Pythagoras' Revenge

Pythagoras' Revenge: A Mathematical Mystery

ARTURO SANGALLI
Copyright Date: 2009
Pages: 208
https://www.jstor.org/stable/j.ctt7snwk
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  • Book Info
    Pythagoras' Revenge
    Book Description:

    The celebrated mathematician and philosopher Pythagoras left no writings. But what if he had and the manuscript was never found? Where would it be located? And what information would it reveal? These questions are the inspiration for the mathematical mystery novelPythagoras' Revenge. Suspenseful and instructive,Pythagoras' Revengeweaves fact, fiction, mathematics, computer science, and ancient history into a surprising and sophisticated thriller.

    The intrigue begins when Jule Davidson, a young American mathematician who trolls the internet for difficult math riddles and stumbles upon a neo-Pythagorean sect searching for the promised reincarnation of Pythagoras. Across the ocean, Elmer Galway, a professor of classical history at Oxford, discovers an Arabic manuscript hinting at the existence of an ancient scroll--possibly left by Pythagoras himself. Unknown to one another, Jule and Elmer each have information that the other requires and, as they race to solve the philosophical and mathematical puzzles set before them, their paths ultimately collide. Set in 1998 with flashbacks to classical Greece,Pythagoras' Revengeinvestigates the confrontation between opposing views of mathematics and reality, and explores ideas from both early and cutting-edge mathematics.

    From academic Oxford to suburban Chicago and historic Rome,Pythagoras' Revengeis a sophisticated thriller that will grip readers from beginning to surprising end.

    eISBN: 978-1-4008-2990-3
    Subjects: Mathematics, Language & Literature

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-viii)
  3. Preface
    (pp. ix-x)
  4. List of Main Characters
    (pp. xi-xii)
  5. Prologue
    (pp. xiii-xv)

    Pythagoras of Samos, the first man to call himself a philosopher—literally, a lover of wisdom—was a dominant figure in the history of ancient Greece. A brilliant mathematician and a mystic thinker, spiritual teacher, and political theorist, he embodies the intellectualism that was later to pervade classical Greek thought. The greatest Greek minds, from Aristotle to Proclus, all agree that he is the one who raised mathematics to the rank of a science.

    But other, more obscure aspects of his personality cast some doubts on the true nature of the personage, such as his belief in the transmigration of...

  6. PART I A TIME CAPSULE?
    • Chapter 1 THE FIFTEEN PUZZLE
      (pp. 3-9)

      “Do you know the game called the Fifteen Puzzle?” asked the man, who had introduced himself simply as “Mr. Smith.” Jule replied that he didn’t think so. “It was invented around 1870 by Sam Loyd,” the man went on, “one of America’s greatest puzzlists, and at the time it became very popular, much as Rubik’s cube did a century later.”

      Jule remembered his fascination with Rubik’s cube as a teenager. The twenty-six brightly colored little cubes he had endlessly rotated searching for the elusive solution, a configuration with a single color on each of the cube’s six faces. He also...

    • Chapter 2 THE IMPOSSIBLE MANUSCRIPT
      (pp. 10-18)

      “I’m afraid that would be impossible,” replied Johnston in a dry tone. That was not the answer Irena wanted to hear. She had made the trip to Oxford expecting to see Dr. Elmer J. Galway, professor of Classical History at Oriel College and a specialist in pre-Socratic philosophy, but instead of meeting the famous scholar she was talking to Bradley Johnston, a junior member of the faculty who had been trying his best to fulfill her expectations, so far with little success.

      Professor Galway had cancelled their appointment at the last moment and asked his colleague and former student to...

    • Chapter 3 GAME OVER
      (pp. 19-24)

      The words “Game Over” appeared on the screen in big, flashing characters. The man who wished to be called Mr. Smith but whose real name was Leonard Richter had been following the game on a monitor from his private study. Not that there had been much to follow. Unlike most of the other candidates who had battled until the very end trying to solve the puzzle, Jule had stopped playing after only a quarter of an hour, so the screen had displayed what looked like a frozen image of the board for the remaining forty-five minutes.

      Richter had first feared...

    • Chapter 4 A TRIP TO LONDON
      (pp. 25-31)

      As soon as he opened his eyes and had a look at his bedside clock on that Thursday morning in the late fall of 1997, Elmer James Galway had the odd feeling that his day was not going to be an ordinary one. To begin with, the sixty-three-year-old professor of classical history at Oxford University had slept late. This was not due to some alarm clock malfunction but rather to a dog failure. Slipper, his golden retriever—so named because of his predilection as a puppy for that particular object—had not climbed on the professor’s bed and gently woken...

    • Chapter 5 A LETTER FROM THE PAST
      (pp. 32-37)

      Elmer Galway and David Green were sitting facing each other in a cluttered office on the third floor of Green’s rare book shop in West London. They were separated by a glass-top table; a single object, wrapped in a piece of cloth, sat on it. Outside it was already dark at three o’clock in the afternoon and a fine drizzle was falling. It was equally dark inside the room, except for a floor lamp that spilled its cone of yellowish light on the table.

      They had been together for fifteen minutes, and up to that point Green had been doing...

    • Chapter 6 FOUND AND LOST
      (pp. 38-45)

      Monday came and went and Green had not yet heard from Galway. The translation may be taking the professor longer than he had anticipated, he thought. But he didn’t mind, for he had his hands full with the preparation of the new catalogue.

      On Tuesday morning, almost one week after he had first called, Alfonso Lopez de Burgos was back at Green’s shop. In the intervening time his hotel room had been broken into and he had spent three days in Hamburg on business. He was in a rather somber mood, contrasting with the expansive customer that had walked into...

    • Chapter 7 A DEATH IN THE FAMILY
      (pp. 46-50)

      Sir Ernest James Galway died peacefully in his sleep on November 28, 1997, the eve of his ninety-fourth birthday. The famous archaeologist lived alone in a semi-detached house with a small garden at the back, situated not far from the center of Cardiff. A housekeeper, who came on Fridays, discovered the old man’s body in his bed and communicated the sad news to his sons.

      By most standards, Ernest Galway’s life had been a full and happy one. Born in London in 1903, he was too young to serve his country in the Great War and too old for combat...

  7. PART II AN EXTRAORDINARILY GIFTED MAN
    • Chapter 8 THE MISSION
      (pp. 53-62)

      Lysis woke up abruptly, his heart thumping, his forehead covered with sweat. He had been dreaming of fire—again. Only this time the dream had seemed so real he could have sworn he had felt the scorching heat on his face and heard the screams, people yelling as if in pain, crying for help. He was an optimist by nature, used to looking at the bright side of things, but lately he had become possessed with a feeling that those dreams forebode some imminent calamity. The time was the second year of the 71st Olympiad, or 495 BC.

      Could my...

    • Chapter 9 NORTON THORP
      (pp. 63-68)

      Norton Thorp was born in Moscow in the spring of 1963, the only child of a middle-aged American diplomat who was serving his country in the Soviet Union during the cold war and a much younger Russian ballerina. Norton’s parents never married, and when Donald Thorp left Moscow to return to the United States, taking his fouryear-old son with him, Marina Golikova, the child’s mother, stayed behind, ostensibly for professional reasons. And so Donald’s younger sister Therese, a divorcee with no children of her own, became for all practical purposes Norton’s second mother—and part-time father as well, for Thorp’s...

    • Chapter 10 RANDOM NUMBERS
      (pp. 69-75)

      Johanna Davidson’s fascination with randomness dated back to her first course in probability and statistics. What she had found most intriguing was the fact that the teacher could not provide a satisfactory definition of “random” (or of “probability,” for that matter), even though notions such as “random variable” and “random sample” lie at the heart of the theory. She would later learn that this was not due to the lecturer’s imperfect knowledge of the subject, but rather to the difficulty of specifying what, for example, a random sequence of 0s and 1s precisely is. In fact, this question has a...

    • Chapter 11 RANDOMNESS EVERYWHERE
      (pp. 76-81)

      McGill University’s main campus is located in downtown Montreal, at the foot of the Mont Royal hill, the city’s principal landmark. Just beyond the semicircular stone-and-iron entrance gate and on the right sits Burnside Hall, a box-shaped concrete building housing the mathematics and statistics department.

      At two o’clock on a sunny afternoon in mid-April 1998, Burnside Hall’s main auditorium was almost packed, even though the lecture was not scheduled to start until 3:30. The speaker’s reputation had attracted an unusually large crowd for a mathematics talk. Its title, “Randomness at the Heart of Mathematics,” had aroused the interest of local...

    • Chapter 12 VANISHED
      (pp. 82-82)

      On Friday May 8, 1998, the news made the front page of every major newspaper:

      The celebrated American mathematician Norton Thorp, internationally acclaimed for his ground-breaking work in mathematics and artificial intelligence, is missing. He was last seen yesterday around noon by Mr. Frank Martino, the doorman of his apartment building. Following what appeared to be a heated discussion with two men in front of the building, Mr. Thorp was forced into a car by the two individuals, Mr. Martino said. He gave a description of the car and the men to the police.

      Mr. Thorp didn’t show up for...

  8. PART III A SECT OF NEO-PYTHAGOREANS
    • Chapter 13 THE MANDATE
      (pp. 85-86)

      The news from Croton could not have been more devastating. Archippus was dumbfounded. He sat motionless under the olive tree, one of the hundreds that dotted the hill overlooking the splendid harbor and the gulf beyond. All life seemed to have drained from his body, his left hand covering his face and the other still holding the papyrus scroll that his servant had just delivered.

      Archippus was amathematiko, a member of Pythagoras’ inner circle of disciples. He had come to Tarentum, his birthplace and one of Greater Greece’s principal cities, to attend to some family business that had kept...

    • Chapter 14 THE BEACON
      (pp. 87-97)

      When Dr. Gregory J. Trench finished his telephone conversation on an unseasonably warm evening in early January 1998, he was wearing a contented smile. The forty-four-year-old physician had been talking to his friend Leonard Richter, who had told him what he wanted to hear: the team was now complete. The team in question had nothing to do with his medical training and everything to do with his religious beliefs. To understand the connection, one must begin with the story of Trench’s conversion to an esoteric faith.

      Dr. Trench came from a Catholic family of second-generation Irish immigrants. His grandfather, Tobias...

    • Chapter 15 THE TEAM
      (pp. 98-105)

      Three years later, Trench had become a Companion, the secondhighest grade in the Order of The Beacon, a Neo-Pythagorean sect whose activities he had generously helped to fund.

      The Order operated in the most secretive fashion, so that practically nothing was known about it outside the close-knit circle of its fifty or so members. These, who called themselves “fellows,” were generally wealthy and influential professionals and businesspeople, some 20 percent of them women. In Pythagoras’ doctrines, which they interpreted with an emphasis on their esoteric aspects, they had found a kind of spiritual fulfillment that mainstream religions had not provided....

    • Chapter 16 THE HUNT
      (pp. 106-114)

      She had been introduced to Jule by Trench as “Professor Hirsch, an authority on ancient Greece.” And, after the customary exchange of polite greetings, Trench had added: “Professor Hirsch is presently writing a book about Pythagoras. She will be your resource person on him and his school.”

      Her full name was Laura Eva Hirsch. She was born in the former German Democratic Republic, where she studied Greek history and mythology before escaping to the United States as a political refugee with the help of a diplomat friend. In 1983, she received her PhD in classical studies from the University of...

    • Chapter 17 THE SYMBOL OF THE SERPENT
      (pp. 115-121)

      A week after Jule and Laura first met at the Temple, the search for Pythagoras reincarnate was in full swing. In the prevailing atmosphere of unwavering belief, Jule’s initial skepticism regarding reincarnation had somewhat abated. He had proposed setting up some kind of bait message on the Internet and in newspapers around the world which might get a response from a potential candidate but would mean nothing to others. Trench, however, would have none of that, for fear of being swamped with calls from all kinds of impostors and freaks in search of attention or worse.

      They began by looking...

    • Chapter 18 PROFESSIONAL JOB
      (pp. 122-125)

      Toward the end of January, Trench had news from one of his London agents: an ancient book believed to refer to Pythagoras was being offered at auction. Trench then decided to send Jule to London to look into the matter.

      “I need you to travel to London and take a look at a book that’s up for auction,” he told Jule over the phone. “You’ll be leaving tomorrow evening. I’ve already made plane and hotel reservations for you. Richter will give you an envelope with addresses and other details. Call me as soon as you know something.”

      “Sure”—that was...

    • Chapter 19 WITH A LITTLE HELP FROM YOUR SISTER
      (pp. 126-136)

      The winter of 1997–98 had been unusually mild and wet around the world, a climate anomaly that meteorologists blamed on the presence of a warm current in the eastern Pacific Ocean known as El Niño. In the Chicago area, the gray, rainy weather had persisted well after spring had set in, but there was not a single cloud in sight the morning of April 15, when Jule and Laura met with Trench and Richter to discuss the state of the Pythagoras search operation. That same morning, one thousand kilometers away, Johanna Davidson was driving from Boston to Montreal to...

  9. PART IV PYTHAGORAS’ MISSION
    • Chapter 20 ALL ROADS LEAD TO ROME
      (pp. 139-151)

      In mid-May 1998, Galway received official confirmation that his article on the Pythagorean manuscript had been accepted for publication in the prestigiousJournal of Ancient Philosophy and History.As for the manuscript itself, it had been bought at the auction by an anonymous collector for the sum of 420,000 pounds. It was not known whether the new owner intended to donate it to a museum or library. That posed a bit of a problem for Galway, who could not include the location of his translation’s primary source in his article.

      His satisfaction at having his paper accepted was tempered by...

    • Chapter 21 KIDNAPPED
      (pp. 152-157)

      The bedside clock read 11:20 p.m. James Parker, better known as Jim or Houdini, was lying in bed on his back, fully clothed, hands clasped under his head, reflecting on the day’s events. What should have been a smoothly executed operation had become a complicated one. He could blame it all on Rocky for mishandling Mr. T, but what was the use of laying blame at this point?

      Houdini remembered the meeting less than one week ago in Dr. Trench’s office. Dr. Trench had then stressed the importance of the operation for the members of the Order, who had long...

    • Chapter 22 THE LAST PIECE OF THE PUZZLE
      (pp. 158-168)

      The journalist fromThe Timeshad been waiting for half an hour when Elmer Galway rushed into the Senior Common Room clutching a pile of papers and file folders to his chest with one arm. He stopped for a moment to catch his breath, looked around, and then headed toward his visitor.

      “I’m terribly sorry for being so late, Mr. Morrison,” he said, extending his free hand. “I was held up at a very important meeting; the fate of our scholarly journals was at stake.”

      Thomas Morrison flashed an understanding smile, got to his feet, and shook Galway’s hand. He...

  10. EPILOGUE
    (pp. 169-170)

    “Cabin crew, take your seats.”The captain’s voice filled the dimly lit business class section of the cabin where Elmer Galway and Bradley Johnston were comfortably seated. British Airways flight 93 from London Heathrow to Toronto’s International Airport was on its final approach to its destination. Galway looked out the window. The aircraft was plunging into a sea of thick clouds and a light drizzle tapped on the window pane. It was the spring of 2000, almost two and a half years from the day Irena Montryan had first come to Oxford to seek Galway’s help for her exhibition and...

  11. Appendix 1: Jule’s Solution
    (pp. 171-172)
  12. Appendix 2: Infinitely Many Primes
    (pp. 173-174)
  13. Appendix 3: Random Sequences
    (pp. 175-176)
  14. Appendix 4: A Simple Visual Proof of the Pythagorean Theorem
    (pp. 177-177)
  15. Appendix 5: Perfect and Figured Numbers
    (pp. 178-180)
  16. Notes, Credits, and Bibliographical Sources
    (pp. 181-183)