#Math
Another "einstein" shape appears. This einstein is better than the last: it doesn't need to use its reflection to tile the plane. https://phys.org/news/2023-06-uk-hobbyist-stuns-math-world.html
TIL: einstein doesn't mean the genius. It means "ein stein," or "one stone" in German, and refers to its tiling capability.
Also, Roger Penrose is still alive. Wow.
#math #geometry #tiling #einstein
"In mathematics, hardships arise when you spend months looking for a solution which does not work out. But what you have then achieved can turn out to be useful for some purpose. Also, finally finding the solution is a source of pure joy." – Margarida Mendes Lopes (1955–)
#quote #mathematics #math #maths
"En mathématiques, des épreuves surviennent lorsque vous passez des mois à chercher une solution qui ne fonctionne pas. Mais ce que vous avez alors réalisé peut s'avérer servir à quelque chose. [...]" – Margarida Mendes Lopes (1955–)
#citation #mathématiques #maths #math
The 2023 Shaw Prize in Mathematical Sciences is awarded in equal shares to Vladimir Drinfeld and Shing-Tung Yau, for their contributions related to mathematical physics, to arithmetic geometry, to differential geometry and to Kähler geometry.
Source : The Shaw Prize
https://www.shawprize.org/laureates/mathematical-sciences
#mathematics #mathématiques #math #maths #physics #geometry #prize
hard mathler 494 3/6
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mathler 494 6/6
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That was close....
easy mathler 494 2/6
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killer mathler 494 3/6
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#mathler #math #game #puzzle #hardMathler #hard #easyMathler #easy #KillerMathler #killer
@straffegast@mastodon.online
Digits #62 (15/15⭐)
55 (55) ➕✖
137 (137) ✖➕
291 (291) ✖➕➖➕
315 (315) ➕✖➕
453 (453) ✖➖➕
291 this is originally how I solved it - I'm almost sure it's the same, because I think I know what we did a little different.
315 was a happy accident.
I'll have to think about 315 & 453 a little more.
#numberGame #math #nmbr14Like #nmbr14 #Digits #game #puzzle
if a #livingwage for metro #boston starts at $46K, why are employers allowed to pay anything less? And, why are #realestate and #property costs (extremely conservatively displayed on this chart) completely off the rails, deepening the pain?
Again, it seems like folks are out here doing the #math wrong, but it doesnt matter to them because some people are just that selfish
🧑🎓 2022's Biggest Breakthroughs in Math | Quanta Magazine
#Math #Research
https://m.youtube.com/watch?v=Nmgl78a02ys&feature=youtu.be
Proved algorithms in geometric group theory. ~ Anand Rao Tadipatri. http://dr.iiserpune.ac.in:8080/xmlui/handle/123456789/7818 #ITP #LeanProver #Math
Digits #62 (15/15⭐)
55 (55) ✖➕➕
137 (137) ✖➕
291 (291) ✖➕➖➕
315 (315) ➖➖➕✖
453 (453) ✖➖➖➖
#numberGame #math #nmbr14Like #nmbr14 #Digits #game #puzzle
I don't understand the Halting Problem
Discussions: https://discu.eu/q/https://youtu.be/ffUnNaQTfZE
speed nerdlegame 507 solved in 0m 34s!
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🟩 🟪 ⬛️ Instant Nerdle 493 solved in 0m 47s!
nerdlegame 507 4/6
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binerdle 394 4&5/7
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mini nerdlegame 507 3/6
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mini binerdle 394 3&4/7
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micro nerdlegame 280 3/6
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#nerdle #nerdlegame #math #game #puzzle #fun #nerdle #miniNerdle #microNerdle #binerdle #mini #micro
Mathle 503 3/5
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mathlegame.com
#mathle #mathlegame #math #game #puzzle
I'm getting #tired of #people responding to my "here's the #situation here today, and how the #engineering works out for this #problem" with #hopes and #dreams about how they wish the world was, or #anecdotes about how that problem doesn't exist where they are (which is utterly unlike here) so it doesn't matter.
It's a "strong #misanthropic #principle kind of day, I guess.
Hint: if my #question includes #math, and your #answer doesn't, it's not an answer. 😂
@straffegast@mastodon.online
Getting closer.....
Digits #61 (15/15⭐)
76 (76) ✖➖✖
131 (131) ➖✖✖➖➖ 🤔
271 (271) ✖➕✖➕➕
312 (312) ➖➖➕✖ 🤔
493 (493) ➕✖➕
#numberGame #math #nmbr14Like #nmbr14 #Digits #game #puzzle
Nice!
The Open Logic Project is an open-source, collaborative, textbook of logic and formal methods, starting at an intermediate level, aimed at a non-mathematical audience, intended for use in logic courses as taught in many philosophy departments https://openlogicproject.org/ #math
An interesting look at language's possible impacts on learning numbers and #math #education - no big magic conclusion, but some interesting data: https://www.bbc.com/future/article/20230511-whats-the-best-language-for-learning-maths
"À mesure que les mathématiques progressent, nous les incorporons dans notre réflexion. À mesure que notre pensée devient plus sophistiquée, nous engendrons de nouveaux concepts mathématiques et de nouvelles structures mathématiques." – William Thurston (1946–2012)
#citation #mathématiques #maths #math
"As mathematics advances, we incorporate it into our thinking. As our thinking becomes more sophisticated, we generate new mathematical concepts and new mathematical structures." – William Thurston (1946–2012)
#quote #mathematics #math #maths
Tadashi Tokieda, le mathé-magicien
Source : podcast France Culture / La Science, CQFD
https://www.radiofrance.fr/franceculture/podcasts/la-science-cqfd/tadashi-tokieda-le-mathe-magicien-8619312
#mathématiques #maths #math #podcast
Two Facts from Eight Triangular Arrays (visual proof)
Source : Youtube / Mathematical Visual Proofs
https://www.youtube.com/watch?v=8Jco4DfK6D0
#mathematics #math #maths #Youtube
hard mathler 493 5/6
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mathler 493 2/6
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easy mathler 493 3/6
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killer mathler 493 3/6
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#mathler #math #game #puzzle #hardMathler #hard #easyMathler #easy #KillerMathler #killer
Oh wow! I didn’t know that the World Book encyclopedia was still in print! This is the exact brand of encyclopedia that I grew up with and exactly why I started contributing to @wikipedia in 2002.
(The World Book was such an influence on me that I emulated their infobox style in Wikipedia: https://en.wikipedia.org/w/index.php?title=Makati&oldid=1704277)
(I also adored their companion Childcraft set; the Mathemagic volume was the very reason I grew up to love #math
@straffegast@mastodon.online
Digits #61 (15/15⭐)
76 (76) ✖➖✖➖
131 (131) ➖✖➖➕
271 (271) ✖✖➕
312 (312) ➖➕➕✖
493 (493) ➕✖➕
🤔
Maybe I need some coffee this morning.... ☕☕😃
#numberGame #math #nmbr14Like #nmbr14 #Digits #game #puzzle
even more more....
Digits #61 (15/15⭐)
76 (76) ✖➕
131 (131) ✖➕➕
271 (271) ✖✖➕
312 (312) ✖✖➕
493 (493) ✖➖➖
#numberGame #math #nmbr14Like #nmbr14 #Digits #game #puzzle
Digits #61 (15/15⭐)
76 (76) ✖✖➕➖
131 (131) ➖✖➖➕
271 (271) ✖✖➕
312 (312) ➕✖➖
493 (493) ➕✖➕
even more solves for digits
#numberGame #math #nmbr14Like #nmbr14 #Digits #game #puzzle
@jik this podcast episode featuring Moon Duchin discussing her work on the theory of gerrymandering is one of my favourites: https://www.quantamagazine.org/moon-duchin-on-fair-voting-and-random-walks-20200407/
I've listened to it a bunch of times and happily link it when it whenever anyone talks about drawing up districts because she does such a great job of clearing up some very intuitive misconceptions
Digits #61 (15/15⭐)
76 (76) ➕➕✖
131 (131) ➕✖➕➕
271 (271) ✖✖➕
312 (312) ✖➖➕✖
493 (493) ➕✖➖➖
or.....
Digits #61 (15/15⭐)
76 (76) ✖➕
131 (131) ➕✖➕➕
271 (271) ✖✖➕
312 (312) ➖➕➕✖
493 (493) ✖➖➗➕➕
271 looks like it's the same, but it's ever so slightly different solve...interesting huh.
#numberGame #math #nmbr14Like #nmbr14 #Digits #game #puzzle
speed nerdlegame 506 solved in 1m 20s!
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🟩 🟪 ⬛️ Instant Nerdle 492 solved in 0m 41s!
nerdlegame 506 3/6
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binerdle 393 3&5/7
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mini nerdlegame 506 3/6
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mini binerdle 393 3&4/7
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micro nerdlegame 279 2/6
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#nerdle #nerdlegame #math #game #puzzle #fun #nerdle #miniNerdle #microNerdle #binerdle #mini #micro
Mathle 502 2/5
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mathlegame.com
#mathle #mathlegame #math #game #puzzle
hard mathler 492 3/6
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mathler 492 3/6
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easy mathler 492 4/6
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killer mathler 492 3/6
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#mathler #math #game #puzzle #hardMathler #hard #easyMathler #easy #KillerMathler #killer
#quizz #puzzle #math #mathematics #logique #logical
Ce test a été posé dans un entretien d'embauche pour un acteur majeur dans l'Internet...
Un câble de 80 mètres (m) est suspendu au sommet de deux poteaux situés à 50 m du sol. Quelle est la distance entre les deux pôles, à une décimale près, si le centre du câble est à 10 m au-dessus du sol❓
Merci de BOOSTER + répondre en mode CW (pour ne pas spoiler).
"La mathématique, telle que nous la connaissons, nous paraît l'une des formes nécessaires de notre pensée." – André Weil (1906–1998)
#citation #mathématiques #maths #math
Pourquoi les mathématiques sont-elles si efficaces en physique ?
Source : Podcast France Culture / Le Pourquoi du comment : science
https://www.radiofrance.fr/franceculture/podcasts/le-pourquoi-du-comment-science/pourquoi-les-mathematiques-sont-elles-si-efficaces-en-physique-7144609
#mathématiques #maths #math #physique #podcast
Summing Arithmetic Sequences Visually (proof without words)
Source : Youtube / Mathematical Visual Proofs
https://www.youtube.com/watch?v=uUByQvoS7ew
#mathematics #math #maths #Youtube
#svod #churnrate average is holding steady 47%.
#churn #math review: 47% annual churn is 5.2% monthly via =1-(1-0.47)^(1/12)
https://www.tvtechnology.com/news/parks-streaming-video-churn-rate-holds-steady-at-47
#math #mathematics #calculus
Une bien jolie et intuitive preuve visuelle que la somme des n premiers nombres entiers est égale à n(n+1) / 2.
PS : "En math, une preuve sans mots (ou démonstration visuelle) est une démonstration d'une affirmation mathématique à l'aide d'un diagramme la rendant évidente, sans qu'un texte plus explicite le commentant soit nécessaire. Quand le diagramme n'en illustre qu'un cas particulier, il faut que sa généralisation ne demande au lecteur qu'un effort minimal."
Deductive verification of chain-of-thought reasoning. ~ Zhan Ling, Yunhao Fang, Xuanlin Li, Zhiao Huang, Mingu Lee, Roland Memisevic, Hao Su. https://arxiv.org/abs/2306.03872 #LLMs #Reasoning #Math
Practical scientific computing. ~ Urbain Vaes. https://urbain.vaes.uk/static/teaching/scientific_computing/build/main.pdf #JuliaLang #Math
Formalization of algebraic theorems in PVS. ~ Mauricio Ayala-Rincon, Thaynara Arielly de Lima, Andréia B. Avelar, André Luiz Galdino. https://www.easychair.org/publications/open/93F2 #ITP #PVS #Math
I ethically hate, but also very much academically love the idea that there are now basically PhDs in #gerrymandering :
https://www.quantamagazine.org/how-math-has-changed-the-shape-of-gerrymandering-20230601/
#Maths #Science #Politics #PoliticalScience #Nerdgasms #Ethics #Data #Elections - And for #Americans -- #Math
eicker.news #technews »#Google claims that #Bard is improving at #math and #programming thanks to a technique called „implicit code execution“.« https://techcrunch.com/2023/06/07/google-claims-that-bard-is-improving-at-math-and-programming/
I am once again reminded that Objectivity is the most underrated channel on YouTube.
https://www.youtube.com/c/objectivityvideos
So....#Lagrange #polynomials. They are pretty dang clever and pretty dang amazing. You can get an analytic (if that's the word I want) polynomial fit! That you can take a continuous derivative!
For arbitrary data, I can see why it might not work.
But for a physical object that actually is moving according to a 2nd-order kinematics (piecewise--really 3rd-order overall) but all you have data for the the first two orders, it might be a good way to recover the higher order(s).
Beaverton: Child’s homework got too difficult for dad to help with a lot earlier than expected https://www.thebeaverton.com/2023/06/childs-homework-got-too-difficult-for-dad-to-help-with-a-lot-earlier-than-expected/ #satire #canada #commentary #FeaturedPost #homework #history #parent #school #Local #child #math #dad #son
Open question for those in #math and/or #ai over the last twenty years: How much did Perelman's work twenty years ago contribute to machine learning capabilities today?
Is it reasonable to suggest that if Perelman hadn't muscled through a gradient flow with metric measure space objects that the usefulness of things like gradient flow on Wasserstein space would not have been as obvious to the machine learning community as early as it was?
"The facts of mathematics are as useful as the facts of any other science. No matter how abstruse they may first seem, sooner or later they find their way back to practical applications. [...]" – Gian-Carlo Rota (1932-1999)
#quote #mathematics #math #maths
Evaluating language models for mathematics through interactions. ~ K.M. Collins, A.Q. Jiang, S. Frieder, L. Wong, M. Zilka, U. Bhatt, T. Lukasiewicz, Y. Wu, J.B. Tenenbaum, W. Hart, T. Gowers, W. Li, A. Weller, M. Jamnik. https://arxiv.org/abs/2306.01694 #LLMs #Math #Reasoning
Love when I accidentally #learn something that brings the whole room together
Have position and velocity; need acceleration. That's easy with v = v0 + at
Oh wait, you can get a better answer with v(n+1)-v(n-1). Wow, a lot better. Oh, because Taylor series. Hey, there's a 5pt version of this that's even better.
And there's something called #lagrange interpolation....oh my christ, THAT'S why ephemeris data uses lagrange interpolation! My data is #ephemerides!
#books #storybooks #reading #math #children #Indonesia #languages
'Following the success of the first phase of the Translate a Story campaign, UNESCO and the Global Digital Library (GDL), in cooperation with the Agency for Language Development and Cultivation (Badan Bahasa) from the Ministry of Education of Indonesia, jointly organized a translation workshop from 29 May to 2 June in the country’s capital, Jakarta.'
Equivalent axiomatizations of euclidean geometry. ~ Jeffrey Ketland. http://philsci-archive.pitt.edu/22198/1/Equiv_Ax_EG.pdf #Math
Un mathématicien voit deux personnes entrer dans une maison. Peu de temps après, trois personnes en sortent.
— “Si une personne entrait maintenant, la maison serait alors vide”, dit-il.
#Humor #mathhumor #math #mathematics #humour #humourMatheux #mathematician
The programme for EAMS 2023 is now online: https://eams.ncl.ac.uk/programme/
There's still plenty of time to register for this free, entirely online conference: https://eams.ncl.ac.uk/register/
The man who tried to redeem the world with logic (Walter Pitts rose from the streets to MIT, but couldn’t escape himself). ~ Amanda Gefter. https://nautil.us/the-man-who-tried-to-redeem-the-world-with-logic-235253/ #Logic #Math #AI
Legendary Dutch computer scientist Edsger W Dijkstra famously remarked that “testing shows the presence, not the absence of bugs”. In fact the only definitive way to establish that software is correct and bug-free is through mathematics
https://ponderwall.com/index.php/2019/04/04/flaw-free-software-possible-math
Discussions: https://discu.eu/q/https://ponderwall.com/index.php/2019/04/04/flaw-free-software-possible-math
It doesn’t add up:
Math teachers who believe women no longer face discrimination tend to be biased against girls’ ability in math. And effects of bias like this can snowball over time.
#genderequality #education #math #stem #implicitbias #WomenInSTEM
https://theconversation.com/math-teachers-hold-a-bias-against-girls-when-the-teachers-think-gender-equality-has-been-achieved-202921
Particularly fond of this one. there's almost something recognisable in it, but each time I think I see it… it's gone. As always, a little bit of #art with a dash of #math for #strangeAttractors
https://strange-attraction.glitch.me/?a=0.16231509928099852&b=-0.9134606100191334&c=-0.22785802108564734&d=2.110404841105856&ho=240&x=-150&y=-75&z=0.9
The formula for the volume of a sphere is 4/3 * pi * r^3.
The high school student thinks "(4 * pi * r^3)/3 would be easier."
The engineer thinks "dude, just use 4 * r^3."
Everything you always wanted to know about Mathematics. ~ Brendan W. Sullivan. https://www.math.cmu.edu/~jmackey/151_128/bws_book.pdf #Math
Let’s verify step by step. ~ Hunter Lightman et als. https://cdn.openai.com/improving-mathematical-reasoning-with-process-supervision/Lets_Verify_Step_by_Step.pdf #ChatGPT #Math
AI to assist mathematical reasoning: A workshop. https://terrytao.wordpress.com/2023/06/02/ai-to-assist-mathematical-reasoning-a-workshop/ #AI #Math
Finding the limit points and derived set using Python. ~ M. Vivek Prabu, K. Geethu Krishna, R. Karthika. https://pubs.aip.org/aip/acp/article/2718/1/030005/2892961/Finding-the-limit-points-and-derived-set-using #Python #Math
Application of Kuratowski's closure operator in Python program. ~ M. Vivek Prabu, M. Rahini. https://pubs.aip.org/aip/acp/article/2718/1/030003/2892959/Application-of-Kuratowski-s-closure-operator-in #Python #Math
A proof of the corrected Sister Beiter cyclotomic coefficient conjecture inspired by Zhao and Zhang. ~ Branko Juran, Pieter Moree, Adrian Riekert, David Schmitz, Julian Völlmecke. https://arxiv.org/abs/2304.09250 #Math
@rust_discussions I'm actually writing a #math paper with it right now. Feels really nice and way easier than #LaTeX. Still there are a lot of features missing.
The #math journey continues and after having given up on the books, I finished two YouTube courses on Abstract Algebra.
The latest and bigger one was this with 43 videos on Visual Group Theory. Knowing a bunch of group theory definitely is useful though I lost track at the end where it gets very number theoretical.
Now I can finally resume reading about Sheaf Theory.
#puzzle #énigme #math
Dans ce mécanisme à 4 engrenages, les nombres à l’intérieur représentent le nombre de dents (30, 10, 5, 90).
Dans l'engrenage à 90 dents se situe une aiguille tournant avec l’engrenage : elle est positionnée au départ sur 12, et pointera alors sur des nombres différents.
Sur quel nombre pointera l’aiguille lorsque l’engrenage à 30 dents aura fait un tour complet dans le sens indiqué❓
Merci de BOOSTER + répondre en mode CW.
Remember awhile back, there were videos to explain the difference between a million dollars vs a billion dollars. 💰💰💰
➡️ Using Rice:
https://youtu.be/qSOVBiEotaw
#Million #Millions #Billion #Bilions #Money #Math #Arithmetic
A familiar math lesson in poem form and an incredible erasure where progressive fractal triangles case new poems by covering words.
(Triangles by Marian Christie, from Penteract Press.)
"Entre deux vérités du domaine réel, le chemin le plus facile et le plus court passe bien souvent par le domaine complexe." – Paul Painlevé (1863–1933). Ces propos sont aussi repris par Jacques Hadamard, et lui sont donc souvent attribués à tort.
#citation #mathématiques #maths #math
The term #Algorithm is Al-Khwarizmi translated into #Latin
The #scientist & #mathematician Muhammad ibn Musa Al-Khwarizmi lived from 780 to 850 AD in Persia & #Iraq.
Also known as the father of #algebra,
Al-Khwarizmi's #book, "Compendious Book on Calculation by Completion and Balancing” introduced systematic methods for solving linear & quadratic equations.
Using letters as symbols to represent unknown quantities, lay the foundation for symbolic algebra.
Dans cette ingénieuse technique japonaise de pliage d'une chemise en 2 secondes, il se trouve qu'il y a une part de TOPOLOGIE* secrète cachée dans le tissu (décidément, il y a des maths partout !).
Rappel : la Topologie est « l'étude des propriétés invariantes dans la déformation géométrique des objets et dans les transformations continues appliquées à des êtres mathématiques. »
#math #topology #topologie #japanesegenius
#énigme #puzzle #math #arithmetic
C'est un vrai devoir donné dans une école, paraît-il : il est demandé de rendre ces quatre égalités correctes en insérant des parenthèses entre caractères.
4 + 8 x 5 - 3 x 5 = 45
3 x 10 - 2 ÷ 4 + 4 =10
16 - 3 x 4 + 7 - 1² = 40
5 x 8 + 8 ÷ 6 - 12 x 2 = 24
Merci de Booster + répondre en mode CW
📖 I'm delighted to announce the publication of my book 'Introduction to Choreographies' with Cambridge University Press!
Concurrency, distribution, and decentralised coordination plans.
I want to send a HUGE thank you to the people who read drafts and gave suggestions. Especially from the communities of choreographic programming, #microservices , and multiparty session types. I'm so grateful!
https://www.fabriziomontesi.com/introduction-to-choreographies/
#alhambra #art #math
Un des aspects réellement fascinants des mathématiques arabes: les pavages.
Mathématiquement, un pavage est un recouvrement complet du plan sans trou ni superposition. Le motif de base s'appelle une "tuile", et on dit qu'un pavage est périodique s'il se répète au moins par une translation.
On peut démontrer qu'il existe précisément 17 pavages périodiques. Cela porte le nom du théorème d'Alhambra car ce palais abrite ces 17 possibilités via ses magnifiques mosaïques.
It's done! And I don't want to know about mistakes now because it's been sent to the printer. LaTeX font catalogue was a nice discovery, I'm in love with the "Beuron" font I used for the title. And thanks to @nrennie for the blog posts on making fancy LaTeX outputs with Quarto, meant the whole thing could be done with Quarto and R. #mathart #math #art #rtistry
In other words, it's like those students who used to sit in the back of the class and clouned about, spouting bs when called on to say something important.
When it comes to advanced math, #ChatGPT is no star student
#AI's ability to handle #math depends on what exactly you ask it to do.
https://arstechnica.com/science/2023/05/when-it-comes-to-advanced-math-chatgpt-is-no-star-student/
#MachineLearning #GenerativeAI #AI #Mathematics
Honestly, I just find it very therapeutic pressing 🔀 and seeing what appears. Next step: I should do this in Three.js with a movable camera... #math + #art = 🖤
https://strange-attraction.glitch.me/?a=1.588871069797266&b=-1.8205115487215173&c=-0.2967706244292678&d=0.911181561270773&ho=0&x=-75&y=0&z=1
Looking for interesting ways to present images of strange attractors. Here I've arranged them like an old botanical print which I think looks cool. Its nice as they are kind of discovered specimens rather than creations as such, so showing them off in this way feels appropriate. If a bit pretentious! #mathart #rtistry #math #art.
Want to understand how AI might change teaching & learning? Ask a math instructor.
No, this isn't about making an analogy between AI in the classroom and calculators. It is about Wolfram|Alpha.
If you are not involved in a discipline that relies on mathematical computations, you may not be familiar with Wolfram|Alpha (W|A
#puzzle #logical #logique #math
Un singe est assis devant une machine à écrire à 26 touches, une par lettre de l'alphabet. Le singe tape au hasard, avec une vitesse constante d'une lettre par seconde. Toutes les lettres à n'importe quelle seconde ont une probabilité de 1/26 d'être tapées.
À long terme (et sans aucune limite de temps), lequel de « abracadabra » ou « abracadabrx » apparaît le plus fréquemment ?
Merci de Booster + justifier votre choix en mode CW
#AskFedi: what advice would you give me for doing a #math #research project for the summer?
(It’s something theoretical about #statistics that’s related to ML. I’m gonna keep it vague just to maintain academic integrity.)
Just realized I never did a #introduction post, and since I have been getting back into Mastodon I guess it is time I make one.
Hi, I'm Tyler (he/him), and I am a student of #computerscience, #math, and #linguistics. I hope to work in the field of #computationallinguistics. I am very interested in the aforementioned fields as well as #freesoftware, #emacs, #linux (currently using #guix), leftist politics, and film.
Gil Strang is giving his final lecture at MIT tomorrow and we have the privilege of watching it live.
Une classe de #math, comme il y en a plein en France, dans nos collèges et lycées. Ou pas. Voici une belle idée de conception de classe de mathématiques!
(Malheureusement, nos écoles sont encore comme des prisons pour de nombreux élèves. Alors que des salles de classe bien conçues et attrayantes pourraient éveiller la curiosité des jeunes !)