#fermat — Public Fediverse posts

From a Mathematical Curiosity to the Foundation of Internet Security 🧮🧐🔐✨

In 1636, Pierre de Fermat made a remarkable observation: if you take an integer a, raise it to a prime power p, and then subtract a, the result is always divisible by p. In other words, for a prime p,

aᵖ ≡ a (mod p).

For example, when p = 5:
2⁵ − 2 = 30, which is divisible by 5, and
3⁵ − 3 = 240, which is also divisible by 5.

Fermat found this property elegant and tried to spark interest in this curious corner of mathematics. Not everyone was impressed. John Wallis reportedly dismissed such results, remarking, “Big deal; I could find other relationships just as interesting without much effort, and none of them are important.”

About a century later, Leonhard Euler was encouraged by Christian Goldbach to study Fermat’s ideas. Though initially unenthusiastic, Euler soon uncovered deeper structure within them. His work laid much of the foundation for what we now call modern number theory.

#Mathematics #Math #NumberTheory #Fermat #Euler #EulerTheorem #FermatsLittleTheorem #ModularArithmetic #RSA #Cryptography #CyberSecurity #HistoryOfMathematics #MathHistory #PrimeNumbers #EulerTotient #AbstractMath #PureMathematics #STEM #ScienceCommunication #MathEducation #EducationalContent #DidYouKnow #MathematicalBeauty #InternetSecurity #Encryption #Curiosity #Innovation #History #Learning #Knowledge

#Codex hat eine interessante Auswahl an Namen für Sub-Agenten eines umzusetzenden Tasks. Und natürlich ist #Fermat der "Letzte". 😃

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 $n > 2$’

1/2

[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’.

1/2

[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 states that no three positive integers a, b, and c can satisfy the equation a^n + b^n=c^n for any integer value of n greater than 2.

https://knowledgezone.co.in/kbits/6920305f2c0108f63e818c8b

#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

Lean proof of Fermat's Last Theorem [pdf]

https://imperialcollegelondon.github.io/FLT/blueprint.pdf

#HackerNews #Lean #Fermat #Last #Theorem #proof #pdf #mathematics #research

#Fermat

F₇ - fully factored 1970
F₈ - fully factored 1980
F₉ - fully factored 1990

wait...

I see a pattern here!

#OnThisDay British #Mathematician Andrew Wiles proved last #Theorem of #Fermat (1993).

Birth Anniversary of #French #Philosopher Jean-Paul Sartre (1905) - one of the leading figures in 20th-century French philosophy and Marxism.

Today is World #MusicDay, International Day of #Yoga.

https://knowledgezone.co.in/news

https://www.wacoca.com/anime/1847744/ Math Whiz Turns Chef?! 🔥 Fermat’s Cuisine Anime Trailer! #2025Summer #2025SummerAnime #2025年夏開始の新作アニメ #Anime #AnimeNews #cooking #DomericaStudio #DXTEEN #FermatNoRyōri #FermatNoRyōri(Fermat'sCuisine) #Fermat'sCuisine #GakuKitada #gamenews #Gaming #KaiAsakura #Kodansha #manga #OpeningTheme #OSHIKIKEIGO #otaku #Trailer #Videogames #YūgoKobayashi #アニメ #フェルマーの料理 #新作アニメ

📐 "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 ?"

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, initially using the pseudonym Monsieur LeBlanc. 🧵1/n
⁠
#linocut #printmaking #sciart #mathart #SophieGermain #ChladniFigures #mathematician #Fermat #womenInSTEM #physicist

Dernier #théorème de #Fermat : à l'épreuve de l' #informatique
Podcast #France #Culture ( 58 min)

https://www.radiofrance.fr/franceculture/podcasts/la-science-cqfd/le-dernier-theoreme-de-fermat-8350706

Random thought: what if Fermat was wrong? I mean that what if he *did* write out his infamous last theorem and the math was incorrect. Would we have still found his hypothesis was correct or would we have given up sooner with it just becoming a play thing every time someone got a spark of inspiration?

#math #maths #fermat

One day, one decomposition
A181780: Numbers n which are Fermat pseudoprimes to some base b, 2 <= b <= n-2

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A181780.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A181780.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #primes #PrimeNumbers #Fermat #pseudoprimes #graph #threejs #webGL

@Erklaerbaer
Im Ernst schau dir den Unterricht an der zbsp an der Schule (Gymnasium Eifel Kreis Euskirchen) unserer Kids abläuft. Da wundert es dich kaum noch, wenn die Lücken haben.
Es fehlen häufig so viele Lehrkräfte das es wundert dass der Schulbetrieb aufrecht erhalten werden kann.

#Fermat #Euler #Euklid

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

"Fermat Gyroscope"

10 minute 4k 60fps version on YouTube:
https://youtu.be/YN3TafRC-Nw

#Tooll3 #realtime #newmediaart #abstractart #generativeart #particles #livingpainting #creativecoding #hlsl #gpu #shader #generative #procedural #visualart #Zen #wuwei #dao #math #opensource #Fermat #sphere

"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

My Fermat-Spiral point generator again, this time I'm animating first sBias between 0 and 1 and then sGain while also animating the step angle offset...

Simple Nerd Fun for a Saturday 🥳

#Tooll3 #realtime #generativeart #particles #creativecoding #hlsl #gpu #shader #generative #procedural #visualart #Zen #wuwei #dao #Fermat #sunflowerseeds #Schlick #Bias #Gain #mastoart

In Toulouse kwam ik dit standbeeld van wiskundige #Fermat tegen.

Ik snap wel waarom hij even geen tijd had om het bewijs van zijn Laatste Stelling helemaal op te schrijven en er alleen even een opmerking in de kantlijn over schreef 😉

https://nl.m.wikipedia.org/wiki/Laatste_stelling_van_Fermat