Sunday, March 29, 2009
JSH: Understanding the situation
The alternates to Pell's Equation provide a simpler route to finding solutions when D is a prime number.
That is, given x^2 - Dy^2 = 1, it is EASIER to find solutions by instead using:
j^2 - Dk^2 = -1, j^2 - Dk^2 = -2, or j^2 - Dk^2 = 2
which are required to exist for D a prime, where only one will be valid when D is an odd prime, but one must.
They are easier as the first j that solves is roughly the square root of the first x that solves.
Now those are the mathematical facts.
The social results are more complicated:
Your fight to hide knowledge is clear here.
No one who is for the human race, or for mathematical progress, or is intellectually honest or who has good intentions at all, would fight to hide this result.
It's knowledge. It's interesting knowledge, and as a "pure math" result it's fascinating for many reasons.
But as a social instrument it is incredible that it has already revealed that some of you are as far out there against mathematics as is possible, yet you have been operating on newsgroups freely for years, as something else.
The world of mathematics has changed because of one discovery.
For me, it is just one of many. But for a lot of you, it is the one you can't just run away from, or be distracted from, or trust that some way there must be more that you don't know so that you can let it stay hidden.
I am the world's latest major mathematical discoverer.
The history of my predecessors is very rich, and their discoveries did much to advance our world.
My hope is to live up to the very high bar of those who preceded me.
And more importantly, to not disgrace the role, for those I truly hope will follow.
As if I am the last major discoverer, it is the end of the human race.
I am increasingly confident, now with this result, that thankfully, I am not the last.
The future should be brighter than the past.
History will be the judge. But make no mistake, you are now a part of history in the making.
That is, given x^2 - Dy^2 = 1, it is EASIER to find solutions by instead using:
j^2 - Dk^2 = -1, j^2 - Dk^2 = -2, or j^2 - Dk^2 = 2
which are required to exist for D a prime, where only one will be valid when D is an odd prime, but one must.
They are easier as the first j that solves is roughly the square root of the first x that solves.
Now those are the mathematical facts.
The social results are more complicated:
- Math society needs to acknowledge the result properly.
- Math textbooks around the world that talk about Pell's Equation will have to be updated.
- Math curricula around the world where Pell's Equation is discussed will have to be updated.
Your fight to hide knowledge is clear here.
No one who is for the human race, or for mathematical progress, or is intellectually honest or who has good intentions at all, would fight to hide this result.
It's knowledge. It's interesting knowledge, and as a "pure math" result it's fascinating for many reasons.
But as a social instrument it is incredible that it has already revealed that some of you are as far out there against mathematics as is possible, yet you have been operating on newsgroups freely for years, as something else.
The world of mathematics has changed because of one discovery.
For me, it is just one of many. But for a lot of you, it is the one you can't just run away from, or be distracted from, or trust that some way there must be more that you don't know so that you can let it stay hidden.
I am the world's latest major mathematical discoverer.
The history of my predecessors is very rich, and their discoveries did much to advance our world.
My hope is to live up to the very high bar of those who preceded me.
And more importantly, to not disgrace the role, for those I truly hope will follow.
As if I am the last major discoverer, it is the end of the human race.
I am increasingly confident, now with this result, that thankfully, I am not the last.
The future should be brighter than the past.
History will be the judge. But make no mistake, you are now a part of history in the making.
# posted by James Harris @ 14:58 
