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 mirahilis 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 hatter. 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
* * *
* The great unsolved problems stated by David Hilbert at the International Congress of Mathematicians in 1900. Some, like the Eighth Problem (the Riemann Hypothesis) are still outstanding, but in others there has been progress and a few have been completely solved — as, for example, the Fifth, proved by Gleason, Montgomery and Zippen; the Tenth, by Davis, Robinson and Matijasevic; the Fourteenth, proved false by Nagata; the Twenty-second, solved by Deligne.
* Gödel subsequently ended his own life, in 1978, while being treated for urinary tract problems at the Princeton County Hospital. His method of suicide was, like his great theorem, highly original: he died of malnutrition, having refused all food for over a month, convinced that his doctors were trying to poison him.
* Mystery-solutions to famous problems by charlatans are two-a-penny.
* Fermat’s Last Theorem was, amazingly, proved in 1993. Gerhard Frey first proposed that the problem could possibly be reduced to an unproven hypothesis in the theory of elliptic curves, called the Taniyama-Shimura Conjecture, an insight later conclusively proven by Ken Ribet. The crucial proof of the Taniyama-Shimura Conjecture itself (and thus, as its corollary, Fermat’s Last Theorem) was achieved by Andrew Wiles; in the final stage of his work he collaborated with Richard Taylor.
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
A Note on the Author
Apostolos Doxiadis received a Bachelor’s Degree in Mathematics from Columbia University in New York and a Master ‘s Degree in Applied Mathematics from the École Pratique des Hautes Etudes in Paris. He has run a number of successful computer companies, as well as written and directed for both the screen and the stage. The second of his two feature films, Tetriem, won the prize of the International Center for Artistic Cinema at the 1988 Berlin International Film Festival. Apostolos Doxiadis lives in Athens, Greece.
Praise for Uncle Petros and Goldbach’s Conjecture
‘The most dramatic book I’ve read all year, with ambition, betrayal and greedy self-sacrifice to rival anything you’d find in an opera.’
–Newsday
‘An intellectual thriller that manages to convey the high drama and
excitement involved in the pursuit of an answer… Delightful, fun,
well-conceived and nicely executed.’ –Kirkus Reviews
‘An intriguing debut… Doxiadis keeps the story engaging…
the novel is captivating.’ –Publishers Weekly
‘A mathematical conjecture unsolved for two centuries; a
mathematical genius uncle driven mad trying to solve it; an
ambiguous relation with a mathematically-minded nephew; and
acute human observation all come together in Uncle Petros to make
a very funny, tender, charming and, to my mind, irresistible novel.’
—Oliver Sacks, M.D.
‘Delightful and original… Although framed by math, the Uncle
Petros story easily extends interest beyond the scientific minded.’
–Booklist
‘A charming novel.’ –LA Times
‘Paints a fascinating picture of how a mathematician could fall into
a mental trap by devoting his efforts to a too difficult problem.’
John Nash, Nobel Laureate, 1994, subject of A Beautiful Mind
‘It is brilliantly written—a mathematical detective story of great
charm—and it certainly succeeds in capturing much of the spirit of
mathematical research.’–Sir Michael Atiyah, winner of the Fields
Medal and world-renowned mathematician
‘A compelling portrait of a talented young mathematician.’
—Professor Ken Ribet, University of California, Berkeley
‘If you think of math as a set of boring rules, Apostolos Doxiadis’
suspenseful, page-turning first novel Uncle Petros & Goldbach’s
Conjecture is certain to shatter your preconceptions… It is a novel
about life choices. At every point, it revolves around the question:
which is better, to pursue a possibly unattainable ideal, or to set
attainable goals? … Without offering any easy answer, Doxiadis gives
us
another vivid dramatization of what the question entails. And it
is greatly to his credit that he manages to lighten the drama with
considerable wit and humor.’ –Boston Herald
‘Petros Papachristos is … the invention of Apostolos Doxiadis. But
the story of his life is enriched with so many authentic details from
history in general and from science in particular that one feels
tempted to look him up in a biographic dictionary.’
–Scientific American
‘A fascinating, captivating, intellectual joy ride.’ –Miami Herald
‘This is a most attractive book—modest, domestic, gracefully and
humbly written. For his attempts to reveal to us some of the
extraordinary beauties of mathematical thought, Apostolos
Doxiadis deserves the gratitude of innumerates everywhere.’
–London Times
‘This charming mathematical detective story is a gripping read; even
to a number theory numbskull, it adds up… Marvelous.’
–UK Daily Mail
Also by Apostolos Doxiadis
The #1 New York Times bestseller
LOGICOMIX: AN EPIC SEARCH FOR TRUTH
“Logicomix is like no other book of its kind … wonderfully imaginative, funny and gripping.”— San Francisco Chronicle
“An engaging, energetic work that makes big ideas accessible without dumbing them down.”— Washington Post
Tis innovative graphic novel is based on the early life of the brilliant philosopher Bertrand Russell and his lifelong pursuit of truth. Haunted by family secrets and unable to quell his youthful curiosity, Russell became obsessed with a Promethean goal: to establish the logical foundations of all mathematics.
In his agonized search for absolute truth, Russell crosses paths with legendary thinkers like Gottlob Frege, David Hilbert and Kurt Gödel, and fnds a passionate student in the great Ludwig Wittgenstein. But the object of his defning quest continues to loom before him. Trough love and hate, peace and war, Russell persists in the dogged mission that threatens to claim both his career and his personal happiness, fnally driving him to the brink of insanity.
Logicomix is at the same time a historical novel and an accessible introduction to some of the biggest ideas of mathematics and modern philosophy. With rich characterizations and expressive, atmospheric artwork, it spins the pursuit of these ideas into a highly satisfying tale.
Probing and ingeniously layered, the book throws light on Russell’s inner struggles while setting them in the context of the timeless questions he spent his life trying to answer. At its heart, Logicomix is a story about the confict between an ideal rationality and the unchanging, flawed fabric of reality.
Paperback * $22.95
Bloomsbury USA
Available wherever books are sold
Copyright © 1992, 2000, 2010 by Apostolos Doxiadis
All rights reserved. No part of this book may be used or reproduced in any manner whatsoever without written permission from the publisher except in the case of brief quotations embodied in critical articles or reviews. For information address Bloomsbury USA, 175 Fifth Avenue, New York, NY 10010.
Published by Bloomsbury USA, New York
LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA HAS BEEN APPLIED FOR.
ISBN 978-1-58234-128-6 (paperback)
First published in Greek by Kastioniotis Editions as O Theios Petros kai i Eikasia tou Golbach
First published in the U.S. by Bloomsbury Publishing in 2000
Reissue published by Bloomsbury USA in 2010
This e-book edition published in 2010
E-book ISBN: 978-1-60819-644-9
www.bloomsburyusa.com
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