Hacker News with Generative AI: Mathematics

Everyone is capable of, and can benefit from, mathematical thinking (quantamagazine.org)
David Bessis claims that everyone is capable of, and can benefit greatly from, mathematical thinking.
Mathematics, Education, Thinking
98 points by sonabinu 6 hours ago | 43 comments
Math4devs.com: List of mathematical symbols with their JavaScript equivalent (math4devs.com)
List of mathematical symbols with their JavaScript equivalent.
Mathematics, JavaScript, Programming, Web Development, Tools
47 points by fagnerbrack 1 day ago | 11 comments
Jim Simons: A short story of my life and mathematics (2022) (youtube.com)
Mathematics, Biography, YouTube
4 points by fuzztester 1 day ago | 2 comments
Show HN: MathGPT – Create math animations for any question (math-gpt.org)
Get instant homework help from your personal AI math solver
Mathematics, AI, Education, Tools
75 points by yannigk 2 days ago | 26 comments
A joke in approximating numbers raised to irrational powers (andreinc.net)
A joke in approximating numbers raised to irrational powers
Mathematics, Humor, Approximation
104 points by nomemory 3 days ago | 40 comments
Mathematical Thinking Isn't What You Think It Is (quantamagazine.org)
The mathematician David Bessis claims that everyone is capable of, and can benefit greatly from, mathematical thinking.
Mathematics, Education, Thinking, Psychology
6 points by isaacfrond 3 days ago | 1 comments
Nothing-up-my-sleeve number (wikipedia.org)
In cryptography, nothing-up-my-sleeve numbers are any numbers which, by their construction, are above suspicion of hidden properties.
Cryptography, Mathematics, Security
43 points by avinassh 3 days ago | 12 comments
/ 0 = 0 (hillelwayne.com)
Have a tweet:
Mathematics, Programming, Computer Science
8 points by Aaronmacaron 3 days ago | 8 comments
AlphaProof's Greatest Hits (rishimehta.xyz)
Here I’ll try to explain the coolest ideas in each of AlphaProof’s IMO 2024 solutions. AlphaProof produces proofs in Lean, and each Lean proof is composed of a series of tactics. So I’ll pick out the tactics that correspond to these ideas in the proofs for problems 1, 2 and 6 (the three problems that AlphaProof solved). AlphaProof has developed its own proving style, so figuring out what it’s doing can involve some detective work.
Programming, Mathematics, Artificial Intelligence
248 points by rishicomplex 4 days ago | 132 comments
Overview of differential geometry for Hamiltonian Monte Carlo (arxiv.org)
Hamiltonian Monte Carlo has proven a remarkable empirical success, but only recently have we begun to develop a rigorous understanding of why it performs so well on difficult problems and how it is best applied in practice.
Machine Learning, Mathematics, Statistics
8 points by somethingsome 4 days ago | 0 comments
A 15-minute intro to involute gears (lcamtuf.substack.com)
Involute gears are everywhere: toys, kitchen appliances, cars. But what's so special about their shape?
Engineering, Mechanics, Design, Mathematics
55 points by lapnect 4 days ago | 8 comments
Tiling with Three Polygons Is Undecidable (arxiv.org)
We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of the three polygons (either allowing or forbidding reflections)? This result improves on the best previous construction which requires five polygons.
Mathematics, Computational Geometry, Algorithms, Theory, Undecidability
132 points by denvaar 4 days ago | 26 comments
How public key cryptography works, using only simple math (quantamagazine.org)
The security system that underlies the internet makes use of a curious fact: You can broadcast part of your encryption to make your information much more secure.
Cryptography, Mathematics, Security, Internet
90 points by pseudolus 5 days ago | 22 comments
Alternative notation for exponents, logs and roots? (stackexchange.com)
As a visually-oriented person I have often been dismayed that the symbols for these three operators look nothing like one another, even though they all tell us something about the same relationship between three values.
Mathematics, Notation, Symbols
15 points by aaraujo002 6 days ago | 1 comments
Terence Tao: Solving problems by abstracting away highly relevant information (mathstodon.xyz)
Mathematics, Problem Solving, Abstraction
11 points by bertman 6 days ago | 1 comments
Making the Mandelbrot Set with Excel (divisbyzero.com)
The Mandelbrot set is one of the most stunning geometric objects in all of mathematics. In this blog post, I will show how to generate the Mandelbrot set below using Excel. It is also an example of how you can use AI (I used ChatGPT) to help with a task like this. (Here is the Excel file I created if you want to play with it.)
Mathematics, Excel, Programming, Artificial Intelligence
7 points by johndcook 7 days ago | 0 comments
The letter ℘: name and origin? (2017) (mathoverflow.net)
Do you think the letter \wp has a name? It may depend on community - the language, region, speciality, etc, so if you don't mind, please be specific about yours. (Mainly I'd like to know the English names, if any, but other information is welcome.) If yes, when and how did you come to know it? When, how, and how often do you mention it? (See below.) What's the origin of the letter?
Mathematics, Language, History
283 points by IdealeZahlen 7 days ago | 142 comments
Terence Tao: "It can become more rational to think and act more boldly" (mathstodon.xyz)
Mathematics, Philosophy, Artificial Intelligence
109 points by bertman 7 days ago | 63 comments
New secret math benchmark stumps AI models and PhDs alike (arstechnica.com)
On Friday, research organization Epoch AI released FrontierMath, a new mathematics benchmark that has been turning heads in the AI world because it contains hundreds of expert-level problems that leading AI models solve less than 2 percent of the time, according to Epoch AI.
Artificial Intelligence, Mathematics, Research, Benchmarking
4 points by amichail 7 days ago | 0 comments
An alternative construction of Shannon entropy (rkp.science)
TL;DR: Shannon’s entropy formula is usually justified by showing it satisfies key mathematical criteria, or by computing how much space is needed to encode a variable. But one can also construct Shannon’s formula starting purely from the simpler notion of entropy as a (logarithm of a) count—of how many different ways a distribution could have emerged from a sequence of samples.
Information Theory, Mathematics, Statistics, Probability
126 points by rkp8000 8 days ago | 11 comments
New secret math benchmark stumps AI models and PhDs alike (arstechnica.com)
On Friday, research organization Epoch AI released FrontierMath, a new mathematics benchmark that has been turning heads in the AI world because it contains hundreds of expert-level problems that leading AI models solve less than 2 percent of the time, according to Epoch AI.
Artificial Intelligence, Mathematics, Research, Benchmarking
8 points by isaacfrond 8 days ago | 2 comments
Inverse Symbolic Calculator (cecm.sfu.ca)
Please enter a number or a Maple expression:
Mathematics, Software, Tools, Computer Science
8 points by luu 8 days ago | 4 comments
A Mathematician in a School of Art (mathvalues.org)
Mathematics, Art, Education
127 points by nkoren 8 days ago | 27 comments
The Laws of Thought by George Boole (1854) (gutenberg.org)
Logic, History, Mathematics, Books
8 points by sandwichsphinx 9 days ago | 0 comments
Homage to Alexander Grothendieck (igrothendieck.org)
To celebrate the 10th anniversary of the death of the great mathematician Alexander Grothendieck, occurred on 13 November 2014, the Grothendieck Institute organises a commemorative conference in his honour.
Mathematics, Anniversaries, Conferences
87 points by jjgreen 9 days ago | 8 comments
Superb undergraduate math study resources from George Bergman of UC Berkeley (math.berkeley.edu)
This webpage contains material of various sorts that has come out of undergraduate courses I have taught; mostly supplementary notes, supplementary exercises, and collections of answers to students' questions from upper division courses.
Mathematics, Education, Resources, Berkeley
7 points by blue-ox 10 days ago | 1 comments
The Doodle Theorem, and Beyond (2016) (chalkdustmagazine.com)
One of the things I like about recreational maths is how we can start with a simple game, play around a bit, poke in the corners, and suddenly fall down a deep hole into some serious mathematics.
Mathematics, Recreational Math, Games
37 points by ColinWright 10 days ago | 6 comments
New elliptic curve breaks 18-year-old record (quantamagazine.org)
In August, a pair of mathematicians discovered an exotic, record-breaking curve. In doing so, they tapped into a major open question about one of the oldest and most fundamental kinds of equations in mathematics.
Mathematics, Cryptography, Records
172 points by calstad 10 days ago | 53 comments
The Postage Stamp Problem (johndcook.com)
I recently stumbled upon the Postage Stamp Problem. Given two relatively prime positive numbers a and b, show that any sufficiently large number N, there exists positive integers x and y such that
Mathematics, Number Theory, Algorithms
6 points by azhenley 10 days ago | 0 comments
A life that added up to something (Obituary of Paul Erdòs) (math.osu.edu)
One of the most extraordinary minds of our time has "left."
Mathematics, Obituaries, Biography
78 points by joebig 11 days ago | 17 comments