As of today, the non-disclosure agreement is expired, so I can share
the good news. I have won the Clay math prize for disproving the
Riemann Hypothesis.
There have been numerous attempts to disprove it over the centuries,
by finding a non-trivial zero of the Riemann zeta function that's off
the critical line. Many of these attempts were ill-fated.
Recent archeological investigation proves that this is the problem
Archimedes was working on when he was killed by a Roman soldier.
It's not known how far he got.
The next known attempt was by John Dee in the 16th century. He built
a primitive mechanical calculator with which he checked all the zeros
with a height up to 100. Since calculation was then held to be the
exclusive domain of man, he was burned at the stake for sorcery.
As is well known, this was the problem Babbage built his Difference
Engine to work on. It ran for over a year, and tested all zeros up
to a height of 1000 before he got impatient and increased the steam
pressure to speed up the calculation. This was a mistake. Not only
did he narrowly escape death from the resulting steam explosion that
destroyed his machine, but he was investigated for wasting taxpayer
money. They took that very seriously in those days. If not for his
many influential friends, he would have been transported to the prison
colony in Australia. As it was, he never worked again.
Alan Turing was driven to suicide by the investigation into whether
he surreptitiously diverted the efforts of Bletchley Park away from
breaking German ciphers into working on this problem instead. It was
claimed that if not for his unauthorized hobby, the war could have
been won a year earlier. He could have been hanged for treason. For
what it's worth, he denied his guilt and claimed that the diversion
was the work of a German mathematician on his staff, Riemann's
grandson. What is known is that as the Axis U-boats and Japanese
Zeros rampaged unchecked, it was confirmed that there were no
off-axis zeros up to a height of 10,000.
Most recently, taking advantage of the lowered security due to
the sequester layoffs, a hacker named A.F. Day "pwned" NSA's main
supercomputer center and used it to check up to a height of 100
trillion. He has been sent to Guantanamo, and is expected to remain
imprisoned there for the remainder of his life. There will of course
be no trial.
So how did I accomplish what none of these people did? I don't have
access to supercomputers. I realized that nobody had ever checked the
zeros *below* the real number line. Using a TRS-80 I found in the
trash, I soon found an off-axis zero at approximately 0.0104 - 4.01 i.
my Color BASIC program took just 0.41 seconds to run.
Now that I've disproven the Riemann Hypothesis, I plan to attempt to
prove or disprove the Generalized Riemann Hypothesis. I will use a
Commodore 64 I found in the Dumpster.
This is quite a comeback for me. I remember the disappointment the
last time I attempted to try for a large prize. I attempted to solve
the RSA factoring challenge, but despite my best efforts was only able
to find one of the two prime factors.
Also, 20 years ago I almost proved Fermat's last theorem, but I got
the sign wrong. I proved that for no distinct integers A, B, and C
are there any solutions to A^N + B^N = C^N. But instead of N being an
integer greater than 2, I proved it for N an integer less than -2. I
came so close! I still think I should have been given partial credit,
and half of a Fields Medal.
You'll be pleased to learn that I plan to use my prize winnings to
further the cause of mathematics. I will create a searchable online
database of all real numbers. This is a rather ambitious undertaking,
so I'll start with just the reals between 0 and 1. To look up a
number, a user need merely type in the number, in his choice of
decimal, octal, or binary.
Even that much will probably take at least a year, so I'll begin with
just the non-computable numbers, as those have received far too little
attention. I can't find an online database of them anywhere.
