Hacker News with Generative AI: Mathematics

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
33 points by mikhael 3 hours 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
115 points by ndrwnaguib 10 hours ago | 26 comments
Notation as a Tool of Thought (1979) (jsoftware.com)
Software, Programming, Mathematics, History
303 points by susam 1 day ago | 94 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
7 points by romes 1 day 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
14 points by Tomte 2 days ago | 1 comments
How much math is knowable? [video] (youtube.com)
Mathematics, Philosophy, Knowledge
110 points by diaphanous 2 days ago | 11 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 2 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
99 points by Fibra 3 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 3 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 3 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
185 points by Areibman 3 days ago | 75 comments
Surprises in Logic (2016) (math.ucr.edu)
There's a complexity barrier built into the very laws of logic: roughly speaking, while lots of things are more complex than this, we can't prove any specific thing is more complex than this. And this barrier is surprisingly low! Just how low? Read this.
Mathematics, Logic, Complexity
91 points by jxmorris12 4 days ago | 42 comments
Flat origami is Turing complete (2023) (arxiv.org)
"Flat origami" refers to the folding of flat, zero-curvature paper such that the finished object lies in a plane.
Origami, Mathematics, Computer Science, Theory
40 points by PaulHoule 4 days ago | 12 comments
Is 1 Prime, and Does It Matter? (wordpress.com)
If you ask a person on the street whether 1 is a prime number, they’ll probably pause, try to remember what they were taught, and say “no” (or “yes” or “I don’t remember”). Or maybe they’ll cross the street in a hurry. On the other hand, if you ask a mathematician, there’s a good chance they’ll say “That’s an excellent question” or “It’s kind of an interesting story…”
Mathematics, Number Theory, Prime Numbers
92 points by jamespropp 4 days ago | 151 comments
PlanetMath (planetmath.org)
PlanetMath is a virtual community which aims to help make mathematical knowledge more accessible.
Mathematics, Online Communities, Education
15 points by synthetictask 5 days ago | 1 comments
New Proof Settles Decades-Old Bet About Connected Networks (quantamagazine.org)
It started with a bet.
Mathematics, Science, History
93 points by rbanffy 5 days ago | 21 comments
What the hell is an elliptic curve? (onlynv.dev)
Have you ever been browsing the web and come across a term that made you go, "huh?" Well, if you're even slightly cryptographcally inclined, you might have stumbled upon the term elliptic curve and thought to yourself, "What the hell?" Don't worry, you're not alone in feeling a bit lost.
Cryptography, Mathematics, Security
65 points by thecommieaxo 6 days ago | 34 comments
100 Years to Solve an Integral (2020) (liorsinai.github.io)
The integral of sec(x) is well known to any beginners calculus student. Yet this integral was once a major outstanding maths problem. It was first introduced by Geradus Mercator who needed it to make his famous map in 1569. He couldn’t find it and used an approximation instead. The exact solution was found accidentally 86 years later without calculus in 1645.
Mathematics, History, Calculus
215 points by blobcode 6 days ago | 61 comments
Electromagnetism as a Purely Geometric Theory (iopscience.iop.org)
This research article derives a nonlinear generalization of Maxwell's equations from a variational approach, when the action measures the variability of the metric tensor.
Physics, Electromagnetism, Mathematics, Geometry
148 points by andyjohnson0 6 days ago | 64 comments
Monsky's Theorem (mathmondays.com)
For which \(n\) can you cut a square into \(n\) triangles of equal area?
Mathematics, Geometry, Puzzles
48 points by hyperbrainer 6 days ago | 13 comments
Which one result in mathematics has surprised you the most? (stackexchange.com)
A large part of my fascination in mathematics is because of some very surprising results that I have seen there.
Mathematics, Surprise, Results
5 points by paulpauper 7 days ago | 1 comments
A Math Lesson From Hitler’s Germany (2017) (undark.org)
In 1934, David Hilbert, by then a grand old man of German mathematics, was dining with Bernhard Rust, the Nazi minister of education. Rust asked, “How is mathematics at Göttingen, now that it is free from the Jewish influence?” Hilbert replied, “There is no mathematics in Göttingen anymore.”
History, Mathematics, Germany
152 points by perihelions 8 days ago | 43 comments
A cute proof that makes e natural (poshenloh.com)
This webpage pulls out the part of the article which uses Pre-Calculus language to explain what is so natural about e, while intuitively connecting the following two important properties:
Mathematics, Proof, Number Theory
101 points by georgecmu 9 days ago | 43 comments
Notes on a claim that a mceliece348864 distinguisher uses only 2^529 operations [pdf] (mceliece.org)
Cryptography, Security, Research, Mathematics
13 points by nabla9 9 days ago | 1 comments
'Mind blowing': quantum computer untangles the mathematics of knots (nature.com)
‘Mind blowing’: quantum computer untangles the mathematics of knots
Quantum Computing, Mathematics, Science
9 points by rbanffy 9 days ago | 0 comments
Eccfrog512ck2: An Enhanced 512-Bit Weierstrass Elliptic Curve [pdf] (arxiv.org)
Whilst many key exchange and digital signature methods use the NIST P256 (secp256r1) and secp256k1 curves, there is often a demand for increased security.
Cryptography, Elliptic Curves, Security, Mathematics
45 points by bikenaga 9 days ago | 16 comments
An Introduction to Stochastic Calculus (2022) (bjlkeng.io)
Many physical phenomena (and financial ones) can be modelled as a stochastic process that is described using a stochastic differential equation.
Mathematics, Stochastic Calculus, Finance, Physics
173 points by ibobev 10 days ago | 44 comments
Harvard Launches New Intro Math Course to Address Pandemic Learning Loss (2024) (thecrimson.com)
The Harvard Math Department will pilot a new introductory course aimed at rectifying a lack of foundational algebra skills among students, according to Harvard’s Director of Introductory Math Brendan A. Kelly.
Education, Pandemic, Mathematics
5 points by TMWNN 10 days ago | 0 comments
The physics of bowling strike after strike (arstechnica.com)
New model uses 6 differential equations relating to a rotating rigid body for best strike conditions.
Physics, Sports, Bowling, Mathematics
47 points by noleary 10 days ago | 23 comments
Markov Chain Monte Carlo Without All the Bullshit (2015) (jeremykun.com)
I have a little secret: I don’t like the terminology, notation, and style of writing in statistics. I find it unnecessarily complicated.
Statistics, Machine Learning, Mathematics
228 points by ibobev 10 days ago | 48 comments