Hacker News with Generative AI: Mathematics

June Huh dropped out to become a poet, now he’s won a Fields Medal (2022) (quantamagazine.org)
June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.
Mathematics, Awards, Education, Biography
216 points by bpierre 2 days ago | 135 comments
Dimension 126 Contains Twisted Shapes, Mathematicians Prove (quantamagazine.org)
A new proof represents the culmination of a 65-year-old story about anomalous shapes in special dimensions.
Mathematics, Geometry, Proof, Scientific Discovery
143 points by baruchel 4 days ago | 84 comments
Geometrically understanding calculus of inverse functions (2023) (tobylam.xyz)
Given a function such as \(\tan x\), could you write \(\frac{d}{dx} \arctan x\) and \(\int \arctan x \; dx\), just from \(\tan x\), \(\frac{d}{dx} \tan x\) and \(\int \tan x \; dx\)? With some caveats, the inverse function theorem answers the former while the Legendre transformation answers the later. We’ll approach this with as much geometric intuition as possible, avoiding the dry application of formulas.
Calculus, Mathematics, Geometry, Inverse Functions
126 points by tobytylam 4 days ago | 5 comments
Mathematical Problem Solving (ifi.lmu.de)
Mathematics, Problem Solving, Education
79 points by ibobev 4 days ago | 6 comments
Orders of Infinity (wordpress.com)
Many problems in analysis (as well as adjacent fields such as combinatorics, theoretical computer science, and PDE) are interested in the order of growth (or decay) of some quantity that depends on one or more asymptotic parameters (such as ) – for instance, whether the quantity grows or decays linearly, quadratically, polynomially, exponentially, etc. in .
Mathematics, Asymptotic Analysis, Combinatorics, Differential Equations
81 points by matt_d 5 days ago | 15 comments
Mathematician solves algebra's oldest problem using intriguing number sequences (phys.org)
A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations.
Mathematics, Algebra, Number Theory
53 points by amichail 7 days ago | 51 comments
Mathematician solves algebra's oldest problem using new number sequences (phys.org)
A UNSW Sydney mathematician has discovered a new method to tackle algebra's oldest challenge—solving higher polynomial equations.
Mathematics, Algebra, Number Theory, Research
8 points by pseudolus 7 days ago | 0 comments
Learn You Galois Fields for Great Good (xorvoid.com)
This is the introduction to a series on Abstract Algebra. In particular, our focus will be on Galois Fields (also known as Finite Fields) and their applications in Computer Science.
Abstract Algebra, Galois Fields, Computer Science, Mathematics
12 points by sebg 7 days ago | 4 comments
Zipf's Law (wikipedia.org)
Zipf's law (/zɪf/; German pronunciation: [tsɪpf]) is an empirical law stating that when a list of measured values is sorted in decreasing order, the value of the n-th entry is often approximately inversely proportional to n.
Statistics, Mathematics, Linguistics, Language, Data Analysis
6 points by baxtr 7 days ago | 0 comments
Just Because You Can Prove It Doesn't Make It True (nytimes.com)
“Even mathematical notions of proof,” Adam Kucharski writes, are “not always as robust and politics-free as they might seem.”
Mathematics, Science, Politics
14 points by pseudolus 7 days ago | 4 comments
Derivation and Intuition behind Poisson distribution (notion.site)
Probability, Statistics, Mathematics, Poisson Distribution
105 points by sebg 8 days ago | 34 comments
The unusual mathematics that gives rose petals their shape (nature.com)
The growth of rose petals exploits a geometric trick previously unobserved in nature, physicists have found.
Mathematics, Nature, Biology, Physics
20 points by gnabgib 8 days ago | 9 comments
Liverpool's title win has completed a mysterious Fibonacci sequence (bbc.com)
Liverpool FC's victory at the weekend has clinched them their second Premier League title but it also resulted in something curious – producing a strange series of numbers in the league's record books.
Sports, Football, Liverpool FC, Mathematics, Statistics
112 points by pseudolus 8 days ago | 55 comments
Comparison with Traditional Mathematics (aplwiki.com)
APL unifies the notations for certain mathematical constructs, while having a more consistent syntax.
Mathematics, Programming Languages, Syntax
10 points by todsacerdoti 10 days ago | 1 comments
The Mathematical Radio: Inside the Magic of Am, FM and Single-Sideband (press.princeton.edu)
The modern radio is a wonder, and behind that magic is mathematics.
Mathematics, Radio, Technology, Physics
5 points by teleforce 11 days ago | 0 comments
DARPA to 'radically' rev up mathematics research. And yes, with AI (theregister.com)
The US Defense Advanced Research Projects Agency, aka DARPA, believes mathematics isn't advancing fast enough.
Mathematics, Research, Artificial Intelligence, Government Funding
7 points by jjgreen 12 days ago | 0 comments
Prime Number Mystery Is Key to Magic: The Gathering Game Strategy (scientificamerican.com)
The popular fantasy card game Magic: The Gathering has a new card related to prime numbers. Now fans are trying to use it to tackle one of the biggest problems in mathematics
Mathematics, Games
12 points by geox 12 days ago | 3 comments
Category Theory [pdf] (logicmatters.net)
Mathematics, Category Theory, Academic Papers
10 points by ColinWright 13 days ago | 2 comments
Mathematicians just solved a 125-year-old problem, uniting 3 theories in physics (scientificamerican.com)
Mathematicians suggest they have figured out how to unify three physical theories that explain the motion of fluids.
Mathematics, Physics, Fluid Dynamics
111 points by mikhael 13 days ago | 12 comments
The Periodic Table of Primes (2024) (ssrn.com)
Over millennia, nobody has been able to predict where prime numbers sprout or how they spread.
Mathematics, Number Theory, Prime Numbers
7 points by toss1 14 days ago | 1 comments
Show HN: Formalizing Principia Mathematica using Lean (github.com/ndrwnaguib)
This project aims to formalize the first volume of Prof. Bertrand Russell’s Principia Mathematica using the Lean theorem prover.
Mathematics, Formal Verification, Theorem Proving, Logic
188 points by ndrwnaguib 14 days ago | 34 comments
Notation as a Tool of Thought (1979) (jsoftware.com)
Software, Programming, Mathematics, History
322 points by susam 14 days ago | 107 comments
Implementing Unsure Calculator in 100 lines of Haskell (alt-romes.github.io)
The recently trendy Unsure Calculator makes reasoning about numbers with some uncertainty just as easy as calculating with specific numbers.
Programming, Haskell, Functional Programming, Mathematics, Uncertainty
8 points by romes 14 days ago | 0 comments
Fight Fiercely (scottaaronson.blog)
Last week I visited Harvard and MIT, and as advertised in my last post, gave the Yip Lecture at Harvard on the subject “How Much Math Is Knowable?” The visit was hosted by Harvard’s wonderful Center of Mathematical Sciences and Applications (CMSA), directed by my former UT Austin colleague Dan Freed. Thanks so much to everyone at CMSA for the visit.
Mathematics, Academia, Lectures
15 points by Tomte 15 days ago | 0 comments
How much math is knowable? [video] (youtube.com)
Mathematics, Philosophy, Knowledge
115 points by diaphanous 16 days ago | 15 comments
Magic: The Gathering Fans Harness Prime Number Puzzle as a Game Strategy (scientificamerican.com)
The popular fantasy card game Magic: The Gathering has a new card related to prime numbers. Now fans are trying to use it to tackle one of the biggest problems in mathematics
Games, Mathematics, Strategy
10 points by bobismyuncle 16 days ago | 3 comments
Collatz's Ant (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, Programming, Visualization
102 points by Fibra 16 days ago | 18 comments
The Tau Manifesto (tauday.com)
The Tau Manifesto is dedicated to one of the most important numbers in mathematics, perhaps the most important: the circle constant relating the circumference of a circle to its linear dimension.
Mathematics, Tau, Pi
7 points by randunel 16 days ago | 0 comments
Reptends and Reciprocals (gregegan.net)
Is there an integer d whose reciprocal, 1/d, has a decimal representation with a recurring block of digits exactly 10 digits long, containing all ten decimal digits?
Mathematics, Number Theory, Puzzles
13 points by pavel_lishin 16 days ago | 2 comments
Are polynomial features the root of all evil? (2024) (alexshtf.github.io)
It turns out that it’s just a MYTH. There’s nothing inherently wrong with high degree polynomials, and in contrast to what is typically taught, high degree polynomials are easily controlled using standard ML tools, like regularization. The source of the myth stems mainly from two misconceptions about polynomials that we will explore here. In fact, not only they are great non-linear features, certain representations also provide us with powerful control over the shape of the function we wish to learn.
Machine Learning, Data Science, Myths, Mathematics, Polynomial Regression
188 points by Areibman 17 days ago | 77 comments