The Strange Case of Mr. Jean D.
João Filipe Queiró
The Mathematical Intelligencer, 5, p. 78-80, 1983
Jean D. woke up late that morning,
feeling slightly indisposed. He was in Paris to attend the 86243rd
session of the Séminaire de Théologie et Mathématiques, which
would take place in the afternoon, and he was staying at the Hôtel
Nicolas, as usual.
He called for breakfast, which was
promptly brought to him with the morning newspaper. He glanced at
the front page and noticed a box in the lower right corner:
“Mathematical Phenomenon Discovered—See page 7.” Intrigued,
Jean D. opened the newspaper and read:
Mathematical Phenomenon Discovered: TOKYO—Two Japanese computer
scientists, after a successful attempt to beat the world record
of the largest number of decimals of π, detected a most
strange phenomenon. In effect, the last ten digits they obtained
coincide exactly with the first ten digits in the
decimal expansion of π: 1415926535. This is an
extraordinary coincidence, and they are now running their
program again to see what comes after that. In the meantime, Dr.
Toshiro Aoki, a Professor of Mathematics at Tokyo University,
where this work is being carried out, has called attention to a
two-century-old theorem that, he says, implies no more
repetitions should be expected.
Jean D. put the paper aside impatiently.
He really had no time to waste with such nonsense. He finished
breakfast, dressed, and left.
At the École Nationale, rue
d’Austerlitz,
he
used
the
stairs,
as
usual,
to
reach
the
seventh floor where the Department of True Mathematics was
situated. He found nobody there. The library was deserted, and the
offices were empty. Jean D. noticed that on some tables there were
books open, as if the readers had left hastily. “Il n’y a
personne?” he asked a woman from the cleaning service who
was passing by. She told him that, some two hours before, all the
professors had gone down to the basement, to the Department of
Computer Science. Jean D., slightly surprised, thanked the woman
and went back into the library.
Forty-five minutes later, in the still
deserted library, he emerged from the rows of shelves with the
decision to go and see what this was all about.
In the Department of Computer Science
all the corridors were empty, but Jean D. could hear the sound of
excited conversations coming from a room. Before entering, he read
the inscription on the door: Salle de l’ordinateur. Inside it was crowded. When he came in,
everybody fell silent. On his left, the big new computer, the
CLAY-3, was surrounded by twenty or so young assistants, who
stared at him coldly. On his right, there was a group of his
colleagues from the Department of True Mathematics, and they
seemed relieved with his appearance. “Qu’est-ce qui se passe?”
Jean D. asked, walking in their direction. To his surprise,
they told him that, since dawn, the CLAY-3 had been repeating the
Japanese calculation of π, just to see what happened. Jean D., who
had almost forgotten about what he had read that morning in the
newspaper, interrupted them, exasperated: “Quoi?” And he
lectured them right there on the foolishness of wasting their
precious time with such things and near such people (pointing
toward the young men around the computer). As he was beginning to
quote a famous sentence from his History of True Mathematics concerning
the work of Lambert on the irrationality of π, one of his
colleagues tried to interrupt and explain something to him. At
that precise moment, red lights began to blink on the other side
of the room, there was a strange sound, and then everybody (except
Jean D.) ran to look at something near the computer. The young
assistants erupted in cheers, and the same colleague that had
tried to interrupt Jean D. came back and told him somberly that,
with the one just produced, there were already nineteen digits in
the decimal expansion of π after the 5000000th that coincided
precisely with the first nineteen after the 3. Jean D. lost his
temper and walked out of the room, violently slamming the door.
He had lunch in a restaurant near the École
and then went for a little walk to spend the time until the
hour of the Séminaire. He
stopped at a bookstore. The afternoon newspapers had just arrived.
A headline caught his attention: “Japanese Experiment Confirmed
All Over the World.” He bought the paper and read:
NEW YORK—Several supercomputers throughout the
U.S. and Europe have been
calculating the decimal expansion of π further
and further. All the results agree that something extraordinary
happens near the 5000000th decimal place. The digits begin to
repeat exactly the original sequence 14159.
. . This repetition has been checked by some computers
for several hundred digits already. This suggests that a
periodicity occurs, contradicting everything mathematicians have
been saying ever since, in the eighteenth century, the Swiss
mathematician Lambert first asserted that π is irrational.
The probability that a number with such behaviour is
irrational is now virtually zero, some experts say. This story
has already had some unexpected implications: a professor at
the University of Chicago was savagely beaten this morning by
a student who two days ago had failed a written examination
precisely because of a question about the irrationality of π.
Jean D. threw the paper away and hurried
to the École. The atmosphere on the seventh floor was
somber. Almost everybody was gone. The Séminaire had been
adjourned. “What do you make of this?” an Irish professor who had
also come to attend the Séminaire quietly asked Jean D.
“Complete stupidity,” he muttered, heading for the basement. In
the Salle de l’ordinateur he found only the young
assistants and some students around the computer. The “right”
digits kept coming. His colleagues from True Mathematics were
gone. He felt a terrible hostility directed against him.
Climbing the stairs to the seventh floor
again, Jean D. tried to keep cool. Everybody was crazy, and the
responsibility rested upon him of protecting True Mathematics in
this crisis.
He found the Irish professor in the
library going through Legendre’s proof of the irrationality of π.
“Are you out of your mind?” Jean D. yelled. “Do you really believe
there’s a mistake in that?” The Irish professor looked at him,
shrugged his shoulders, and resumed his meditation. Jean D. headed
for the stairs. This was too much for him.
Down in the lobby he was recognized by
some students who insulted him. They blocked the way out and began
shouting slogans against True Mathematics. Jean D. looked for an
escape. He tried the door of the Department of Computer Science.
It was locked. The students approached, shouting and insulting
him. Jean D. turned to them, his vision clouded, and said: “Vivent
les Mathématiques Vraies!” He then tottered and fell to the
floor, losing consciousness.
At this moment, Jean D. woke up for
real. Still haunted by his nightmare, he called for breakfast. The
waiter brought it, and with it the morning newspaper. Jean D. took
the paper from the waiter’s hands and feverishly looked through
all the pages. Then he sat down on the couch, an expression of
immense relief on his face. The waiter, meanwhile, looked at him
astonished. “Que voulez-vous?” yelled Jean D., “Allez-vous-en!
Allez-vous-en!”
The stunned waiter left the
room. “Ils sont fous, ces mathématiciens,” he thought.
(I stole this idea from a story by the late
Yugoslavian writer Ivo Andric. The original character was a rich
man who woke up in a world where money, even the idea of money,
had ceased to exist.)