Hacker News with Generative AI: Mathematics

Mathematics of the daily word game Waffle (arxiv.org)
We investigate the combinatorics of permutations underlying the the daily word game Waffle, and learn why some games are easy to solve while extreme games are very hard. A perfect unscrambling must have precisely 11 orbits, with at least one of length 1, on the 21 squares.
Mathematics, Word Games, Combinatorics, Algorithms, Games
37 points by belter 7 hours ago | 12 comments
The Curious History of Venn Diagrams (scientificamerican.com)
In his book The Mathematical Universe, mathematician William Dunham wrote of John Venn’s namesake legacy, the Venn diagram, “No one in the long history of mathematics ever became better known for less.”
Mathematics, History, Science, Data Visualization
3 points by Brajeshwar 1 day ago | 0 comments
Mathematicians discover new way for spheres to 'kiss' (quantamagazine.org)
A new proof marks the first progress in decades on important cases of the so-called kissing problem. Getting there meant doing away with traditional approaches.
Mathematics, Geometry, Science
156 points by isaacfrond 2 days ago | 69 comments
Finite Field Assembly: A Language for Emulating GPUs on CPU (leetarxiv.substack.com)
FF-asm is a programming language founded on the thesis: Math is mostly invented, rarely discovered.
Programming Languages, GPU Emulation, Computer Architecture, Mathematics
28 points by muragekibicho 4 days ago | 22 comments
Treewidth? (ams.org)
The treewidth of a graph, a positive integer defined using a tree of sets of vertices, is central to graph structure theory and the parametrized complexity of algorithms.
Graph Theory, Algorithms, Computer Science, Mathematics
33 points by RafelMri 6 days ago | 12 comments
Ingrid Daubechies awarded National Medal of Science (today.duke.edu)
Mathematician Ingrid Daubechies will receive the National Medal of Science, the highest possible recognition bestowed on scientists and engineers in the nation.
Mathematics, Science, Awards
185 points by sedtacet 7 days ago | 14 comments
Very Wrong Math (charlespetzold.com)
The difference between misinformation and disinformation is the difference between ignorance and malice. Trolling is somewhat different, incorporating an element of provocation and narcissism. But what the hell is this?
Mathematics, Misinformation, Trolling, Language
192 points by breadbox 7 days ago | 104 comments
Who Can Understand the Proof? A Window on Formalized Mathematics (stephenwolfram.com)
For more than a century people had wondered how simple the axioms of logic (Boolean algebra) could be. On January 29, 2000, I found the answer—and made the surprising discovery that they could be about twice as simple as anyone knew. (I also showed that what I found was the simplest possible.)
Mathematics, Logic, Boolean Algebra, Research, History
188 points by ColinWright 8 days ago | 115 comments
An Introduction to Neural Ordinary Differential Equations [pdf] (diposit.ub.edu)
Neural Networks, Machine Learning, Differential Equations, Mathematics
79 points by gballan 8 days ago | 10 comments
Rational or not? This basic math question took decades to answer (quantamagazine.org)
It’s surprisingly difficult to prove one of the most basic properties of a number: whether it can be written as a fraction. A broad new method can help settle this ancient question.
Mathematics, Number Theory, Science
173 points by nsoonhui 9 days ago | 137 comments
Collatz's Ant and similarity of Collatz sequences (gbragafibra.github.io)
This is a brief continuation of a previous post (Repo), which introduced such visualization for collatz sequences based on Langton’s Ant.
Mathematics, Computer Science, Algorithms, Visualization
13 points by Fibra 9 days ago | 1 comments
Multiplicative Infinitesimals (github.com/Ericson2314)
This goes with Multiplicative Calculus, but where as that is mostly summarizing others work, this is original as far as I know, and so I split it out.
Mathematics, Calculus, Open Source
83 points by Ericson2314 9 days ago | 44 comments
Robotics 101 at UMich: Applied numerical linear algebra as intro linear algebra (robotics.umich.edu)
Computational Linear Algebra is a pilot first-semester, first-year undergraduate course that will show how mathematics and computation are unified for reasoning about data and making discoveries about the world.
Robotics, Education, Linear Algebra, Mathematics, Computation
296 points by jamesliudotcc 10 days ago | 73 comments
The Elements of Euclid (c82.net)
A reproduction of Oliver Byrne’s celebrated work from 1847 plus interactive diagrams, cross references, and posters designed by Nicholas Rougeux
Mathematics, History, Design
24 points by simonsarris 10 days ago | 9 comments
How many real numbers exist? New proof moves closer to an answer (2021) (quantamagazine.org)
For 50 years, mathematicians have believed that the total number of real numbers is unknowable. A new proof suggests otherwise.
Mathematics, Infinity, Proof, Real Numbers
58 points by lisper 10 days ago | 60 comments
Dice, (De)Convolution and Generating Functions (demofox.org)
I stumbled across a very cool YouTube video today that talks about how to look for alternate ways of labeling sides of two dice to give you the same random number distribution as if you added two standard dice together.
Mathematics, Probability, Dice, Games, YouTube
4 points by zdw 12 days ago | 0 comments
Einsum in Depth (joelburget.com)
Mathematics, Linear Algebra, Python
87 points by joelburget 14 days ago | 31 comments
Mandelbrot deep zoom theory and practice (2021) (mathr.co.uk)
The complex beauty of the world's most famous fractal, the Mandelbrot set, emerges from the repeated iteration of a simple formula:
Mathematics, Fractals, Theory, Visualizations
183 points by fanf2 14 days ago | 60 comments
The Maxwell-Heaviside Equations Explained by the Theory of Informatons (researchgate.net)
Physics, Mathematics, Information Theory
22 points by keepamovin 16 days ago | 7 comments
Show HN: 2025 = sum(I^3) for I = 0..9 (ycombinator.com)
This year's number is kinda fun:<p>2025 = 0^3 + 1^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 + 7^3 + 8^3 + 9^3<p>Which is equivalent to:<p>2025 = (0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) ^ 2 = 45 ^ 2<p>Next time this will happen is 1000 years from now, in 3025. See y'all then!
Mathematics, Number Theory, Programming, Show HN
12 points by temporalparts 16 days ago | 3 comments
One of my papers got declined today (mathstodon.xyz)
Academic Research, Mathematics, Peer Review
853 points by GavCo 16 days ago | 290 comments
DAC: Revolutionizing LLM Accuracy in Mathematical Applications (github.com/JasonAlbertEinstien)
This repository showcases our recent research aimed at improving the accuracy of large language models (LLMs) in mathematical domains. We believe our approach has surpassed previous methods, such as chain-of-thought and graph-of-thought techniques, achieving state-of-the-art performance.
Generative AI, Mathematics, Research, Software
5 points by jasonalbert 17 days ago | 2 comments
“A Course of Pure Mathematics” – G. H. Hardy (1921) [pdf] (gutenberg.org)
Mathematics, Books, History
317 points by bikenaga 18 days ago | 97 comments
A Puzzle about a Calculator (aperiodical.com)
It’s now been a year since I took over the puzzle column at New Scientist and turned it into the BrainTwisters column. By way of celebration, I thought I’d write up an interesting bit of maths behind one of the puzzles, which I made a note of at the time and have been meaning to share.
Mathematics, Puzzles, Columns, Science
31 points by surprisetalk 18 days ago | 13 comments
Visual Algebra (math.clemson.edu)
Mathematics, Education
29 points by mathgenius 19 days ago | 3 comments
Category Theory Illustrated (abuseofnotation.github.io)
Discover the beauty of mathematics through the lens of category theory with this unique exploration that goes beyond problem-solving. In this book, you’ll find a refreshing perspective on math as an art form, a language, and a way of thinking that unifies diverse fields of knowledge. Delve into the fascinating world of sets, groups, types, and partial orders, and explore the deep connections between these concepts.
Mathematics, Category Theory, Education, Books
81 points by zdw 19 days ago | 3 comments
Penrose Mazes (2020) (justinpombrio.net)
Mazes are typically constructed on regular grids: square, triangular, hexagonal, etc. But what if you generate a maze on top of a Penrose tiling, which is guaranteed to be irregular? (It is an aperiodic tiling.) The resulting mazes have a very characteristic appearance: they are filled with circles and stars, but the tiling they are built on guarentees they never repeat exactly.
Mathematics, Computer Science, Art, Design
104 points by 082349872349872 21 days ago | 13 comments
Machine-Assisted Proof [pdf] (ams.org)
Mathematics, Computer Science, Proofs
199 points by jalcazar 21 days ago | 96 comments
Mathematician Reveals New Enigmas for Time Travelers (discovermagazine.com)
First, the good news for time travelers. Physicists have long recognized that nothing in the laws of physics specifically forbids time travel.
Time Travel, Physics, Science, Mathematics
15 points by austinallegro 21 days ago | 1 comments
Invariants: Computation and Applications (arxiv.org)
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena.
Mathematics, Computer Science, Theory
47 points by crete 22 days ago | 1 comments