Link Catalog

Both previous threads of this nature are outdated and can't be added to anymore, so here's the third edition of this megathread.

This list is by no means comprehensive, so please contribute suggestions in the comments below!

For the sake of brevity, not everything in the comments is included here; those resources with more general or strictly mathematical appeal are preferenced in this list.

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Videos

• K-12 material (* = linear algebra, differential equations, etc)

• Khan Academy*

• PatrickJMT*

• MathTV

• UKMathsTeacher

• ProfRobBob

• HippoCampus*

• Professor Leonard*

• University-Level Mathematics

• MIT Math OpenCourseWare

• Math Overflow's List of Free Online Lectures

• The Catsters - Category theory videos

• Math Dr. Bob

• IHES' youtube channel

• njwildberger's Insights into Mathematics videos

• Worldwide center of mathematics

• Hausdorff Research Institue for Mathematics

• Fields Institute Video Archive - a mix of general audience talks and conference broadcasts

• Institute for Advanced Study

• Recreational mathematics

• 3Blue1Brown

• Vi Hart

• Numberphile

• Mathologer

• Standupmaths

• PBS Infinite Series

Online Notes/References

• A massive compilation of online lecture notes - see also this comment.

• Paul's Online Math Notes - Extensive Calc I-III and Differential Equations notes.

• Wolfram Mathworld - Similar to Wikipedia in scope, but more strictly controlled with respect to editing.

• Rough Guides to Mathematics - An incomplete but still very useful series of guides to a number of advanced subjects, capturing lots of general overview and intuition.

• J.S. Milne's Site

• History of Math

• Harvey Mudd College's Online Math Tutorials

• Real (and some complex) Analysis & Programming

• Academic Earth

• Encyclopedia of Mathematics

• Expii has a number of K-12 math and science tutorials and problems.

Computer Algebra Systems (* = download required)

• SAGE

• Maxima*

• Octave*

• Wolfram Alpha

• Geogebra

Graphing & Visualizing Mathematics (* = download required)

• Geogebra

• gnuplot*

• Wolfram Demonstrations Project *

• Wolfram|Alpha

• scipy*

• Microsoft Mathematics*

• Desmos

• Symbolab

• Scilab*

Typesetting (LaTeX)

• Detextify - draw a shape and get the LaTeX command for it

• Overleaf - Collaborative online LaTeX editor

• Mathpix converts images and screenshots into LaTeX code. Currently designed for Mac and iOS.

• TeX Users Group

• The Comprehensive TeX Archive Network

• Art of Problem Solving Tutorial

• TexPaste

• Xfig

• WriteLaTeX WYSIWYG

• TeXample.net

• MathIM - LaTeX-enabled chat rooms

• The Comprehensive LaTeX Symbol List - 338 page PDF with over 500 tables; when they say comprehensive, they mean comprehensive.

Community/General Websites: very general-purpose things that almost anyone in their target audience ought to know about.

• r/math

• Math Stack Exchange

• MathOverflow

• The Art of Problem Solving - lots of resources for middle and high school students, especially those involved in math contests.

• arxiv.org

• Online Encyclopedia of Integer Sequences

• Sci-hub (URL changes over time, Google it) offers free (pirated) access to most scientific papers given a DOI. Accessing such papers deprives large publishing companies of access fees, but does not particularly affect the authors of said papers. r/math officially recommends that you not use sci-hub to access papers conveniently for free and not use this trick to easily redirect papers to sci-hub.

Blogs/Articles (* = occasional non-math political content)

• Blogs - There are of course an incredible number of blogs out there; this list covers just a few of the most well-known and high-quality. More in the subject-specific comment on this post.

• Terry Tao* - Summaries of interesting research, notes for courses, and miscellaneous musings from the frontiers of mathematical research.

• Gowers' Weblog* - Exposition of mathematical and meta-mathematical topics, generally written in a fairly accessible manner.

• Shtetl-Optimized* - Excellently-written explanations and examinations of quantum computing and the public perception thereof by Scott Aaronson.

• AMS Blog on Math Blogs* - Recently retired, but lots of archived content.

• Notices of the AMS

• The n-Category Café

• Articles

• Lockhart's Lament - Thoughts on the inadequacy of K-12 mathematics education in America. Worth reading, especially for anyone who has/had a poor experience with math in school.

• How to Write a Clear Math Paper by Igor Pak - a number of excellent pieces of advice on clear and effective communication of mathematics to others.

• The Grammar According to West is a graph theory centric but more generally useful series of tips on style, terminology, and usage in writing mathematics.

• General recreational miscellania

• My favorite theorem podcast

• Quanta magazine covers a number of scientific topics, including a significant amount of high-quality mathematics content.

• Chalkdust magazine is a mathematics-focused magazine featuring various articles and puzzles (including a crossnumber puzzle whose solvers can win prizes!)

Math Problems and Puzzles

• r/mathriddles

• Project Euler is a collection of hundreds of challenging problems, testing both mathematical and programming skills. Especially for higher-numbered problems, mathematical knowledge (and often research) is necessary to obtain a solution. See this comment for additional programming-related resources.

• brilliant.org offers a number of problems for free, along with a wiki. They also have additional premium content and courses.

• Contest archives:

• AMC, AIME, USAMO

• IMO

• Putnam

• Example problems:

• Example Problems

• Calculus.org

Misc

• Large List of Recommended books, online resources

• Summer Math Camps (high school)

• mathprograms.org (primarily undergraduate)

• Open Problem Garden

• Proof Wiki

• Librarian is a Chrome extension that provides easy access to references, BibTeX, and comments for all papers on the arXiv.

• The Inverse Symbolic Calculator takes in a constant and tries to find a closed form for it.

• Approach0 is a mathematical search engine, particularly useful for cases where you would like to search for a specific formula that e.g. may use different variable names.