gutenberg_org, to books
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Spanish playwright, economist, mathematician, and politician José Echegaray was born in 1832.

One of his most famous plays is "El gran Galeoto", which explores themes of jealousy, honor, and redemption. Another notable work is "El loco Dios", which delves into the relationship between faith and reason. He won the fourth Nobel Prize for Literature in 1904, making him the first Spaniard to receive this award.

Books by José Echegaray at PG:
https://www.gutenberg.org/ebooks/author/40983

Cover of The great Galeoto; Folly or saintliness by José Echegaray

gutenberg_org,
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«Las matemáticas forman una salsa que viene bien a todos los guisos del espíritu. Armonizan con la música y el arte en general. Como que todas son armonías, variedades en una o en otra forma, que se resuelven en una alta y bella unidad».

"Mathematics forms a sauce that goes well with all the stews of the spirit. They harmonize with music and art in general. As it were, they are all harmonies, varieties in one form or another, resolving into a high and beautiful unity."

Echegaray

mindaslab, to mathematics
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uniinnsbruck, to mathematics
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Today, 200 students from schools in Tirol, Vorarlberg and Salzburg are taking part in the international Competition at the University of Innsbruck

danyal, to mathematics
@danyal@neuromatch.social avatar

I’m also apparently failing fourth grade math 💀😭

jcponcemath, to opensource
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smote, to KindActions
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matty,
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video/mp4

OscarCunningham, to math
@OscarCunningham@mathstodon.xyz avatar

Mathematicians sometime talk about algebra and geometry being dual to each other. One way to formalise this is by talking about opposite categories. If the objects of a category act like algebras, then in the opposite category they act like spaces.

But the category of finite dimensional vector spaces is its own opposite! This suggests that linear algebra is in some sense the place where algebra and geometry meet. Perhaps that explains why it's so tractable and efficacious.

#Math #Maths #Mathematics #CategoryTheory #LinearAlgebra

JeremyMallin, to physics
@JeremyMallin@autistics.life avatar

What would the universe look like if there were more than one time-like dimensions?

#RandomThoughts #Physics #Cosmology #Mathematics

gimulnautti, to mathematics
@gimulnautti@mastodon.green avatar

people:

I feel there has to be a way of training neural networks to recognise the influence of their training data on the output.

This would probably include training a complementary indexing network + database that would then ”reverse-training” resolve and offer at some predetermined accuracy the -viable sources for each generated

I need some help though. A proof would show the companies know it can be done, but they just don’t want to.

tao, to ai
@tao@mathstodon.xyz avatar

@TaliaRinger has helped put together a useful list of resources for in , that was initiated during the National Academies workshop on "AI in mathematical reasoning" last year. This list is now publicly available at https://docs.google.com/document/d/1kD7H4E28656ua8jOGZ934nbH2HcBLyxcRgFDduH5iQ0/edit

ulaulaman, to mathematics
@ulaulaman@mastodon.social avatar

Geometric Shapes and Their Symbolic Meanings

https://www.learnreligions.com/geometric-shapes-4086370

Forms ranging from circles to dodekagrams have significance in many philosophies

@mathematics @mathematics

ulaulaman, to mathematics
@ulaulaman@mastodon.social avatar

Merging Fields, Mathematicians Go the Distance on Old Problem

https://www.quantamagazine.org/merging-fields-mathematicians-go-the-distance-on-old-problem-20240401/

Mathematicians have illuminated what sets of points can look like if the distances between them are all whole numbers.

@mathematics @mathematics

monsoon0, to mathematics
@monsoon0@mathstodon.xyz avatar

Suppose E is an elliptic curve. I have groups of transformations that are compositions of automorphisms of E and a translation of the marked point on E. Is there a name for these transformations?

paninid, to politics
@paninid@mastodon.world avatar

"I must study politics and war, that my sons may have liberty to study mathematics and philosophy.

“My sons ought to study mathematics and philosophy, geography, natural history, naval architecture, navigation, commerce, and agriculture, in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry, and porcelain."

  • John Adams

ulaulaman, to mathematics
@ulaulaman@mastodon.social avatar

Mathematics Ancient Egypt, The Incredible Achievements

https://mythologis.com/blogs/egyptian-mythology/mathematics-ancient-egypt

The were known for their advanced understanding of and its many practical uses. From the construction of the iconic to their use of algebraic techniques to solve problems, the ancient Egyptians were masters of the mathematical arts.

@mathematics @mathematics

jcponcemath, to opensource
@jcponcemath@mathstodon.xyz avatar
kravietz, to random Polish
@kravietz@agora.echelon.pl avatar

Taka obserwacja kulturowo-socjologiczna: na Fediverse od dawna jest trochę Rosjan “z Rosji” (w sensie, że nie emigrantów), głównie uciekinierów z mainstreamowych rosyjskich sieci społecznościowych typu VK po wprowadzeniu cenzury kilka lat temu. Poza grupą autentycznie szurniętych nacjonalistów (którzy też byli wtedy w Rosji ścigani, stąd ucieczka z VK) z większością z nich do wojny i przez pierwszy rok można było normalnie dyskutować. Mam tu na myśli dyskusję na poziomie jaki mogą prowadzić ludzie mający czasem odmienne poglądy ale potrafiący wysłuchać argumentów drugiej strony i z nimi polemizować lub je przyjąć. Ale w ciągu ostatniego roku dokonała się ciekawa zmiana kulturowa. Jeżeli mogę dokonać kilku uogólnień na podstawie niedawnej (i chyba ostatniej) dyskusji z nimi:

  • W złym tonie jest podawanie… źródeł informacji. W dobrym tonie jest pisanie “swoimi słowami”. To znaczy, jeżeli ktoś napisze “ja wiem, że rakiety S-300 nie mogą trafiać w cele naziemne” to ma to z ich punktu widzenia większą wartość poznawczą niż ”nawet ze źródeł rosyjskich wynika, że mogą - tutaj jest link do TopWar.ru” (popularny portal wojskowy w Rosji). Nie mam pojęcia z czego to wynika, podejrzewam jakiś podprogowy komunikat o tym, że wszystkie linki mogą prowadzić do exploitów i wirusów.
  • Całkowite pogrążenie w oficjalnej rosyjskiej narracji - oni nie wiedzą, że Charków był regularnie ostrzeliwany od lutego 2022 i autentycznie myślą, że rosyjskie ostrzały Charkowa zaczęły się dopiero w odwecie za ukraińskie ostrzały Biełgorodu czyli około grudnia 2023.
  • Całkowita brak zdolności do konfrontacji z informacją nie pasującą do tej oficjalnej narracji. W naszej kulturze, jeżeli ktoś poda informację sprzeczną z naszą wiedzą to zaczyna się kopanie w źródłach - albo ja mam błędne źródło, albo on/ona i na podstawie uznawanych przez obie strony można to ustalić. Rosyjskie “pokolenie wojenne” po prostu kończy dyskusję, nie było tematu.
  • Ciekawe zjawisko “podwójnej moralności” - wobec “swoich” przyznajemy nieco więcej (np. ludobójcze cele Kremla w zakresie “złamania Ukrainy”) niż wobec “obcych” (negowanie tych wypowiedzi i upieranie się, że to tylko “”emocje”). Ale to akurat Rosjanie mieli zawsze, to nie jest nowe zjawisko.
  • Odrzucanie dowolnych relacji świadków czy wręcz materiałów wideo z miejsc wydarzeń na tej podstawie, że “nie było cię tam na miejscu, nie wiesz jak było”. W konsekwencji tuzin bezpośrednich relacji wideo z danego miejsca jest odrzucany jako “niewiarygodny” ale obwieszczenia oficjalnych przedstawicieli władzy jest traktowane przynajmniej jako wyraz oficjalnej wersji.
  • Bezkrytyczne podejście do częstych w rosyjskiej oficjalnej narracji zmian stanowiska o 180°. Fakt, że dzisiaj władza mówi coś całkowicie odwrotnego niż wczoraj nie wywołuje absolutnie żadnych refleksji na temat tego, że władza może w danym przypadku kłamać oraz, że jutro powie coś inne niż dzisiaj. Jest prawda życia, i jest “prawda etapu”.

W większości są to zjawiska dość oczywiste dla każdego kto ma kontakt z Rosjanami “z Rosji”, nowością dla mnie była obsesyjna fiksacja na “swoimi słowami” oraz odrzucanie źródeł. Nie wiem w jaką stronę to idzie ale wygląda na to, że oni sami siebie zagnali w jakąś sekciarską informacyjną czarną dziurę. Długofalowe konsekwencje, przede wszystkim dla rosyjskiego społeczeństwa, będą dramatyczne.

doboprobodyne, (edited )
@doboprobodyne@mathstodon.xyz avatar

@kravietz

May I add some hashtags in order to solicit views of psychologists and others who deal with human (or animal) cognitive modelling of reality? I would be fascinated to read about the degree to which we're all vulnerable to bias, the highest-yield methods of protecting oneself from bias (especially in social media), and of helping reflect back to others their own views in a way that lets them critique them. I think the last point is especially hard, especially if the other person has no desire for critical thinking (and as humans, we are terrible at critical thinking!).

If there are any textbooks on the subject, ideally written by scientists &/or aimed at scientists, I'd be keen as mustard to know about them!

If anyone has opinions on the work of Han, Lee, Wang, & Baldwin (librai fact checking automation - https://github.com/Libr-AI/OpenFactVerification ) I'd be all ears too.

Please feel free to boost this if you think answers might interest you.

metin, to animation
@metin@graphics.social avatar
metin, to science
@metin@graphics.social avatar
gutenberg_org, to books
@gutenberg_org@mastodon.social avatar

German painter, engraver, and mathematician Albrecht Dürer died #OTD in 1528.

Beyond his artistic achievements, Dürer also wrote extensively on art theory and mathematics, contributing to the intellectual discourse of his time. He produced treatises on perspective, proportion, and the theory of art, which were influential in shaping artistic practice in the Renaissance and beyond.

Books by Albrecht Dürer at PG:
https://www.gutenberg.org/ebooks/author/1135

#books #art #literature #mathematics

Melencolia I (1514), engraving
Dürer's study of human proportions Albrecht Dürer - https://archive.org/stream/hierinnsindbegri00dure#page/151/mode/1up Face transformations by Albrecht Dürer

ulaulaman, to mathematics
@ulaulaman@mastodon.social avatar

How the number pi inspired a writing style

https://www.bbc.com/future/article/20160311-how-the-number-pi-inspired-a-writing-style

The number pi, which is celebrated with its own day on 14 March, has inspired “Pilish” – a fiendishly challenging form of writing. There’s even a Pilish novel. Give it a go yourself, it can be strangely addictive...

@mathematics @mathematics

ksoltys, to mathematics
@ksoltys@twit.social avatar

This is remarkable. It's the mathematics equivalent of Einstein's theory of relativity in terms of significance. If the math holds up (I've skimmed their paper and there's no way I can judge, but the examples look convincing) they are guaranteed a Fields Medal (the mathematical equivalent of the Nobel Prize). There's a link to the paper at the end of the article if you want to have a look at what really advanced number theory looks like.

https://phys.org/news/2024-04-breakthrough-prime-theory-primes.html

@gregeganSF

gutenberg_org, to books
@gutenberg_org@mastodon.social avatar

Scottish mathematician, physicist, and astronomer John Napier died #OTD in 1617.

Napier's most famous work is his treatise "Mirifici Logarithmorum Canonis Descriptio", published in 1614. In this work, he introduced logarithms as a means to simplify complex mathematical calculations, particularly in the field of astronomy and navigation. He invented the concept of Napier's bones used for multiplication, and he made advancements in spherical trigonometry.

#books #science #mathematics #astronomy

Page from the end of Napier's 1614 logarithm table Mirifici Logarithmorum Canonis descriptio. The page cover angles between 44 degrees 30 minutes and 45 degrees 30 minutes. Adjacent to each outermost column is the sine of that angle, followed by the absolute value of the natural log of the sine. One can obtain cosines easily by reading across the page. The middle column gives the difference between the two logs, which is the natural log of the tangent function (cotangent if you reverse sign).

diffgeom, to mathematics
@diffgeom@mathstodon.xyz avatar

Yesterday I learned:

Let (n \geq 2) be an integer. The regular (n)-gon inscribed in the complex unit circle and having (1) as a vertex, a.k.a., the convex hull of the (n)th roots of unity, is closed under complex multiplication.

https://math.stackexchange.com/questions/4892153/is-multiplication-of-two-complex-numbers-that-are-inside-a-complex-regular-polyg

To summarize the accepted answer,

  1. The set of (n)th roots of unity is closed under multiplication, and
  2. The product of two convex linear combinations of the vertices is itself a convex linear combination.

It's crucial to take the "standard" (n)-gon whose vertices are the (n)th roots of unity, i.e., not to take an arbitrary regular (n)-gon inscribed in the unit circle. The animations show the situation for (n = 7), with roots of unity ("standard") on the left, and the polygon rotated by one-tenth of a radian ("non-standard") on the right.

An animation loop showing "the standard regular heptagon" multiplied by a point along the edge from unity to the first non-trivial seventh root of unity. The light green "product" heptagon is contained in the light blue original.
An animation loop showing a "non-standard regular heptagon" multiplied by a point along the "first edge." The light green "product" heptagon is generally not contained in the light blue original.

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