A while ago, Terence Tao sent me this great link to a list of professional math blogs. As many of you know, I am an amateur mathematician which means that there is every chance that you may find mistakes and typos on this blog.
I am very open to corrections and I am proud to tell you that whenever anyone finds a mistake, I am very careful to update the blog accordingly.
My goal in this blog is to provide an amateur's perspective on the history of number theory from the perspective of Fermat's Last Theorem. Based on the many comments I have received, I feel some satisfaction that for many folks out there, I have achieved this goal.
Even as I feel that an amateur's perspective can shed light on understanding the foundations of mathematics, there is no substitute for the insights of the greatest mathematical minds and the writings of today's professional mathematicians. My writing should at all times be a supplement to these authoritative viewpoints.
Please take a look at this list of blogs. Here is a great way to find out about the viewpoints of professional mathematicians.
Special thanks to Terence Tao for sending me these links.
Saturday, May 08, 2010
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18 comments:
Was this intentional? ;-)
"As many of you know, I am an amateur mathematician which means that there is every change that you may find mistakes and typos on this blog."
Thanks for noticing. :-)
Cheers,
-Larry
Hi there Larry
I understand that a 'cube' is now described as a modual ellipse.
How is this applied graphically?
Also, what is the connection between FLT and the Collatz Conjecture (the 3n+1 problem)?
Surely, 3n+1 should be a simple problem.
Hope you may be able to answer.
Leigh Lewis - Perth
Hi Adam,
You ask a good question about the relationship between cubes and modular forms.
I don't have a clear enough understanding of modular theory to answer your question at this time. I hope to be able to provide an answer in the future. This blog is the result of my own investigation into understanding Andrew Wiles' proof. :-)
I don't know much about the Collatz Conjecture so I can't really comment on its relation to FLT.
Hello Larry
Thanks. Sorry for my slow reply but I only get on net from time to time.
I'll give you the tip though; the 1+3n relationship inherent in the "number line" is really simple and evident from first principles. 'All the rest' is hard.
We don't need to use it to show the 1+3n relationship but you are more familiar with Fermat's Last Theorem. Of course, since they both relate to Number, they are both concurrently contained in the one solution.
You should note that Fermat does not speak consistently in his descriptions of "powers of numbers". He said "cube" (not 3rd power) and "2nd power" (not square)... He mixes his metaphors. That's why he is the "Riddler" of mathematics. He basically said that "Squares work; Cubes don't."
Consider the (3,4,12,13) combination: where in the "cubic" representation are the 169 square units?
We may question the formation of the original "unit cube"...
Basically the point, line, square/planar, cube/spatial is simply misconceived mytho-dology. It's all Greek to me...
Exponentiation is not "dimension-ation", is it? The "first" cube is also not possible as such. "A cube" is really a sum-zero entity over time(s). Surely then, Andrew Wiles should not have stopped... and Stephen Hawking should not park his wheelchair at the "corner" of a cube...
The Collatz Conjecture is about 3n+1 - it is surely simple. Too simple for the advanced?
We know that n+1, n-1, 2n+1, 2n-1, 4n+1 and 4n-1 are also "simple" relationships. Is there no "3n-1" problem?
Anyway, the respective "internal" time units for "our" XYZ number line 1, 2, 3, 4, 5, 6,... translate from our XYZ (3D) axis to 1, 4, 7, 10, 13, 16,... of each XYZ (1D) axis. The "process" of 3n+1 // 2n is something of a red herring. The 2n division is unnecessary as such but it does indeed indicate the translation to each XY XZ YZ (2D)axis. The ratio of units of X:Y:Z is irrelevent.
I have met no mathematician that explains the mathematical relationship regarding how the initial "one" is formed.
Perhaps that is just my bad luck and you know the answer.
If I may ask anyone for specific clarification:
How do we make a "one" unit? or,
How do we make a "line" from a "point"? or,
How do you make a "1D finitesimal" from an "infinitesimal"? and then,
How does this then relate to how a 2D (or 3D) finitesimal is made concurrently from an infinitesimal?
Straight forward stuff, eh? After all, who said space is "spatial"? We are people of the hypotenuse; not the axes. We count to the axes; not from the axes. We are "of" the truncation of the cube, not the cube itself.
My apologies for my attempts at humor but it is all so obvious as to be funny. And I have given more than a tip.
Happy to send you the solution to the problem if you can answer the above. Just joking, I will send it to you next week if you want it.
But, can you answer the 4 phrased question above...?
Kind regards
Adam Lewis
Hi again Larry
I forgot to mention that the modular ellipse nature of the cube is a description of the double-helix nature of our "incrementum" through time(s).
Let me know about the "one" question. Thanks.
Adam Lewis
Hi Adam,
I focus more on the mathematical side of the issues you mention.
It sounds like you are leaning more toward the philosophical side.
I've had a chance to study the Collatz Conjecture and it is like Fermat's Last Theorem, very easy to state and incredibly tough to prove one way or the other. Thanks very much for mentioning it.
Cheers,
-Larry
Hi Larry
3n+1 is still basic but it sounds like you're not convinced. There is not much effort for you to see it: but you have only reflected on it for all of 23 minutes. I will send you a file next week that makes it even more obvious that 3n+1 is very "ordinary".
Regarding inherent philosophy; the father of mathematics is Pythagoras and he is the father of philosophy. He literally worshipped it... Do you think that had no influence? He thought "the universe" was infinite whereas it is the opposite - finite. He applied his error to the concept of number.
Mathematics as the so-called "continuum of number" is a philosophical expression. It confused the distinction between the time(s)less infinite and our temporal finitude. Continuum causing temporal finitude. Numberless expressing number. Unlimited making limits. A number is an increment
Hopefully I will clearly explain the situation to youur satisafaction next week.
I suppose from your response that you don't know how to make a "one unit" from a "point". That doesn't seem peculiar to you?
Kind regards
Adam Lewis
Hi Larry Freeman
I joined your blog More Proposed Proofs but was unable to leave a message there. I think I proved the FLT at least I do not see any flaws in my proof. It does not mean that others willing to examine it would not find flaws may be even fatal there. Then it may go to your blog False Proofs. Do you still run these blogs?
McPogor
Hi McPogor,
The blogs that you mentioned are not directly related to this site but are run by me.
The proposed proofs is actually, my blogger account for trying to put together my own proofs.
False proofs is about topics that are deceptive. These are proofs that have known flaws. That blog has been inactive for some time.
My suggestion is to create your own blog account, write up your proof, and then seek out math experts to help you evaluate your proof. knol.google.com, for example, is free, and has support for mathematical equations.
From my experience, it is a great learning experience to attempt a proof so long as you realize that you have probably made a mistake. An attempted proof should always be about learning. Brilliant minds have spent years thinking about these issues without finding any new insights.
Good luck.
-Larry
My formula is
if x^2+y^2=z^2
Then n>2
x^n+y^n=z^n{(sinA)^n+ (cosA)^n}
an example
If x=1,y=(3)^1/2,z=2
and for n=2
Therefore,
x/z=1/2=sin(45 degree)
=>1^5+{(3)^1/2}^5=2^5{(sin45)^5+(cos45)^5}
My formula is
if x^2+y^2=z^2
Then n>2
x^n+y^n=z^n{(sinA)^n+ (cosA)^n}
an example
If x=1,y=(3)^1/2,z=2
and for n=2
Therefore,
x/z=1/2=sin(45 degree)
=>1^5+{(3)^1/2}^5=2^5{(sin45)^5+(cos45)^5}
Hi Larry and Bhaskar,
I don't get Bhaskars comment but I can say...
The solution to the Collatz Conjecture, 3x+1, is the confirmation to FLT and provides the obvious nature and representation of a cube as a "modular ellipse".
The fact that Andrew Wiles does not understand 3x+1 shows that he has only "somewhat" proved the theorem. Andrew seems to have no concept of the "double-helix" of number.
Consider:
Fermat made his observation while reconsidering ancient Greek geometry of Pythagoras and Euclid which he understood to be wrong.
He didn't need to try to make up "higher" mathematics to understand that the very foundations of number theory are misconceived through Pythagorean philosophy.
If number theory is "right" then 3x+1 (and, of couse, 3n+1) would be very clearly evident to everyone.
Since we can easily disqualify traditional mathematical mytho-dology from lowest level of the "origin/null point" [and readily determine the n+1 (n-1), 2n+1 (2n-1), 3n+1 (---) functions as dimensional rates of "time(s)" while showing the coherent/decoherent (post-coherent and pre-coherent) nature of "inter-time(s)"], there is obviously something wrong current thinking.
No wonder that there is no Unification in the physical sciences.
"Point, line, square, cube" is mis-conceived from inception; so what hope the "higher"...? Exponentiation is purely an AXIAL function not a dimensional one; but you don't see it that way.
The "cube" is a nullifying entity over time(s) as it progresses from "infinitesimal to infinitesmail through finitesimals".
A cube is not what you think it is; nor is a square; nor a line; nor even a point... so what on earth do you think you are doing?
With empathetic reagrds
Adam Lewis
Here's hoping that I don't get censored. :-)
Larry, it's all about the one thing, number as INCREMENTUM.
Why is a "singularity/infinitesimal/point" described as both "(next-to-) zero and infinite"?
Start with an infinitely POWERED ascribed base and "stretch the line" by de-powering that point. The result of de-powering along the perpendicular XYZ axis is the "establishment of time(s)" at n+1 which then translates to 2n+1 in the planes and 3n+1 axially as number relationship is projected over time(s). It also disqualifies the "infinitely divisible finite".
Anyone can do this simple method; but you don't. Why not?
One philo/theo/logical answer only; Incremetnum of finitude is Numero ex Nihilo. But, that is "unacceptable" to Greek philosophy... is it not?
Kind regards
Adam Lewis
Larry,
I am studying your blog of 2004 and want to ask if you have the refence to the paper that Euler wrote where he made the mistake you mention as he tried to prove FLT. I imagine it is given in Edward's book you refer to, but I have not been able to get a copy.
If you would be so kind to show at least in which year Euler attempted his proof, I may figure out the paper.
Thank you
Hi Dora,
You are right. I got that information from the Edwards book.
It is also talked about here:
http://www-history.mcs.st-and.ac.uk/PrintHT/Fermat%27s_last_theorem.html
So, the source seems to be Algebra (1770).
I hope that helps.
Cheers,
-Larry
I only want to mention that the link to math blogs appears to be dead now.
The best blog I've ever seen. I hope you will continue working on this one till the end of your life.
I would like to show you mine:
mishabucko.wordpress.com
/Misha
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