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Topic:
Major announcement
Replies:
4
Last Post:
Apr 2, 2013 9:28 AM




Major announcement
Posted:
Apr 1, 2013 7:04 PM


As of today, the nondisclosure 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 nontrivial zero of the Riemann zeta function that's off the critical line. Many of these attempts were illfated.
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 Uboats and Japanese Zeros rampaged unchecked, it was confirmed that there were no offaxis 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 TRS80 I found in the trash, I soon found an offaxis 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 noncomputable numbers, as those have received far too little attention. I can't find an online database of them anywhere.  Keith F. Lynch  http://keithlynch.net/ Please see http://keithlynch.net/email.html before emailing me.



