email@example.com (James Harris) wrote in message news:<firstname.lastname@example.org>... > The big bad issue from my work is that it takes away a bad assumption > made about the work of Evariste Galois. > > For instance, take > > x^2 + 3x + 2, and solve using the quadratic formula and you get > > x = (-3 +/- sqrt(1))/2 > > but if it's irreducible like x^2 + 3x + 3, you get > > x = (-3 +/- sqrt(-3))/2 > > and mathematicians have latched on to sqrt(-3) in the second, and > blamed their fixation on Evariste Galois, but they're just wrong. >
This is just too bizarre. There is no need whatsoever to invoke Galois here. Why don't you say what really bothers you about this example? In the first polynomial you have two roots, -2 and -1, and one of them is not divisible by 2, while the other one clearly is.
In the second polynomial, you have two roots. _Neither_ is divisible by 3 and _neither_ is coprime to 3; _each_ is divisible by sqrt(3) [or sqrt(-3)] in the algebraic integers. No surprise here. This is exactly what you should expect, because the second polynomial is _irreducible_. Galois theory predicts this, but it is totally not necessary to use Galois theory to prove it.
> Algebraically, there's little difference between the two examples, and > Galois Theory tells you little more about the second than it does > about the first! > > So where does the work of Galois actually apply? >
Jesus. Why don't you read some math and find out? Especially pay attention when you see the word "irreducible."
> In terms of forms available for *expressing* roots, but it doesn't say > anything about the properties of the roots themselves. >
It most certainly does. What this shows is, if you don't know beans about something (like Galois theory), you shouldn't make pronouncements about it.
> Now I can prove that with rather basic algebra to the point that my > paper is so short with such a simple argument that it looks like it > could be a college homework assignment, but notice it's been argued > about for months!!! >
That's only because you refuse to admit that there is a big fat error in your so-called proof.
I have and lots of other people. We all agree. It is wrong.
> Barry Mazur replied to an email where I sent an early draft, and had a > basic question about it which I answered.
What was his question?
> He was also nice and > encouraging which is why I feel a bit guilty continuing to drag his > name into this, but hey, I think he should have done more. >
He is a smart guy. He was wise to stop replying to you.
> Andrew Granville as editor of the New York Journal of Mathematics > replied when I sent the paper to that journal. >
He actually _replied_ ? Wow.
> A math graduate student at Cornell University contacted me out of the > blue offering his help, so I sent him a slightly watered down version, > which he traced through in his own words.
What did he say at the end?
> Yes, I have those emails > still. >
I can but again say, Wow. That is very impressive. To have saved those emails, still. Wow, wow, wow.
> The paper ended up at SouthWest Journal of Pure and Applied > Mathematics, an electonic journal, where I kept in contact with the > editors of that journal over the months, and told them my amateur > status, and was repeatedly informed that they just cared about the > mathematics. >
Now, right away, if they said that and yet took nine months to answer, I would start to wonder if they were being totally, um, honest.
> Yet someone then posted and sci.math'ers went in a frenzy attacking > the journal and the editors in posts, which apparently the editors > never read, as other posters conspired to mount an email campaign > claiming my paper to be false. >
It _is_ false.
> The result: > > <a href="http://rattler.cameron.edu/swjpam/vol2-03.html">http://rattler.cameron.edu/swjpam/vol2-03.html</a> > > I was informed AFTER my paper was yanked by Ioannis Argyros, who > refused to even listen to a defense, and promptly went on vacation to > Greece. He had all mention of the paper simply yanked, which left a > hole, which they later filled as you can see at the link above. >
Argyros did the wrong thing. He should have admitted that they totally screwed up.
> And notice that I've personally squashed the objections of at least > some of the posters who emailed him noting that their claims apply in > the ring of algebraic integers, which algebraically can be shown to be > flawed. >
No, I don't notice that at all. You have not, for example, "squashed" the objections of W. Dale Hall. You have simply run away from them. Plus, what is the flaw with the ring of algebraic integers?
-- Is it not a ring?
-- Is it not well-defined?
-- What? Does it fail to have some property that somebody claims it does have? What property?
> Some of them, if you read carefully, are now just coming out and > claiming that it's Galois Theory against me, when I point out that > algebra came before. >
Why is 'came before' important? Does that mean Galois theory is wrong?
Besides, it is now clear that your argument is some kind of voodoo, not algebra. Someone has pointed out that you jump from m = 0 to other m with no proof. That's voodoo.
> So, algebra is no longer good enough for mathematicians? >
Nothing wrong with it. But what you did is not algebra. It's voodoo.
> I have a basic argument in a short paper, and yet, mathematicians who > I'm sure STILL claim they are objective, logical, and accept > mathematical truth, just behave badly over and over and over again, as > if they never really cared at all about any of it. > > Why? >
Because you are wrong. _Provably_ wrong.
> My guess is that it's just so huge of a thing that they forget that > people are just surveyors of the mathematical landscape and not its > creators. > > Maybe today's mathematicians have decided they are bigger than > mathematics itself! > > Sound far-fetched? >
Sounds like B.S.
> Consider a quote from a mathematician so that you can see how far > mathematicians have gone, away from mathematics. > > In his June 2003 column "Devlin's Angle" mathematician Keith Devlin > wrote: > <Quote> > What is a proof? The question has two answers. The right wing > ("right-or-wrong", "rule-of-law") definition is that a proof is a > logically correct argument that establishes the truth of a given > statement. The left wing answer (fuzzy, democratic, and human > centered) is that a proof is an argument that convinces a typical > mathematician of the truth of a given statement. > > While valid in an idealistic sense, the right wing definition of a > proof has the problem that, except for trivial examples, it is not > clear that anyone has ever seen such a thing. > </Quote> > A quote from "When is a proof?" > <a href="http://www.maa.org/devlin/devlin_06_03.html">http://www.maa.org/devlin/devlin_06_03.html</a> > > So now, mathematics is believed to just be another social thing. Why? >
Thank god you are not a dictator. You would get to define right and wrong. Mostly wrong.
> Because losing Galois Theory as they currently have it is so huge that > for many mathematicians it might be like losing everything. >
That's not the choice. On the one hand, Galois theory says you are wrong. On the other hand, algebra _also_ says you are wrong. That's the choice.
> But you see, mathematics is a HARD discipline for many reasons. > > Facing the truth is the greatest test of a mathematician. > > And now you know how I can know how few of the people today who claim > to be mathematicians, actually are. >
The first thing you should say when someone asks you if a certain guy is or isn't a mathematician is, "Am I the certain guy?" If the answer is yes, then he isn't.