goldbach's Conjecture, you idiot – what else!'
I chose my next words very carefully. 'Look, Uncle Petros,' I said, 'I promise to be with you as soon as my car will get me there. Let's be reasonable, mathematicians aren't kept on call – how on earth can I get one at two o'clock in the morning? You'll tell me all about your proof tonight and tomorrow we will go together -'
But he cut me off, screaming. 'No, no, no! There's no time for any of that! I need my two witnesses and I need them now!’ Then he broke down and started sobbing. 'O nephew, it's so… it's so…'
'So what, Uncle? Tell me!'
'Oh, it's so simple, so simple, my dearest boy! How is it possible that all those years, those endless years, I hadn't realized how blessedly simple it was!'
I cut him off. ‘I’ll be there as soon as I can.'
'Wait! Wait! Waaaaa-it!!!' He was now in panic. 'Swear you won't come alone! Get the other witness! Hurry… Hurry up, I implore you! Get the witness! There's no time!'
I tried to appease him: 'Oh, come on, Uncle; there can't be such a rush. The proof won't go away, you know!'
These were his last words: 'You don't understand, dear boy – there's no time left!' His voice then dropped to a low, conspiratorial whisper, as if he didn't want to be overheard by someone close by: 'You see, the girls are here. They are waiting to take me.'
By the time I arrived in Ekali, breaking all speed records, it was too late. Our family doctor (I had picked him up on the way) and I found Uncle Petros' lifeless body slumped on the paving of his little terrace. The torso was leaning against the wall, the legs spread open, the head turned towards us as if in welcome. A flash of distant lightning revealed his features fixed in a wonderful smile of deep, absolute contentment – I imagine it was that which guided the doctor in his instant diagnosis of a stroke. All around him were hundreds of lima beans. The rain had destroyed their neat parallelograms and now they were scattered all over the wet terrace, sparkling like precious jewels.
The rain had just stopped and the air was infused with the invigorating smell of wet earth and pine trees.
Our last exchange over the telephone is the only evidence of Petros Papachristos' mystery-solution to Goldbach's Conjecture.
Unlike Pierre de Fermat's illustrious marginal note, however, it is extremely unlikely that my uncle's demonstratio mirabilis of his famous problem will tempt a host of mathematical hopefuls to attempt to reproduce it. (No rise in the price of beans is expected.) This is as it should be. Fermat's sanity was never in question; no one ever had reason to believe he was in anything less than total possession of his senses when he stated his Last Theorem. Unfortunately, the same cannot be said of my Uncle Petros. When he announced his triumph to me he was probably as mad as a harter. His last words were uttered in a state of terminal confusion, the total relinquishment of logic, the Night of Reason that dimmed the light of his final moments. It would thus be extremely unfair to have him posthumously declared a charlatan by attributing a serious intention to a declaration obviously made in a half-delirious state, his brain most probably already ravaged by the stroke that, a short while later, killed him.
So: did Petros Papachristos prove Goldbach's Conjecture in his final moments? The wish to protect his memory from any chance of ridicule obliges me to state it as unequivocally as possible: the official answer must be 'No'. (My own opinion need not concern mathematical history – I will therefore keep it to myself.)
The funeral was strictly family, with only a wreath and a single representative from the Hellenic Mathematical Society.
The epitaph later carved on Petros Papachristos' tomb, below the dates marking the limits of his earthly existence, was chosen by me, after I had overcome the initial objections of the family elders. They form one further addition to the collection of posthumous messages that make the First Cemetery of Athens one of the world's most poetic:
EVERY EVEN NUMBER GREATER THAN 2
IS THE SUM OF TWO PRIMES
Post Scriptum
At the time this book was completed, Goldbach's Conjecture was two hundred and fifty years old. To this day it remains unproven.
Acknowledgements
I wish to thank Professors Ken Ribet and Keith Conrad, who carefully read the revised manuscript and corrected numerous mistakes, as well as Dr Kevin Buzzard for the clarification of various points – obviously, any remaining mathematical flaws are my own. Also my sister, Cali Doxiadis, for her invaluable linguistic and editorial advice.
APOSTOLOS DOXIADIS
