Posted on 10/12/2015 3:59:01 PM PDT by LibWhacker
For example, Fermat conjectured that 22k+1 was prime for every positive integer k. The great Leonhard Euler blew up this conjecture in a few hours.
The correct name is Fermat's Last Conjecture, which has been Andrew Wiles Theorem since 1995.
Thanks!
I just checked my “Number Theory and Its History” by Oystein Ore (Dover Books, what else?) and see that it’s:
A regular polygon with n sides can be constructed by compass and straight-edge if and only if n = (power of 2) times distinct Fermat primes.
The first Fermat primes are 3, 5, 17, 257.
IIRC Gauss’s proof used complex roots of unity.
Primal importance The abc conjecture refers to numerical expressions of the type a + b = c. The statement, which comes in several slightly different versions, concerns the prime numbers that divide each of the quantities a, b and c. Every whole number, or integer, can be expressed in an essentially unique way as a product of prime numbers—those that cannot be further factored out into smaller whole numbers: for example, 15 = 3 × 5 or 84 = 2 × 2 × 3 × 7. In principle, the prime factors of a and b have no connection to those of their sum, c. But the abc conjecture links them together. It presumes, roughly, that if a lot of small primes divide a and b then only a few, large ones divide c.
- - -
This is just Common Core, and the 10 frame.
"The abc conjecture refers to numerical expressions of the type a + b = c.
The statement, which comes in several slightly different versions, concerns the prime numbers that divide each of the quantities a, b and c.
Every whole number, or integer, can be expressed in an essentially unique way as a product of prime numbers—those that cannot be further factored out into smaller whole numbers:
for example, 15 = 3 × 5 or 84 = 2 × 2 × 3 × 7.
In principle, the prime factors of a and b have no connection to those of their sum, c.
But the abc conjecture links them together. It presumes, roughly, that if a lot of small primes divide a and b then only a few, large ones divide c."
I would say that you can make a better case that the Riemann Hypothesis [still unsolved] is more famous, and it is certainly more important in terms of its theoretical and practical implications. It doesn't go back as far. Goldbach's conjecture is also not quite as old, but just as famous [until Andrew Wiles proved the Fermat Conjecture it wasn't that well known to lay audiences -- it was not one of the Hilbert Problems; the Riemann Hypothesis is.]
And Stokes’ Theorem is really Lord Kelvin’s Theorem.
I was not questioning your comment...just using it to say what I wanted to say.
I sometimes wish I had pursued more math, but it’s a long story about a bad teacher and some government changes in the way math is taught that screwed up my education a bit..
I was a victim of the transition from standard mathematics teaching to something they called “new math”. But I do understand it as a science, and I can see what this guy has done here and why it’s so hard to verify what he did.
Sounds to me that he is doing something akin to what Newton did. He was trying to solve a Physics problem and had to invent Calculus in order to do it.
In this case the individual was attempting to solve a mathematical problem around whole numbers and had to expand the multiplication of whole numbers such that the normal multiplication we are used to is only one set instead of the whole.
With that he was able to expand the solution set and arrive at an answer. The difficulty is that it’s such a brand new vista that even the abstract mathematicians are having a hard time following the thought process.
Like you, mathematics is not my friend; but I think this story is fascinating. My sense of it is similar to your conclusion, especially from these portions of the article:
To complete the proof, Mochizuki had invented a new branch of his discipline, one that is astonishingly abstract even by the standards of pure maths. “Looking at it, you feel a bit like you might be reading a paper from the future, or from outer space,” number theorist Jordan Ellenberg, of the University of Wisconsin–Madison, wrote on his blog a few days after the paper appeared.
In December 2014, he wrote that to understand his work, there was a “need for researchers to deactivate the thought patterns that they have installed in their brains and taken for granted for so many years”.
From the Guide..
Well, our dear leader, bo, loves to use the word “calculus” when lecturing his subjects.
That’s math, right? (Asks Barbie)
Yup....and this guy is totally capable creating a entirely new branch of math that could in time expand and all the high flyers will be trying to break it, and create even more mathematics that can now be used to solve or pose even more potential questions in mathematics.
I cannot imagine what that might mean to....physics and other sciences.
Good book.
I like simplexes better than cubes though.
OK, thank you for taking the time to try and explain that to me, I think I sort of get it.
numbers approaching infinity
- - -
Like the debt?
Gregory Peck
It was from Fermat himself (but in Latin).
Everyone knows you can't put Descartes before the whores.
"Ceterum censeo 0bama esse delendam."
Garde la Foi, mes amis! Nous nous sommes les sauveurs de la République! Maintenant et Toujours!
(Keep the Faith, my friends! We are the saviors of the Republic! Now and Forever!)
LonePalm, le Républicain du verre cassé (The Broken Glass Republican)
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.