Saturday, July 22, 2000


My hypothesis

For several years I've been making posts on two subjects on math newsgroups:

I've talked about my attempts at proving Fermat's Last Theorem.

And I've talked about the difference between belief and truth, and how that relates.

I've done the latter because I've been bothered by a question about human sources.

School is about teaching people knowledge gathered from approved sources. Becoming an approved source of "truth" should have to do with successfully proving truth or doing so with a high level of probability. For instance, I assume that becoming a math professor depends on actually producing correct "proofs" to "prove" that one is not only a repository of information from approved sources, but can also add to that body of information.

However, in any discipline, becoming an approved source also depends on absorbing the "truths" of a particular academic community, and those include beliefs.

(Now beliefs are necessary for normal human functioning, and I won't go into details about them except to say that they aren't necessarily true.)

So, the question I had was, given a contradiction between beliefs from an approved source and truth presented by a disapproved source, would human beings go with truth or belief?

There wasn't exactly a lot of point to the question since history has shown time and again that people will take an untrue belief from an approved source, and discount a truth from a disapproved source.

However, FLT offered a unique opportunity to prove it yet again with a community that makes the bold claim that it cared only for truth, and wasn't based on belief.

It was too great an opportunity to pass up.

Making myself a disapproved source took a bit of work because of the nature of the Internet.

An unknown source isn't necessarily a false one in most people's minds. I had to make sure that I was a known, but disapproved source.

That meant not only getting people's attention, with numerous attempts at solving FLT, but I had to figure out how to keep it, even when I didn't deliver the goods.

The answer was to be in some sense an entertainer. I used various strategies in doing this (like what I call "push - pull" where I put in negative posts of doom and gloom versus posts of just about anything else), and I found that I was successful.

I even now had people following me around making replies in any thread I posted with a link to a website that set about discrediting me. It was what I was looking for, and I no longer had to make any further efforts towards making myself a discredited source.

It helped to see that the website had some success, so I popularized it at its inception, by attacking it. The strategy worked to the extent that not only the websites creator posted, but others posted his link as well.

Finally, as I could be satisfied that I was a completely discredited source, I produced a partial of the correct argument to prove FLT back in December of last year.

I then tested sci.math with this information. It rejected it, as I expected. But, the test was not complete. I needed to give some time to emphasize my hypothesis.

I waited several months and then in May I went ahead and completed the argument.

What I found was not only was the proof ignored or rejected despite its simplicity, but some in rejecting it were denying well-known mathematical truths.

Now that's a fascinating result that has also been proven time and time again—When the beliefs of human beings are tested they will often deny intellectual truths that aren't classified as beliefs before they will deny the tested beliefs.

Now, in making this post, I'm obviously interested in the end of my little test.

That is a two step process.

First, I tell people about the methodology of what I was doing and then I'll give the link to the website and challenge them to find anything wrong.

I know there's nothing wrong, but I also know that it's useless to tell people that it's right.

Most people who read this post will simply assume that I'm being manipulative in a way that will get me attention by getting a lot of people to look at the website.

I'm likely to attract several of the same type posters as before, who will once again try to highlight that I'm a disapproved source.

A very small percentage will check the website anyway, and some will find something they don't understand that well and then will quit immediately feeling a bit silly that they even checked, because they will think they were manipulated into doing so by a disapproved source.

A few others will look more closely, and see that they can find nothing wrong, but will reject the proof simply because they have been told by approved sources that it can't exist.

Some will recognize it is correct, but will do nothing because I'm a disapproved source.

The second part of the process doesn't concern the readers here. I just wanted to mention that it is a two step process.

The link to the proof is at

and you can't prove the argument is wrong.

Oh, there is one other little thing.

What I've proven here, rather dramatically, is that mathematicians are just like everyone else. That casts doubt on certain bodies of mathematical work only because they are known as true only because mathematicians say they are.

There have been any number of scandals in other fields, which were found out primarily because evidence was at some point required for a particular "truth".

Some mathematicians, by making highly complex proofs that no one else can understand, are the only evidence for much of their work.

("Practical" mathematicians, on the other hand, at least have to produce mathematics that works, so it's tested in the real world.)

I've been looking for a way to test my certainty in Wile's proof of FLT without having to actually go over it because of its complexity.

By testing the mathematical community, as I have, I now believe that it is quite possible that the entire community may have more invested in the "truth" of the proof than in the truth.

The story of how the proof came about adds to my unease:

Wiles looks for a proof for seven years in secret. Finally he believes he has it and gives a lecture that become a major event. World wide publicity soon follows and then it is checked and there's an error. (Can you imagine such a thing, being in Wiles' position?) Wiles works his butt off for a year and with some help manages to fix the mistake, and the fix is actually a little bit simpler than what he was originally trying!

Mathematicians in talking about the proof continually emphasize that it takes graduate degrees to completely understand it.

That's not so surprising. Einstein's General Theory of Relativity is the same way. But, it can be tested.

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