Hacker News with Generative AI: Mathematics

Lehmer's Continued Fraction Factorization Algorithm (leetarxiv.substack.com)
In 1931, at Stanford University, D.H Lehmer and R.E. Powers1 published a general integer factorization algorithm based on the theory of continued fractions.2
Matrix Calculus (For Machine Learning and Beyond) (arxiv.org)
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and return a matrix inverse or factorization, derivatives of ODE solutions, and even stochastic derivatives of random functions.
Accessible open textbooks in math-heavy disciplines (richardzach.org)
The authoring platform of choice in many math-heavy disciplines is LaTeX. It produces typeset documents of excellent quality and handles formulas and mathematical diagrams extremely well. Practically every researcher or instructor in mathematics, physics, and computer science is adept at using it, and it has a wide user base outside these core disciplines as well (e.g., philosophy and economics).
Terence Tao: A short text about when to consider using an AI for a task (mathstodon.xyz)
The Matrix Calculus You Need for Deep Learning (explained.ai)
Most of us last saw calculus in school, but derivatives are a critical part of machine learning, particularly deep neural networks, which are trained by optimizing a loss function.
Mathematician who reshaped theory of symmetry wins Abel Prize (nature.com)
Mathematician Masaki Kashiwara has won the 2025 Abel Prize, the Norwegian Academy of Science and Letters announced today.
Superhyperbola (johndcook.com)
Decomposing a Factorial into Large Factors (wordpress.com)
Mathematicians Find Proof to 122-Year-Old Triangle-to-Square Puzzle (scientificamerican.com)
Mathematicians Find Proof to 122-Year-Old Triangle-to-Square Puzzle
Microsoft Math Solver (microsoft.com)
Escher's Art and Computer Science (replicated.wiki)
While on a small vacation in the Hague I had a blissful chance to visit the Escher’s museum. It is now hosted in an actual royal palace which many Europeans may find surprisingly modest. Maurits Cornelius Escher was a 1940x Dutch graphic artist known for his math-rich works.
Mathematician who reshaped theory of symmetry wins Abel Prize (nature.com)
Mathematician Masaki Kashiwara has won the 2025 Abel Prize, the Norwegian Academy of Science and Letters announced today.
Abel Prize Awarded to Japanese Mathematician Who Abstracted Abstractions (nytimes.com)
Masaki Kashiwara, a Japanese mathematician, received this year’s Abel Prize, which aspires to be the equivalent of the Nobel Prize in math. Dr. Kashiwara’s highly abstract work combined algebra, geometry and differential equations in surprising ways.
Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares (web.stanford.edu)
This book is used as the textbook for our own courses ENGR108 (Stanford) and EE133A (UCLA), where you will find additional related material.
Yann LeCun "Mathematical Obstacles on the Way to Human-Level AI" [video] (youtube.com)
Three Hundred Years Later, a Tool from Isaac Newton Gets an Update (quantamagazine.org)
A simple, widely used mathematical technique can finally be applied to boundlessly complex problems.
Mathematicians uncover the logic behind how people walk in crowds (news.mit.edu)
Next time you cross a crowded plaza, crosswalk, or airport concourse, take note of the pedestrian flow. Are people walking in orderly lanes, single-file, to their respective destinations? Or is it a haphazard tangle of personal trajectories, as people dodge and weave through the crowd?
Peano's Axioms (principlesofcryptography.com)
Thinking of numbers intuitively brings to mind the simplest and most fundamental set of numbers, namely the set of natural numbers. These numbers are used to count objects like cars, books, pens, etc. If we associate natural numbers such as 1, 2, 3, etc. with counting, then with what corresponding concepts do we relate numbers like -4, \sqrt{3} \text{ and } \frac{22}{7}?
Making math fun by prepping for friendly competition (2022) (news.mit.edu)
In MIT class 18.A34 (Mathematical Problem Solving), students prep for a major collegiate mathematics competition — and learn to love math.
The Prospero Challenge (mattkeeter.com)
prospero.vm is a plain-text file containing 7866 math expressions.
What is PLUS times PLUS? [video] (youtube.com)
Older editions of which books were better than the new ones? (2010) (mathoverflow.net)
When choosing some mathematics book to study, is it always the case that one should look for the current edition of the book. Are there any examples when the older edition of some book is clearly better than the latest version?
Mathematical Methods for Physics [pdf] (imperial.ac.uk)
Differential Geometry: A First Course in Curves and Surfaces [pdf] (franklin.uga.edu)
AI for the Working Mathematician (connorgs.net)
We suggest ways that AI can be useful to the working mathematician.
LibreTexts Mathematics (libretexts.org)
This central Bookshelves area in this LibreTexts Library holds texts that are curated by the LibreTexts Development team and can be used either directly or as content for building customized remixes (i.e., texts that are generated from existing content often with customized editing and/or content interspersed) for use in Course Shells housed in Campus Bookshelves. For details on how to have a text added to the bookshelves or how to remix content into your customized remix contact us at info@libretexts.org.
Coding Theory and Cryptography [pdf] (ualberta.ca)
Math for Computer Science and Machine Learning [pdf] (cis.upenn.edu)
Pen and Paper Exercises in Machine Learning (2022) (arxiv.org)
This is a collection of (mostly) pen-and-paper exercises in machine learning.
Advanced Algorithms [pdf] (ethz.ch)