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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"Le seul objet naturel de la pensée mathématique, c’est le nombre entier. C’est le monde extérieur qui nous a imposé le continu, que nous avons inventé sans doute, mais qu’il nous a forcés à inventer." – Henri Poincaré (1854-1912)
#citation #mathématiques #maths #math
Portrait photographique de Henri Poincaré, et une citation : "Le seul objet naturel de la pensée mathématique, c’est le nombre entier. C’est le monde extérieur qui nous a imposé le continu, que nous avons inventé sans doute, mais qu’il nous a forcés à inventer."
November 18, 2025 at 5:05 PM
paysmaths.bsky.social
"The only natural object of mathematical thought is the whole number. It is the external world that has imposed on us the continuum, which we have undoubtedly invented, but which it has forced us to invent." – Henri Poincaré (1854-1912)
#quote #mathematics #maths #math
Photographic portrait of Henri Poincaré, and a quote : "The only natural object of mathematical thought is the whole number. It is the external world that has imposed on us the continuum, which we have undoubtedly invented, but which it has forced us to invent."
November 18, 2025 at 5:03 PM
paysmaths.bsky.social
Theorem of the Day (November 18, 2025) : Cantor’s Theorem
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/qb4zymY
notes : buff.ly/IaCnHHb

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Cantor’s Theorem :The power set 2^X of a set X cannot be put into one to one correspondence with X. Thus the cardinality of 2^X is strictly greater than that of X.
November 18, 2025 at 11:00 AM
paysmaths.bsky.social
"[Pure mathematics is] good to give chills in the spine to a certain number of people, me included. I don't know what else it is good for, and I don't care. But I speak for myself only. Like von Neumann said, one never knows [...]"–Serge Lang (1927-2005)
#quote #mathematics #maths #math
Photographic portrait of Serge Lang, and a quote : "[Pure mathematics is] good to give chills in the spine to a certain number of people, me included. I don't know what else it is good for, and I don't care. But I speak for myself only. Like von Neumann said, one never knows whether someone is going to find another use for it."
November 17, 2025 at 5:04 PM
paysmaths.bsky.social
"[Les mathématiques pures servent] à donner des frissons dans le dos à un certain nombre de gens, dont moi. Je ne sais pas à quoi ça sert d'autre, et ça m'est égal. Mais je parle pour moi [...]"–Serge Lang (1927-2005)
#citation #mathématiques #maths #math
Portrait photographique de Serge Lang, et une citation : "[Les mathématiques pures servent] à donner des frissons dans le dos à un certain nombre de gens, dont moi. Je ne sais pas à quoi ça sert d'autre, et ça m'est égal. Mais je parle pour moi. Comme l'a dit von Neumann, on ne sait jamais à qui ou à quoi ça va servir."
November 17, 2025 at 5:02 PM
paysmaths.bsky.social
Theorem of the Day (November 17, 2025) : Frieze’s Theorem on Expected Minimum Tree Length
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/FPEIpIh
notes : buff.ly/GJu2id4

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. Frieze’s Theorem on Expected Minimum Tree Length : If the edges of the complete graph on n vertices are assigned weights independently uniformly at random from the interval [0, 1] then the expected length of a minimum-weight spanning tree tends, as n → ∞, to ζ(3) ≈ 1.20206.
November 17, 2025 at 11:01 AM
paysmaths.bsky.social
"By strictly observing the few rules I had chosen, I became very adept at unravelling all the questions which fall under these two sciences [geometrical analysis and algebra]. So much so, in fact, that in the two or three months [..]" – René Descartes (1596-1650)
#quote #mathematics #maths #math
Portrait of René Descartes, and a quote : "By strictly observing the few rules I had chosen, I became very adept at unravelling all the questions which fall under these two sciences [geometrical analysis and algebra]. So much so, in fact, that in the two or three months I spent in examining them – beginning with the simplest and most general and using each truth I found as a rule for finding further truths – not only did I solve many problems which I had previously thought very difficult, but also it seemed to me towards the end that even in those cases where I was still in the dark I could determine by what means and to what extent it was possible to find a solution."
November 16, 2025 at 5:01 PM
paysmaths.bsky.social
"L’exacte observation de ce peu de préceptes que j’avais choisis, me donna telle facilité à démêler toutes les questions auxquelles ces deux sciences [analyse géométrique et algèbre] s'étendent, qu’en deux ou trois mois [...] – René Descartes (1596-1650)
#citation #mathématiques #maths #math
Portrait de René Descartes, et une citation : "L’exacte observation de ce peu de préceptes que j’avais choisis, me donna telle facilité à démêler toutes les questions auxquelles ces deux sciences [analyse géométrique et algèbre] s'étendent, qu’en deux ou trois mois que j’employai à les examiner, ayant commencé par les plus simples et plus générales, et chaque vérité que je trouvais étant une règle qui me servait après à en trouver d’autres, non seulement je vins à bout de plusieurs que j'avais jugées autrefois très difficiles, mais il me sembla aussi vers la fin que je pouvais déterminer, en celles même que j'ignorais, par quels moyens, et jusqu'où, il était possible de les résoudre."
November 16, 2025 at 5:01 PM
paysmaths.bsky.social
Theorem of the Day (November 16, 2025) : The Friendship Theorem
Source : Theorem of the Day / Robin Whitty
pdf : buff.ly/isqlhQV
notes : buff.ly/YYPnTEN

#mathematics #maths #math #theorem
Comprehensive presentation of the "Theorem of the Day", starting with a statement of this theorem. The Friendship Theorem : In a finite graph in which any two distinct vertices share exactly one common neighbour some vertex is adjacent to all other vertices.
November 16, 2025 at 11:01 AM
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"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." – Bertrand Russell (1872–1970)
#quote #mathematics #maths #math
Photographic portrait of Bertrand Russell, and a quote : "Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."
November 15, 2025 at 5:02 PM
paysmaths.bsky.social
"Les mathématiques peuvent être définies comme le domaine dans lequel on ne sait jamais de quoi on parle, ni si ce qu'on dit est vrai." – Bertrand Russell (1872–1970)
#citation #mathématiques #maths #math
Portrait photographique de Bertrand Russell, et une citation : "Les mathématiques peuvent être définies comme le domaine dans lequel on ne sait jamais de quoi on parle, ni si ce qu'on dit est vrai."
November 15, 2025 at 5:02 PM
paysmaths.bsky.social
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
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"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
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"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
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"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
paysmaths.bsky.social
"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