>>5905

Here is a quote from Andrew Wiles to inspire you anon. (see pic).

I'll wait WHILES you think on that and be back in a bit with some more Crummey (as in Chis Crummey, aka Chris Curtis).

To celebrate the latin in VA's handle, Fermat's words (copypasta) around 1630, when Pierre de Fermat wrote in the margin of his Latin version of Diophantus’ ARITHMETICA the following enigmatic lines, unaware of the passions they were about to unleash:

Cubum autem in duos cubos, aut quadrato-quadratum in duos quadrato-quadratos, et generaliter nullam in infinitum ultra quadratum, potestatem in duos ejusdem nominis fas est dividere. Cujus rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet.

In plain English, for those unfamiliar with Latin:

One cannot write a cube as a sum of two cubes, a fourth power as a sum of two fourth powers, and more generally a perfect power as a sum of two like powers. I have found a quite remarkable proof of this fact, but the margin is too narrow to contain it.

The sequel is well-known: Fermat never revealed his alleged proof. Thousands of mathematicians (from amateurs to most famous scholars) working desperately hard at refinding this proof were baffled for more than three centuries.

>>5909

Hmmm - was just writing the above, and then you popped in. Coincidence?? Your ears were burning…

>>5911

Lupus in fabula - The wolf in the tale (i.e. Speak of the wolf, and he will come) (Terence)

(copy pasta from epic Fishing for Chris bread)

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In vein of blackboard images from RSA#10 of John Conway

>>4934 but more importantly, see:

>>4915

(Notice the n x (n+1) square, with triangle, with a section of it erased, leaving a cap?)

Attached is a blackboard image of Andrew Wiles. Couple more coming.

Notice the Q near his ear? Q?? haha.

So I had dug on this in mid Jan. Led to several tangents, geometric algebra, etc., so never finished. Jsut looked at notes and saved file and "cyclotomic fields", Earst Kummer, "Roots of Unity" were some of the terms that first popped up.

Back in a bit, but some symmetry for here, with some Q variables for fun.

More blackboard Wiles.

Excellent read/flip, in powerpoint format:

https:// folk.uio.no/rognes/papers/wileskoll.pdf

Fermat, Taniyama–Shimura–Weil and Andrew Wiles

by John Rognes, University of Oslo, Norway, May 13th and 20th 2016

Short, accessible article

https:// sites.math.washington.edu/~morrow/336_14/papers/vladimir.pdf

Fermat’s Last Theorem

Vladimir Korukov, May 15, 2014

More technical getting beyond me

http:// www.numdam.org/article/AFST_2009_6_18_S2_5_0.pdf

Interesting readable abstract, but rest of this paper by Tom Lovering of Harvard is jibberish to me. Muh math skillz lacking.

https:// tlovering.files.wordpress.com/2015/02/cyclotomic-fields-and-flt5.pdf

gnite/gday anons.

>>5882

>The square of x plus the square of y being equal to r doesn't look like a circle either.

Important bit, back to Pythagorean triples? Core to Fermat's definition of problem.

>>5920

Then there's the Cardioid, linking unit circles to Mandelbrot set (right lobe), and a perfect circle (left lobe). (see pics).

Some Cardioid love for you anons.

>>5882

>I'll bring it tomorrow if no one finds it before then…

…tick tock

Homomorphism: Homomorphism, (from Greek homoios morphe, "similar form"), a special correspondence between the members (elements) of two algebraic systems, such as two groups, two rings, or two fields.

Britannica.com

>>5943 That's cool, thanks.

So, seems you've dropped another crumb.

There's Shimura-Taniyama-Weil bit for the Modularity Conjecture that Wiles used.

Now it seems you're hinting at the Birch and Swinnerton-Dyer conjecture?

"The Birch-Swinnerton-Dyer (BSD) conjecture is one of the seven Clay Millennium problems" - hmmm, another Millennium prize…