Live and recent posts from across the Fediverse tagged #galois, aggregated by home.social.
Have you ever heard of Evariste Galois?
He was a French mathematician who died at the age of 20 in a duel.
He founded Group Theory and the Galois Theory, but it took decades for other mathematicians to understand his concepts.
There is a wonderful book about him by astronomer Mario Livio: "The equation that could not be solved", highly recommended.
PrivateBin
Current version: 2.0.3
Anyone on the FediVerse running PrivateBin on their own (small) network?
Data is encrypted & decrypted in your browser with 256bit AES in Galois Counter mode.
#encryption #programming #PrivateBin #Zero #Knowledge #plausable #deniability #networking #AES256 #Galois #Counter #technology
"L'énorme importance des groupes en algèbre a [...] été mise en évidence pour la première fois par Galois, dont la théorie de la résolution des équations algébriques est l'une des grandes réalisations du siècle. Son influence s'est étendue bien au-delà des limites étroites de l'algèbre." – James Pierpont (1866–1938)
#citation #mathématiques #Galois #maths #math
"The enormous importance of groups in algebra was [...] first made clear by Galois, whose theory of the solution of algebraic equations is one of the great achievements of the century. Its influence has stretched far beyond the narrow bounds of algebra." – James Pierpont (1866–1938)
#quote #mathematics #Galois #maths #math
#Galois #Theory, developed by Évariste Galois, is a branch of abstract #Algebra linking #Field theory (studying number systems) and #Group theory (studying symmetries) to understand #Polynomial #Equations.
Automated Lean Proofs for Every Type
https://www.galois.com/articles/automated-lean-proofs-for-every-type
#HackerNews #AutomatedLeanProofs #Lean #TheoremProving #Automation #Technology #Galois
Une #équation #polynômiale d’ #algèbre , de degré >= 5 , vieille de 3 700 ans percée à jour grâce aux #Nombres de #Catalan.
Un #chercheur #australien #révolutionne les méthodes de #résolution d’ #équations #polynomiales : La théorie d'Évariste #Galois en échec..
Une #équation #polynômiale d’ #algèbre , de degré >= 5 , vieille de 3 700 ans percée à jour grâce aux #Nombres de #Catalan.
Un #chercheur #australien #révolutionne les méthodes de #résolution d’ #équations #polynomiales : La théorie d'Évariste #Galois en échec..
dailygeekshow.com/une-equation...
Une équation d’algèbre vieille...
@catselbow
Astonishing! I hadn't come across this before - absolutely fascinating!
#maths #mathematics #polynomial #polynomials #CatalanNumbers #combinatorics #Galois #GaloisTheory
https://www.tandfonline.com/doi/epdf/10.1080/00029890.2025.2460966?needAccess=true
🛠️ Ah, #Galois and their magical #GREASE, the tool that promises to make #vulnerabilities pop like pimples - because who knew binary code needed a skincare routine? 🧴 Meanwhile, they're tackling bold topics like Advanced Cryptography and #AI, but maybe it's just a smokescreen for their real expertise: crafting tools with names that sound like failed indie bands. 🎸
https://www.galois.com/articles/introducing-grease #AdvancedCryptography #IndieBands #HackerNews #ngated
Point-&-Click-#Adventure „Hilbert’s Holidays“
im #Browser kostenlos spielbar
Der Spieler wandert darin im Hotel von Zimmertür zu Zimmertür und lernt #Mathematiker wie Evariste #Galois oder Kurt #Gödel und deren Problemstellungen kennen.
Im Vordergrund steht das spielerische Lernen, z.B. warum unendlich viele Leute bei Hilbert ein Zimmer bekommen können, obwohl alle belegt sind.
Danke an @ct_Magazin für den Hinweis
@dmm
That's exactly what I mean; honestly, getting yourself shot dead in an illegal duel, probably over the favours of a woman, when you could be sat at home doing even more maths is just plain stupid.
#Galois #maths #math #mathematics
F# Crypto #AES equivalent of #Golang #Galois Counter Mode #Encryption
#fsharp #dotnet
https://gist.github.com/giuliohome/b564c3283676599af71222ad2b75b675 (btw 🆒 Fesh editor ✨ ... and dotnet fsi also works well in #windows #terminal)
RAID6 的 Erasure code 實作
Daily Hacker News 上看到的紋章，「Erasure Coding for Distributed Systems」這篇討論了 Erasure code。
以前在學校裡面學 coding theory 的時候有學到一些經典的演算法，尤其是一定會教到 Reed-Solomon error correction 這個演算法，不過實務上 Reed-Solomon 因為用到 finite field 運算 (又稱 Galois field，所以簡寫常用 )，所以效率並不算好，在 RAID 系統上面除非 controller 的
https://blog.gslin.org/archives/2024/09/06/11964/raid6-%e7%9a%84-erasure-code-%e5%af%a6%e4%bd%9c/
#Computer #Murmuring #code #coding #erasure #field #finite #galois #raid #theory #xor
@jbz
But it *was* solved - doesn't that make it not the hardest problem?
Or does hardness refer to how long it took (357 years)?
In which case surely Trisecting an Angle was considerably harder as it took 1500 years.(?)
Also, that woman pronounces "Pythagorean" really weirdly.
:-)
#maths #problems #Fermat #Galois #math #pedantic #JustSaying
Muchas gracias a mi buen amigo @zarzoilustrador por estos cómics, que están rebonitos, ¡me da mucho gusto contar con tu amistá después de tantos años! ¡Sigan su trabajo, es un wenazo! #comics #science #galois #emmynoether #nightingale #graphicnovels #cartoons
"L'énorme importance des groupes en algèbre a [...] été mise en évidence pour la première fois par Galois, dont la théorie de la résolution des équations algébriques est l'une des grandes réalisations du siècle. [...]" – James Pierpont (1866–1938)
#citation #mathématiques #Galois #maths #math
"The enormous importance of groups in algebra was [...] first made clear by Galois, whose theory of the solution of algebraic equations is one of the great achievements of the century. [...]" – James Pierpont (1866–1938)
#quote #mathematics #Galois #maths #math
I am once again trying to understand Galois's original memoir.
#Galois was a very poor expositor, but his ideas are interesting. He does everything as computationally as possible. I'm following Edwards' account, because I honestly cannot understand Galois's original presentation (I don't know how Liouville ever managed to understand him):
http://www.galois.ihp.fr/wp-content/uploads/2011/12/H.-Edwards.pdf
One of the first things he does is define is what we would now call a primitive element and he denotes by 𝑉, an integer linear combination of the roots of the polynomial. But the way he constructs this primitive element is interesting. He constructs a gigantic polynomial (for an equation of degree, this gigantic polynomial is of degree \(5!(5! - 1) = 14280\) in the coefficients of 𝑉 and as long as you pick a non-zero value of this polynomial, you have your primitive element.
The argument is very constructive, albeit clumsy by today's standards. A modern construction of a primitive element doesn't go to such lengths to show that you only need to avoid a linear space of smaller dimension to get your primitive element.
Finito ora. Non è una recensione, che forse scriverò in futuro (dove possa finalmente scrivere più di 500 caratteri 😞)
Devo dire molto simpatico tuttavia: la "sorpresa" romanzata che si sono inventati gli autori, secondo è talmente sopra le righe e tirata per le orecchie, che non regge tanto.
Il setup funziona benissimo, ma poi va via via perdendo. Peccato. Cmq simpatico da leggere, sono contento e lo consiglio.
#EvaristeGalois #Galois #matematica #rivoluzionefrancese #teoriadeigruppi
@dmm I see, thanks! To me it seems then that \( \sqrt{x^2+1} +x \) is the key to the observation. The first term more or less stays on and then the integral is a complicated way to hide the addition of x?
In that sense it sounds trivial but what is less simple is to consider #Galois theory, maybe somebody from #mathematics can pitch in?
Within #Galois theory getting the golden ratio is ok, it comes out from the quadratic equation. The integral is a limit of a Riemann sum and turns out to go outside of the expressive power of the the integrands and the log appears.
This integral appears a lot in classical electrodynamics at undergraduate level. It usually surprises students why there is a closed form.
My best answer is that solving an integral is a question of Galois theory or then more specifically in that case #Liouville theory.
#FinishedReading a fictionalised novel about #Galois by #TomPetsinis , picked up at a #littleFreeLibrary . Galois is a remarkably unpleasant protagonist in this - conceited, sexist, and paranoid, among other faults - but the book is still very readable, carried through by vivid depictions of the revolutionary chaos of 1830s Paris. #Bookstodon #AustralianFiction
Crypto Hedge Fund Galois Capital Shuts Down — ‘We Lost Almost Half Our Assets to FTX Disaster’ - Crypto hedge fund Galois Capital is shutting down after losing about half of its a... - https://news.bitcoin.com/crypto-hedge-fund-galois-capital-shuts-down-we-lost-almost-half-our-assets-to-ftx-disaster/ #cryptohedgefundshutsdownftx #galoisshuttingdown #galoisclosingdown #cryptohedgefund #galoishedgefund #galoiscapital #ftxcontagion #ftxcollapse #galoisftx #featured #galois #ftx
Crypto Hedge Fund Galois Capital Shuts Down — ‘We Lost Almost Half Our Assets to FTX Disaster’
https://news.bitcoin.com/crypto-hedge-fund-galois-capital-shuts-down-we-lost-almost-half-our-assets-to-ftx-disaster/
#cryptohedgefundshutsdownFTX #Galoisshuttingdown #Galoisclosingdown #cryptohedgefund #Galoishedgefund #GaloisCapital #FTXcontagion #FTXcollapse #GaloisFTX #Featured #Galois #ftx
Cómo funciona una #VPN? Derivando nos lo explica en el vídeo: https://www.youtube.com/watch?v=XC4SX3iEeRM