Before I say what it is, I am NOT posting this as clickbait (which is how it's often used)! 😂 I'm posting this as a Maths teacher who knows this topic inside-out and wants to help people to understand it better. There are MANY mistakes that people make and get the wrong answer, and I'm going to cover them in bite-size chunks each week for a few weeks
Mathematics academics (or people with a PhD in a maths-y subject), I have just been told about a great toy: Mathematics Genealogy. You can type in any academic's name and find who their PhD supervisor was and who they supervised. It goes all the way back to Newton (and back even before that). Someone I met today can trace their supervisor chain all the way back to Newton himself...
Pythagorean Theorem Found On Clay Tablet 1,000 Years Older Than Pythagoras
"The conclusion is inescapable. The Babylonians knew the relation between the length of the diagonal of a square and its side: d=square root of 2," mathematician Bruce Ratner writes in a paper on the topic.
I’m taking a flight to Brisbane tomorrow. On the way up, I stop in Melbourne. Total flight time for two flights is 2 hours and 15 mins (35 mins in between waiting time). On the way home one flight with a total of 3 hours and 40 minutes. I don’t get it. #maths
Edit: It’s Daylight Saving Time! @sortius
And here's another book I’ve just finished, for anyone who has studied (or is studying) maths. It’s a lovely gallop through the parts of mathematical history that we don’t hear about, steering away from the stories that focus on the “Great Men” of the white western world, and digging around in a far more global and diverse view of how mathematics was developed. Especially highly recommended for anyone teaching maths at any level. It’s out in a couple of weeks. #maths#books#history
A curious math problem I came up with: given a target, what's the fewest digits an integer must have (in a given base) to contain all integers from 0 to the target, as substrings?
e.g. for a target of 19 a candidate representative would be 1011213141516171819 in base 10, that has 19 digits. Can it be done in less, or is $\sigma_10(19) = 19$?
Can we find a general rule? Any properties of this function?
In this thread with @johncarlosbaez I was mentioning how when I first encountered Category Theory it seemed like little more than a curiosity (for my purposes, as a physicist), even though mathematicians seemed excited about it.
I had almost the opposite experience with Nonstandard Analysis (i.e. the hyperreal numbers), in the sense that I bumped into this notion, read a bit about it, and it sounded potentially quite useful. Physicists tend to talk in terms of infinitesimals anyway, so a framework where that could be done rigorously seemed useful, and I was curious if it might provide nice ways to think about other things such a path integrals or even renormalization. But the only mathematician I talked to about it dismissed it as basically a curiosity. I believe the way he put it was that it was "just a trick to avoid an extra quantifier in in proofs."
You don't have to be a mathematician, or even "good" at #maths, to help your #children learn maths. You just have to model resilience and positivity towards what they're doing, and to avoid reinforcing negative tropes.
A #thread:
An interesting and original (I think) puzzle from Micky Bullock.
"Last week Negligent Neil calculated length AC. He had forgotten to switch his calculator from radians to degrees but, fortunately, he still got the answer right.
"An inky splodge has now obscured the angle at A. Negligent Neil has forgotten what his answer was for length AC, but he insists it was between 40 cm and 50 cm.
⚠️ 1 element, no pseudos
⚠️ no SVG, no images in general save for CSS gradients
🚫 no JS
⚠️ no lists of values of length > 8
⚠️ same amount of compiled CSS regardless of whether we have 6 or 25 bars
⚠️ at most 7 CSS declarations
Leslie Lamport, of LaTeX fame, is a very accomplished mathematician and computer scientist with a Turing award for his work on “fundamental contributions to the theory and
practice of distributed and concurrent systems”. He just published a draft of his new book:
True to his pedagogic approach to everything he does, "The book assumes only that you know the math one learns before entering a university." Even the appendices are fantastic. Can only wish I'll remain this lucid at his 82 years old.
Je suis donc GLenPLonk (la casse est importante¹). J'aime bien (et tout cela est à mettre sur un pied d'égalité, l'ordre n'a aucune importance ici) : les #maths (au point d'avoir passé et réussi le concours le l'agreg -- concours un peu 🤮 mais néanmoins bien pratique dans mon cas), faire du #crochet (attention, on ne parle pas ici de tricot), pas mal de loisirs créatifs (écriture², maths, maccramé, couture, pâtisserie, cuisine, …), être pédé (comme un foc), le standard Unicode (mais si, vous savez, le truc qui permet in fine de faire des glyphes genre ầ (un a accent grave et circonflexe), 🔥 (je connais son point de code par cœur : u1f525) ou encore 𓂸 (mon pref, u130b8)), tout ce qui touche de près ou de loin à l'informatique (programation, typographie, systèmes automatisés, réseaux, communications, …) et aussi Wikipedia (mon second cerveau, ma seconde mémoire), ainsi que la surabondance de parenthèses, les listes sans fin, les digressions, le caractère "…", le point virgule³ …⁴
J'aime moins ma dépression, mon trouble anxieux généralisé, mon apnée du sommeil, les transphobes, les homophobes, les racistes, les sexistes, le capitalisme (or should I say … cacapipitalisme), les fachos (ainsi que, dans une moindre mesure, le fait qu'on écrive "facho" et "fascisme") …⁴
[1] : surtout dans un état policier, mais ce n'était pas le sens initial de ce mot dans ce contexte. ACAB, nonobstant.
[2] vous pouvez même trouver ce que je publie ici même sur le Fediverse : @haikus et @the@wf.glenplonk.fr
[3] pour finir les lignes des listes à puces 🫦
[4] liste non exhaustive
Is there anyone reading this who could give a talk on "Math(s) and Artificial Intelligence"?
It would need to be aimed at a general audience, so while the material itself doesn't need to be deep, the person giving the talk would need to have some first-hand experience of the actual math(s) that's involved.
Anyone?
If you're comfortable doing so, please boost for reach ... Mastodon-the-platform relies on networking effects.
Dites, gens qui vous y connaissez en maths et/ou en histoire, profs, chercheureuses, etc : Histoire universelle des chiffres de Georges Ifrah, c'est un bon bouquin ou bien une fumisterie (ça peut être bien sûr plus nuancé) ? Je lis sur Wikipédia que les travaux d'Ifrah sont controversés mais je ne sais pas où chercher des infos, je suis même pas sûre de comprendre… Merci d'avance, que des pétales de violette et des tissus moelleux soient sur votre chemin.
#onthisday in 1915: Albert Einstein submitted a paper to the journal "Sitzungsberichte der Preussischen Akademie der Wissenschaften zu Berlin" that would fundamentally alter our understanding of the universe [1]. The four page paper contained what became known as the Einstein field equations, which relate the geometry of spacetime to the distribution of matter within it [2].
Einstein's field equations were presented in the form of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor) [3].
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.
I have a bot, @esoterica, which posts entries from my collection of interesting and unusual maths references once a day.
I'm one of the editors of @aperiodical, a maths news/magazine blog. You can follow @mathnews for breaking maths news.
I'm involved with @MathsJam and the @TMiP conference, which I'm hosting in #Newcastle this summer.
I'm disabled in a few ways: I'm #ActuallyAutistic, dyspraxic, I have hypermobile Ehlers-Danlos syndrome #hEDS, and protanopia colour vision deficiency. I'm interested in #accessibility, particularly digital accessibility things that come up at work.
I live in #WhitleyBay in the North-East of England.
Born #onthisday in 1835, Josef Stefan was an ethnic Carinthian Slovene physicist, mathematician, and poet of the Austrian Empire [1].
During his lifetime Stefan published nearly 80 scientific articles, most appearing in the Bulletins of the Vienna Academy of Sciences.
Stefan is perhaps best known for his study of blackbody radiation [2] and for discovering what we now call Stefan's law, a physical power law which states that the total radiation from a blackbody is proportional to the fourth power of its (thermodynamic) temperature. Stefan's law was later extended to grey bodies by one of Stefan's students, Ludwig Boltzmann [3], and is now known as the Stefan–Boltzmann law [4].