Tuesday, April 07, 2009
JSH: And they will wait to see
I have little doubt that the mathematical community not only will not acknowledge my finds of really just trivial stuff with Pell's Equation that makes it a lot easier to solve, but, I believe, they will keep teaching it as they have.
So yeah, you could take a course from a "top" mathematician at your pick of the supposedly best schools in the world, and have some guy, confidently and arrogantly teach you Pell's Equation without mentioning trivial solutions for D = n^2 - 2, and not telling you that it's best to solve alternates to Pell's Equation that have solutions that are roughly the square root of the Pell's Equation solution.
And God forbid if this paragon of mathematical society would ever sink to the low of daring to talk about RATIONALS with Pell's Equation, a Diophantine equation mind you so rationals are verboten, right?, and give you the rational parameterization for circles, ellipses and hyperbolas:
Given x^2 - Dy^2 = 1, in rationals:
y = 2t/(D - t^2) and x = (D + t^2)/(D - t^2)
And you get a parameterization for hyperbolas with integer D>0, for circles with D=-1, and for ellipses in general with D<0.
A poster on a math newsgroup after railing at me with lots of insults for daring to note this area as a massive failing of math society then said that result wasn't worth mentioning, or noting.
They don't wish to record it. They as in math society, which is still quiet.
In THEIR society they will keep getting math prizes including the big prizes. They can still get acclaim, and accolades, advance their careers and have wonderful mathematician lives with junk results as they do not have Mother Nature looking over their shoulders forcing them to be right.
But you do.
Mathematicians will happily not teach you common knowledge now because I'm making it such, because they are waiting to see if you will let them. And they will keep getting funding, keep getting awards, keep getting prestige no matter how wrong they are as they have a committee society.
A group of mathematicians says "great!", and you get a prize.
But YOU need experiments that shows theories work. YOU need mathematics that is the best knowledge available.
Because YOU have real competition, and need real results, not a committee to hand you a prize or grants or whatever.
I shot down standard usage of Galois Theory years ago with fairly trivial algebra.
Mathematicians have still gotten prizes using it since I did.
They destroyed an entire mathematical journal versus face the result. Google: SWJPAM
Mathematics professors have still advanced their careers in mathematics. Grad students in mathematics have received their Ph.D's for bogus work.
Their society has gone on just fine as it is completely disconnected from reality.
So they will wait to see what you do.
Maybe the end of this impasse will be the day when one of you is sitting in some prestigious course from some distinguished mathematician teaching you Pell's Equation without any of the easy knowledge that I've pointed out and you will flip out, and run from the place screaming in agony, and when you regain some of your sanity, you will finally say: THIS MUST STOP.
Until that day. We all wait. With them.
So yeah, you could take a course from a "top" mathematician at your pick of the supposedly best schools in the world, and have some guy, confidently and arrogantly teach you Pell's Equation without mentioning trivial solutions for D = n^2 - 2, and not telling you that it's best to solve alternates to Pell's Equation that have solutions that are roughly the square root of the Pell's Equation solution.
And God forbid if this paragon of mathematical society would ever sink to the low of daring to talk about RATIONALS with Pell's Equation, a Diophantine equation mind you so rationals are verboten, right?, and give you the rational parameterization for circles, ellipses and hyperbolas:
Given x^2 - Dy^2 = 1, in rationals:
y = 2t/(D - t^2) and x = (D + t^2)/(D - t^2)
And you get a parameterization for hyperbolas with integer D>0, for circles with D=-1, and for ellipses in general with D<0.
A poster on a math newsgroup after railing at me with lots of insults for daring to note this area as a massive failing of math society then said that result wasn't worth mentioning, or noting.
They don't wish to record it. They as in math society, which is still quiet.
In THEIR society they will keep getting math prizes including the big prizes. They can still get acclaim, and accolades, advance their careers and have wonderful mathematician lives with junk results as they do not have Mother Nature looking over their shoulders forcing them to be right.
But you do.
Mathematicians will happily not teach you common knowledge now because I'm making it such, because they are waiting to see if you will let them. And they will keep getting funding, keep getting awards, keep getting prestige no matter how wrong they are as they have a committee society.
A group of mathematicians says "great!", and you get a prize.
But YOU need experiments that shows theories work. YOU need mathematics that is the best knowledge available.
Because YOU have real competition, and need real results, not a committee to hand you a prize or grants or whatever.
I shot down standard usage of Galois Theory years ago with fairly trivial algebra.
Mathematicians have still gotten prizes using it since I did.
They destroyed an entire mathematical journal versus face the result. Google: SWJPAM
Mathematics professors have still advanced their careers in mathematics. Grad students in mathematics have received their Ph.D's for bogus work.
Their society has gone on just fine as it is completely disconnected from reality.
So they will wait to see what you do.
Maybe the end of this impasse will be the day when one of you is sitting in some prestigious course from some distinguished mathematician teaching you Pell's Equation without any of the easy knowledge that I've pointed out and you will flip out, and run from the place screaming in agony, and when you regain some of your sanity, you will finally say: THIS MUST STOP.
Until that day. We all wait. With them.
# posted by James Harris @ 21:57 
