Paysages Mathématiques
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paysmaths.bsky.social
Paysages Mathématiques
@paysmaths.bsky.social
250 followers 58 following 1.4K posts
Une citation mathématique chaque jour & quelques actualités mathématiques.
A mathematical quote every day & some mathematical news.
Site : https://paysmaths.net

#mathématiques #mathematics #maths #math
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Theorem of the Day (November 15, 2025) : The Spherical Law of Cosines
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/ZHvsFX4
notes : buff.ly/A47uyCK

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Spherical Law of Cosines : Suppose that a spherical triangle on the unit sphere has side lengths a, b and c, and let C denote the angle adjacent to sides a and b. Then (using radian measure): cos(c) = cos(a) cos(b) + sin(a) sin(b) cos(C)
November 15, 2025 at 11:00 AM
paysmaths.bsky.social
"And perhaps posterity will thank me for having shown it that the ancients did not know everything." – Pierre de Fermat (v.1607-1665)
#quote #mathematics #maths #math
Portrait of Pierre de Fermat, and a quote : "And perhaps posterity will thank me for having shown it that the ancients did not know everything."
November 14, 2025 at 5:02 PM
paysmaths.bsky.social
"Et peut-être la postérité me saura gré de lui avoir fait connaître que les Anciens n’ont pas tout su." – Pierre de Fermat (v.1607-1665)
#citation #mathématiques #maths #math
Portrait de Pierre de Fermat, et une citation : "Et peut-être la postérité me saura gré de lui avoir fait connaître que les Anciens n’ont pas tout su."
November 14, 2025 at 5:01 PM
paysmaths.bsky.social
Theorem of the Day (November 14, 2025) : Cantor’s Uncountability Theorem
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/G4NZ6aT
notes : buff.ly/Keq6cjS

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Cantor’s Uncountability Theorem : There are uncountably many infinite 0-1 sequences.
November 14, 2025 at 11:00 AM
paysmaths.bsky.social
"Srinivasa Ramanujan était l'homme le plus étrange de toutes les mathématiques, et probablement de toute l'histoire des sciences. Il a été comparé à une supernova éclatante, illuminant les recoins les plus sombres [...] – Michio Kaku (1947–)
#citation #mathématiques #maths #math
Portrait photographique de Michio Kaku, et une citation : "Srinivasa Ramanujan était l'homme le plus étrange de toutes les mathématiques, et probablement de toute l'histoire des sciences. Il a été comparé à une supernova éclatante, illuminant les recoins les plus sombres et les plus profonds des mathématiques, avant d'être tragiquement terrassé par la tuberculose à l'âge de 33 ans, comme Riemann avant lui. Travaillant totalement isolé des principaux courants de son domaine, il a pu redéduire à lui seul 100 ans de mathématiques occidentales. La tragédie de sa vie est qu'une grande partie de son travail a été gaspillée à redécouvrir des mathématiques connues."
November 13, 2025 at 5:04 PM
paysmaths.bsky.social
"Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics [...] – Michio Kaku (1947–)
#quote #mathematics #maths #math
Photographic portrait of Michio Kaku, and a quote : "Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33, like Riemann before him. Working in total isolation from the main currents of his field, he was able to rederive 100 years' worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics."
November 13, 2025 at 5:04 PM
paysmaths.bsky.social
Theorem of the Day (November 13, 2025) : Euler’s Continued Fraction Correspondence
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/Hey1bCx
notes : buff.ly/fK6qUF2

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem : Euler’s Continued Fraction Correspondence.
November 13, 2025 at 11:00 AM
paysmaths.bsky.social
"À chaque étape majeure, la physique a nécessité, et souvent stimulé, l'introduction de nouveaux outils et concepts mathématiques. Notre compréhension actuelle des lois de la physique, avec leur extrême précision [...]" – Michael Atiyah (1929–2019)
#citation #mathématiques #maths #math
Portrait photographique de Michael Atiyah, et une citation : "À chaque étape majeure, la physique a nécessité, et souvent stimulé, l'introduction de nouveaux outils et concepts mathématiques. Notre compréhension actuelle des lois de la physique, avec leur extrême précision et leur universalité, n'est possible qu'en termes mathématiques."
November 12, 2025 at 5:04 PM
paysmaths.bsky.social
"At every major step, physics has required, and frequently stimulated, the introduction of new mathematical tools and concepts. Our present understanding of the laws of physics, with their extreme precision and universality [...]" – Michael Atiyah (1929–2019)
#quote #mathematics #maths #math
Photographic portrait of Michael Atiyah, and a quote : "At every major step, physics has required, and frequently stimulated, the introduction of new mathematical tools and concepts. Our present understanding of the laws of physics, with their extreme precision and universality, is only possible in mathematical terms."
November 12, 2025 at 5:03 PM
paysmaths.bsky.social
Theorem of the Day (November 12, 2025) : Heath’s Finitely Discontinuous Function Theorem
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/mUa6Rgm
notes : buff.ly/2yEYC1y

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Heath’s Finitely Discontinuous Function Theorem : Let G and H be graphs whose edge and vertex sets have cardinality eG and eH, and vG and vH, respectively. There is a k-to-1 finitely discontinuous function from G onto H if and only if eG − vG ≤ k(eH − vH), with equality being required to hold in the case k = 2.
November 12, 2025 at 11:00 AM
paysmaths.bsky.social
"When the difficulty of a problem lies only in finding out what follows from certain fixed premises, mathematical methods furnish invaluable wings for flying over intermediate obstructions." – Arthur Mellen Wellington (1847–1895)
#quote #mathematics #maths #math
Portrait of Arthur Mellen Wellington, and a quote : "When the difficulty of a problem lies only in finding out what follows from certain fixed premises, mathematical methods furnish invaluable wings for flying over intermediate obstructions."
November 11, 2025 at 5:04 PM
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"Quand la difficulté d'un problème réside uniquement dans la détermination de ce qui découle de certaines prémisses fixes, les méthodes mathématiques fournissent des ailes précieuses pour survoler les obstacles intermédiaires." – Arthur Mellen Wellington (1847–1895)
#citation #mathématiques #maths
Portrait de Arthur Mellen Wellington, et une citation : "Quand la difficulté d'un problème réside uniquement dans la détermination de ce qui découle de certaines prémisses fixes, les méthodes mathématiques fournissent des ailes précieuses pour survoler les obstacles intermédiaires."
November 11, 2025 at 5:02 PM
paysmaths.bsky.social
Theorem of the Day (November 11, 2025) : The Strong Perfect Graph Theorem
Source : Theorem of the Day / Robin Whitty
pdf : www.theoremoftheday.org/Combinatoria...
notes : www.theoremoftheday.org/Resources/Th...

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Strong Perfect Graph Theorem : A graph G is perfect if and only if neither G nor its complement contains an induced odd circuit of length ≥ 5.
November 11, 2025 at 11:01 AM
paysmaths.bsky.social
"I think you can't do mathematics without the ability to concentrate. But also, that's where the fun is, the rest of the world fades away and it's you and the mathematics. And I think there isn't any other way to do mathematics." – Karen Uhlenbeck (1942–)
#quote #mathematics #maths #math
Photographic portrait of Karen Uhlenbeck, and a quote : "I think you can't do mathematics without the ability to concentrate. But also, that's where the fun is, the rest of the world fades away and it's you and the mathematics. And I think there isn't any other way to do mathematics."
November 10, 2025 at 5:05 PM
paysmaths.bsky.social
"Je pense qu'on ne peut pas faire de mathématiques sans la capacité de se concentrer. Mais c'est aussi là qu'est le plaisir, le reste du monde s'efface et il n'y a que vous et les mathématiques.[...] – Karen Uhlenbeck (1942–)
#citation #mathématiques #maths #math
Portrait photographique de Karen Uhlenbeck, et une citation : "Je pense qu'on ne peut pas faire de mathématiques sans la capacité de se concentrer. Mais c'est aussi là qu'est le plaisir, le reste du monde s'efface et il n'y a que vous et les mathématiques. Et je pense qu'il n'y a pas d'autre façon de faire des mathématiques."
November 10, 2025 at 5:04 PM
paysmaths.bsky.social
Theorem of the Day (November 10, 2025) : The Borsuk–Ulam Theorem
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/IMkcDEP
notes : buff.ly/hbhWEcr

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Borsuk–Ulam Theorem : Let f : S^n → R^n be a continuous map. Then some pair of antipodal points on S^n is mapped by f to the same point in R^n.
November 10, 2025 at 11:01 AM
paysmaths.bsky.social
"The analytical equations [...] which Descartes was the first to introduce into the study of curves and surfaces, are not restricted to the properties of figures, and to those properties which are the object of rational mechanics [...]" – Joseph Fourier (1768-1830)
#quote #mathematics #maths #math
Portrait of Joseph Fourier, and a quote : "The analytical equations [...] which Descartes was the first to introduce into the study of curves and surfaces, are not restricted to the properties of figures, and to those properties which are the object of rational mechanics ; they extend to all general phenomena. There cannot be a language more universal and more simple, more free from errors and from obscurities, that is to say more worthy to express the invariable relations of natural things."
November 9, 2025 at 5:02 PM
paysmaths.bsky.social
"Les équations analytiques [...] que Descartes a introduites le premier dans l'étude des courbes et des surfaces, ne sont pas restreintes aux propriétés des figures, et à celles qui sont l'objet de la mécanique rationnelle [...]" – Joseph Fourier (1768-1830)
#citation #mathématiques #maths #math
Portrait de Joseph Fourier, et une citation : "Les équations analytiques [...] que Descartes a introduites le premier dans l'étude des courbes et des surfaces, ne sont pas restreintes aux propriétés des figures, et à celles qui sont l'objet de la mécanique rationnelle ; elles s'étendent à tous les phénomènes généraux. Il ne peut y avoir de langage plus universel et plus simple, plus exempt d'erreurs et d'obscurités, c'est-à-dire plus digne d'exprimer les rapports invariables des êtres naturels."
November 9, 2025 at 5:00 PM
paysmaths.bsky.social
Theorem of the Day (November 9, 2025) : Netto’s Conjecture (Dixon’s Theorem)
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/eWQ4C4N
notes : buff.ly/ElCux2H

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Netto’s Conjecture (Dixon’s Theorem) : Two random permutations of {1, . . . , n} generate either the symmetric group Sn or the alternating group An with probability tending to 1 as n tends to infinity.
November 9, 2025 at 11:00 AM
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"La mathématique est la science dominante de notre époque ; ses conquêtes grandissent chaque jour, bien qu'en silence ; celui qui ne l'a pas pour lui l'aura un jour contre lui." – Johann Friedrich Herbart (1776-1841)
#citation #mathématiques #maths #math
Portrait de Johann Friedrich Herbart, et une citation : "La mathématique est la science dominante de notre époque ; ses conquêtes grandissent chaque jour, bien qu'en silence ; celui qui ne l'a pas pour lui l'aura un jour contre lui."
November 8, 2025 at 5:02 PM
paysmaths.bsky.social
"Mathematics is the predominant science of our time; its conquests grow daily, though without noise; he who does not employ it for himself, will some day find it employed against himself." – Johann Friedrich Herbart (1776-1841)
#quote #mathematics #maths #math
Portrait of Johann Friedrich Herbart, and a quote : "Mathematics is the predominant science of our time; its conquests grow daily, though without noise; he who does not employ it for himself, will some day find it employed against himself."
November 8, 2025 at 5:01 PM
paysmaths.bsky.social
Theorem of the Day (November 8, 2025) : Moessner’s Magic
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/euK0PhS
notes : buff.ly/uLECAU2

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Moessner’s Magic : For integers n ≥ 1 and k ≥ 2, the value of n^k is given by ∑_(r=1)^n ∑_(c=2)^k ((n − r)k + c − 1) r^(k−c)(r − 1)^(c−2).
November 8, 2025 at 11:01 AM
paysmaths.bsky.social
"À partir de rien, j'ai créé un étrange nouvel univers." – János Bolyai (1802-1860), à propos de sa découverte de la géométrie non euclidienne.
#citation #mathématiques #univers #maths #math #géométrie
Portrait de János Bolyai, et une citation : "À partir de rien, j'ai créé un étrange nouvel univers."
November 7, 2025 at 5:05 PM
paysmaths.bsky.social
"Out of nothing I have created a strange new universe." – János Bolyai (1802-1860), on his discovery of non-Euclidean geometry.
#quote #mathematics #maths #math #geometry #universe
Portrait of János Bolyai, and a quote : "Out of nothing I have created a strange new universe."
November 7, 2025 at 5:03 PM
paysmaths.bsky.social
Theorem of the Day (November 7, 2025) : Brun’s Theorem
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/1osboRM
notes : buff.ly/S82D1tJ

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Brun’s Theorem : The series 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/29 + 1/31 + 1/41 + 1/43 + 1/59 + 1/61 + ..., where the denominators are twin prime numbers, is convergent or finite.
November 7, 2025 at 11:00 AM