Miss Liberty and I were standing
outside a gypsy doctor’s tent. The sign at the door read:
Enter
here.
!!!
SEE !!!
the
amazing DOCTOR MEMORY!!
Sees all!
Hears
all!
Tells
all!
-
prognostications and divinations a specialty -
The
Key To The Future Is Yours!
We entered the tent. Bells jingled.
Inside was Dr. Memory, sitting at a
small circular desk. Dr. Memory was wearing a star-spangled robe and a turban.
On the desk were two glowing crystal balls.
“Ahh!” Dr. Memory cried as we
entered. “The balls are clearing again! The left ball is the Sun, the right
ball is the Moon. Put what you want between them, and your future begins.”
Liberty put a $0 bill in between.
“Thank you,” Dr. Memory said
greasily. Then he closed his eyes and
said. “Alas, I see the seal of doom upon you! You shall soon meet your
unmaker!”
Liberty asked, “When?”
Dr. Memory said, “After I answer
your questions. First question, please.”
“I assume that you have heard of the
Pythagorean Theorem,” said Liberty.
Dr. Memory touched his turban. One
of the crystal balls clouded over; then it showed the following formula:
a2 + b2
= c2.
She continued, “And I assume you
know the solutions to that equation, in the integers.”
The other crystal ball clouded over,
then showed:
a = (m2
- n2) k,
b = (2mn)
k,
c = (m2
+ n2) k,
“And those are all the integer
solutions,” said Dr. Memory.
“Very exact!” said Miss Liberty.
“But I was wondering about that equation there.” She pointed to the first
crystal ball. “Suppose we change the exponent to a general integer n.” The
first crystal ball clouded over, then showed:
an + bn
= cn
“I was wondering about its solutions
for n bigger than 2. Are there any?”
“That equation has no solutions in
integers when n is greater than or equal to three.”
Miss Liberty asked, “You’re sure of
this.”
“I have memorized the proof,” said
Dr. Memory. “Next question, please.”
Miss Liberty said, “Well, I noticed
a funny pattern. Take a look at this.” She pointed at the second crystal ball.
It clouded over, then showed:
4 = 2+2
6 = 3+3
8 = 3+5
10 = 5+5
12 = 5+7
14 = 7+7
16 = 5+11
Miss Liberty said, “Note how all the
numbers on the left are even.”
Dr. Memory said, “I so note.”
She continued, “And note how all the
numbers on the right are prime.”
Dr. Memory said, “I so note.”
Miss Liberty said, “So I wonder if
this pattern continues. Is every even number bigger than 2 a sum of two
primes?”
“Every even integer from four to a
thousand is a sum of two primes,” said Dr. Memory.
“So far, so good.”
“I have proven that every even
integer from four to a million is a sum of two primes.”
“This looks like a trend!” said
Liberty.
“Now I have proven it for every even
integer from four to a billion.”
“Good work!”
After thinking awhile, Dr. Memory
said, “Now I have a proof for four to a trillion.”
“You’re getting closer! Now on to a
quadrillion! A googol! A googolplex!”
Dr. Memory said, “I must meditate
further on this question.” He closed his eyes, then re-opened them. “Next
question, please.”
Miss Liberty pointed at the second
crystal ball; it clouded over and showed:
zeta(s) = 1/1s
+ 1/2s + 1/3s + 1/4s + ...
“Zeta is defined on the complex
numbers, you understand,” said Miss Liberty.
“I understand,” said Dr. Memory.
“I was wondering about the real part
of zeta’s roots.”
After thinking awhile Dr. Memory
said, “I have found a root of the zeta function. Its real part is one-half. I
have found another root. Its real part is also one-half. I have found all roots
within one hundred units of the real axis. All their real parts are one-half.”
“Another trend! So my third question
is: do all of zeta’s roots have real part one-half?”
“Every root within one thousand
units of the real axis has real part equal to one-half.”
“Almost a proof!”
“Within one million units.”
“Closer still!”
“I am not done yet,” said Dr.
Memory. “I must meditate further on this question.” And he closed his eyes
again.
Miss Liberty sang; “Oh where are the zeros of zeta of s?
I
cannot inform you, I truly confess!
Their
real part is always one-half, I suppose;
But
no-one can prove it, so nobody knows!”
Then the lights went out.
In the sudden darkness we heard Dr.
Memory say, “This program is jammed. Consult supervisor.”
* click *
mmmmmmmmmmmmmmmmMMMMMMMMMMMMM....
Thus Miss Liberty mystified Doctor
Memory with Goldbach’s Conjecture and the Riemann Hypothesis.
Doctor Memory said, “You now have
Full Access to #2. Beware, Master! She’s a glitch! Burn her!”
FLASH
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