#fermat — Public Fediverse posts

It is possible to develop bug-free software using the "piped" development model. I have a truly marvellous demonstration of this proposition, which this career
is too small to contain. #fermat #variation #iactuallydohaveatheory

Results ranging from visualizable theorems of solid geometry to abstract propositions of analysis were called beautiful by Leonhard Euler (1707–83). For instance, he thought beautiful the following result:

If an elliptical cylinder is cut by any plane at an angle θ, then the ratio of the product of the principal axes of the section and of the product of the principal axes of the base is 1:cos θ (see attached image).

Aesthetic concerns seem to have been part of what drew Euler to number theory. Christian Goldbach (1690–1764) persuaded him to take an interest in the subject and to make a serious study of Fermat's work. His attention was drawn by the theorem:

Every natural number can be expressed as a sum of four squares.

With presumably deliberate understatement, Euler described it as a ‘not inelegant theorem’. The result remained unproven in Euler's time, and the first proof was given by Joseph-Louis Lagrange (1736–1813), becoming known as ‘Lagrange’s four-square theorem’.

Thus, for Euler, *unproven* conjectures could have aesthetic value. And so he judged another well-known then-unproven result of Fermat:

‘In Fermat there is another very beautiful theorem for which he claims to have found a proof. […] the formula $a^n + b^n = c^n$ is impossible whenever $n > 2$’

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[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

#Euler #Fermat #Goldbach #Lagrange #FermatsLastTheorem #MathematicalBeauty

Number theory was the one area of mathematics on which Pierre de Fermat (1607–65) worked throughout his life, and he found it ‘very beautiful and very subtle’.

Among other results, he said that the Polygonal Number Theorem (which asserts that every natural number is the sum of at most $n$ $n$-gonal numbers) was ‘a most beautiful and wholly general proposition […] this marvellous proposition’.

(He offered no proof of this result, but claimed to have one in a marginal note to Diophantus' Arithmetica; this was the same book in which he noted what became known as Fermat's Last Theorem.)

Fermat also seems to have counted magic squares and analogous configurations as part of number theory, and wrote that: ‘I know hardly anything more beautiful in arithmetic than these numbers that some call planetary and others magic’. (The term ‘planetary’ is derived from certain treatises linking the magic squares to planets used in talismans.)

He said he had found a rule to find magic cubes (one of his examples is in the attached image) and also determined how many different ways each such cube can be arranged, which he called ‘one of the most beautiful things in arithmetic’.

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[Each day of February, I am posting a short interesting story/image/fact/anecdote related to the aesthetics of mathematics.]

#Fermat #NumberTheory #HistMath #MathematicalBeauty #MagicSquare

#Fermat’s Last #Theorem: The 350-Year-Old #Mathematical #Drama That Finally Ended : Medium

#Amazon lakes hit ‘#Unbearable’ hot-tub temperatures amid mass die-offs of pink #River #Dolphins – study : Guardian

Great #Nicobar #Island: Hurtling Towards an #Environmental #Catastrophe : Misc

Latest #KnowledgeLinks

https://knowledgezone.co.in/resources/bookmarks

How Fermat's 'last theorem' was proved:
https://www.youtube.com/watch?v=nUN4NDVIfVI
#maths #Fermat #mathematics #elliptic #modular

It is possible to develop bug-free software using the "piped" development model. I have a truly marvellous demonstration of this proposition, which this career
is too small to contain. #fermat #variation #iactuallydohaveatheory

📐 "Dernier théorème de #Fermat : à l'épreuve de l'informatique" (La Science, CQFD, 27 mars 2025)
https://www.radiofrance.fr/franceculture/podcasts/la-science-cqfd/le-dernier-theoreme-de-fermat-8350706
"Un projet collaboratif s’est donné pour objectif de formaliser la #preuve du #théorème de Fermat afin de pouvoir l’apprendre à un ordinateur. Quel est l’enjeu de cette formalisation ? Pourquoi est-ce si compliqué ? Qu’est-ce qu’un assistant de preuve et quel est son rôle en mathématiques ?"

Fermat conjectured that for \(n\) a non-negative integer, all numbers of the form \(2^{2^n}+1\) are prime.

Was there ever a worse conjecture in maths than that?

#Maths #Math
#MathsEd #MathEd
#MathsChat #MathChat
#Fermat #Conjecture
#Primes #FermatPrimes

"Golden Angle"

1000 small squares go from an angular offset of 0 up to the golden angle of 137.508°.
From a line to the perfect distribution in a Fermat spiral based on the Fibonacci series.

This is the speedramp-version.
Watch the full one-hour math meditation / living painting on a big screen at 4k 60fps on YouTube:
https://youtu.be/PmOVaKauq8U

#Tooll3 #realtime #Fermat #Fibonacci #Spiral #meditation #math #creativecoding #HLSL #mathtodon #abstractart #beautyofmath #opensource

#Langlands - The Biggest Project in Modern #Mathematics

https://www.youtube.com/watch?v=_bJeKUosqoY&ab_channel=QuantaMagazine

#LanglandsProgramme #LanglandsProject #NumberTheory #Arithmetic #Math #Maths #Mathematics #Harmonics #HarmonicTheory #Numbers #Ramanujan #Fermat #Wiles #Weil #Frey #Proof #MathematicalProof

Vandaag is de 70ste verjaardag van Andrew Wiles. In 2016 won hij de Abelprijs voor zijn bewijs van de laatste stelling van Fermat. Hij was toen de jongste Abelprijswinnaar ooit.
#andrewwiles #abelprize #fermat https://www.nrc.nl/nieuws/2016/03/17/wederopstanding-van-een-bewijs-1599430-a1092174

Happy birthday to French mathematician, physicist and philosopher Marie-Sophie Germain (1776 – 1831), known as Sophie. She taught herself mathematics using books in her father's library and by corresponding with leading mathematicians of her day, including Lagrange, Legendre and Gauss, …

#linocut #printmaking #sciart #mathart #SophieGermain #ChladniFigures #mathematician #Fermat #womenInSTEM #physicist #elasticity #Gauss #histstm #printmaker #ReliefPrint #WomensHistoryMonth