Hacker News with Generative AI: Mathematics

The Fourier Transform: A tutorial introduction (sheffield.ac.uk)
The Fourier Transform is a fundamental tool in the physical sciences, with applications in communications theory, electronics, engineering, biophysics and quantum mechanics.

Mathematics, Signal Processing, Education, Physics

4 points by teleforce 13 hours ago | 1 comments

Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad (arxiv.org)
Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, o3-mini, achieving scores comparable to top human competitors.

Mathematics, Benchmarking, AI, Olympiads

5 points by mauriziocalo 2 days ago | 1 comments

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

Mathematics, Algorithms, Number Theory

18 points by muragekibicho 5 days ago | 5 comments

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.

Machine Learning, Calculus, Linear Algebra, Mathematics

182 points by ibobev 5 days ago | 30 comments

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).

Open Textbooks, Mathematics, LaTeX, Education

235 points by volemo 5 days ago | 74 comments

Terence Tao: A short text about when to consider using an AI for a task (mathstodon.xyz)

Artificial Intelligence, Mathematics, Advice

6 points by ColinWright 5 days ago | 0 comments

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.

Deep Learning, Machine Learning, Mathematics, Neural Networks

67 points by Anon84 5 days ago | 3 comments

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.

Mathematics, Awards, Science

3 points by ibobev 6 days ago | 0 comments

Superhyperbola (johndcook.com)

Mathematics, Computer Science, Algorithms

64 points by jihadjihad 6 days ago | 20 comments

Decomposing a Factorial into Large Factors (wordpress.com)

Mathematics, Algorithms, Factorials

134 points by surprisetalk 6 days ago | 27 comments

Mathematicians Find Proof to 122-Year-Old Triangle-to-Square Puzzle (scientificamerican.com)
Mathematicians Find Proof to 122-Year-Old Triangle-to-Square Puzzle

Mathematics, Geometry, Puzzles, History

12 points by IdealeZahlen 7 days ago | 0 comments

Microsoft Math Solver (microsoft.com)

Microsoft Products, Mathematics, Tools

31 points by danielam 8 days ago | 4 comments

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.

Art, Computer Science, Mathematics

19 points by gritzko 8 days ago | 0 comments

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.

Mathematics, Awards, Science

5 points by sohkamyung 9 days ago | 0 comments

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.

Mathematics, Awards, Japan, Algebra, Geometry

12 points by donohoe 9 days ago | 0 comments

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.

Linear Algebra, Mathematics, Education, Computer Science, Engineering

7 points by ibobev 10 days ago | 0 comments

Yann LeCun "Mathematical Obstacles on the Way to Human-Level AI" [video] (youtube.com)

Artificial Intelligence, Machine Learning, Computer Science, Yann LeCun, Mathematics

5 points by mariuz 10 days ago | 0 comments

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.

Mathematics, Science, History

153 points by rbanffy 10 days ago | 46 comments

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?

Mathematics, Human Behavior, Pedestrian Dynamics, Crowds

51 points by geox 10 days ago | 19 comments

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}?

Mathematics, Number Theory, Set Theory

91 points by ulugh 10 days ago | 33 comments

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.

Education, Mathematics, Competition

8 points by rnjailamba 11 days ago | 2 comments

The Prospero Challenge (mattkeeter.com)
prospero.vm is a plain-text file containing 7866 math expressions.

Mathematics, Programming, Challenges

106 points by jstanley 11 days ago | 39 comments

What is PLUS times PLUS? [video] (youtube.com)

Mathematics, YouTube, Education

14 points by weinzierl 11 days ago | 0 comments

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?

Mathematics, Books, Education

41 points by susam 12 days ago | 44 comments

Mathematical Methods for Physics [pdf] (imperial.ac.uk)

Mathematics, Physics, Education

130 points by ibobev 12 days ago | 42 comments

Differential Geometry: A First Course in Curves and Surfaces [pdf] (franklin.uga.edu)

Differential Geometry, Mathematics, Education, Textbooks

147 points by ibobev 13 days ago | 8 comments

AI for the Working Mathematician (connorgs.net)
We suggest ways that AI can be useful to the working mathematician.

Mathematics, Artificial Intelligence, Tools

6 points by treebrained 13 days ago | 0 comments

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.

Education, Open Source, Textbook, Mathematics

7 points by ibobev 13 days ago | 0 comments

Coding Theory and Cryptography [pdf] (ualberta.ca)

Cryptography, Coding Theory, Computer Science, Mathematics

15 points by ibobev 13 days ago | 1 comments

Math for Computer Science and Machine Learning [pdf] (cis.upenn.edu)

Mathematics, Computer Science, Machine Learning, Education

80 points by ibobev 13 days ago | 12 comments