This page lists links to blogs, and online mathematical communities like forums and wikis. For links to main repositories of free books, lectures, videos, reviews and math papers see math archives and for a list of societies and institutions see math institutions. A higher level branch page is math resources. Math is here just a mnemo, this page pertains also to the related areas of interest for $n$Lab like LaTeX, physics, philosophy, theoretical computer science etc.
For a quick introduction to math blogging, see
John Baez, What do mathematicians need to know about blogging? AMS notices, March 2010 (pdf)
See also MO question: most helpful math resources on the web, the directory of many math blogs with alerts on recent updates www.mathblogging.org.
For a decent list of online seminars see researchseminars.org/
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Deferential Geometry – wiki started by Garrett Lisi. Constructing a concise and beautiful theoretical description of reality unifying General Relativity, Quantum Field Theory, and the Standard Model using the foundations and language of basic differential geometry.
DispersiveWiki – wiki on local and global well-posedness problems for nonlinear dispersive and wave equations
eom.springer.de – free online access to 8000 entries of Springer online Encyclopedia of Mathematics
GreenApples – Resources for new math teachers
Liber Mathematicae – site under construction, featuring a new free online journal and some expositional math resources
Mathematics Literature Project, listing recent journals with freely available alternatives for papers, as well as hosting a copy of mathematics journals in Elsevier’s Open Archives (torrents of complete journals up to and including 2009 issues)
Model theory and Analysis by Patrick Speissegger
PolyMath Wiki for massively collaborative online mathematical projects.
The nLab, or $n$-Category Lab, which you are reading right now!
imomath unofficial site for IMO-level mathematics (under “training”), problem collections and IMO info
Math Overflow has become a universal clearinghouse for questions and answers “of interest to mathematicians”, modeled on stackoverflow and daughters of <http://area51.stackexchange.com>, including math.stackexchange dedicated to lower level math questions (“MathUnderflow”), tex.stackexchange about TeX and LaTeX. The similar physicsoverflow.com is deprecated; use physics.stackexchange instead. There is also the new PhysicsOverflow, which “comprises of a discussion forum for Physics at a graduate-level and beyond, and a section for research paper refereeing (reviews)”.
n-Forum For discussions about material (both maths and metas) here on the nLab.
the category theory mailing list (email discussion forum about category theory) and archives
ALGTOP mailing list archives
Art of Problem Solving – math school problems, math olympiads, talent search – features online forum with subforums in other languages and AoPS Resources including AoPSwiki, LaTeX forum section and LaTeX guide included.
Physics Forums has a large mathematics community. Offers homework help and normal discussion.
Foundations of Mathematics is where Harvey Friedman works openly on his research. Also moderated by Stephen Simpson, Martin Davis, Andreas Blass, William Tait, John Baldwin and Alasdair Urquhart.
Azimuth Project led by John Baez is an online hub for mathematicians, scientists and engineers working together to address global warming and other potential catastrophes.
Alasdair’s Musings Mainly (but not entirely) mathematics education and computer algebra systems.
Aleph Zero Categorical A blog mostly about algebra, counterexamples, and short proofs of random observations.
A Mind for Madness “Musings on art, philosophy, mathematics, and physics” (topics like differential geometry, homological algebra, but also belletristics)
AMS blogs several blogs under American Mathematical Society website
AMS Graduate Student Blog (career advices, education and entertainment “for and by” math grad students)
Azimuth (stochastic processes, network theory, ‘green mathematics’ and expository fun stuff)
bit-player Math/computer science blog of science writer Brian Hayes (writer for American Scientist)
“blog on math blogs” https://blogs.ams.org/blogonmathblogs
Continuous Everywhere but Nowhere Differentiable blog of a Brooklyn high school math teacher
Chromotopy (“chromatic”) stable homotopy theory blog – last update August 2011
dy/dan blog of Dan Meyer, a former high school math teacher now pursuing a Phd in math education – includes many videos for use in the classroom
Dan’s Geometrical Curiosities A collection of art and math projects by a Physics student, with help from a friend who likes blog posts.
Disquisitiones Mathematicae (dynamical systems, ergodic theory, randomness in number sequences, Ricci flow)
Division by Zero (Dave Richeson: “A blog about math, puzzles, teaching, and academic technology”)
E. Kowalski’s blog (analysis, esp. summation formulas, probability distributions, stochastic processes…)
empg Edinburgh Mathematical Physics Group
Explaining Math math teaching with multimedia, screencasts
Ganit Charcha (“Designing Mathematics Learning”)
galoisrepresentations.wordpress.com – a number theorist’s blog
Geomblog Ruminations on computational geometry, algorithms, theoretical computer science and life
Good Math, Bad Math (largely dedicated to chasing math crackpots; also math exposition)
theHigherGeometer by David Roberts
Hydrobates (dynamical systems, differential equations, biomedical modelling)
Joel David Hamkins “mathematics and philosophy of the infinite”, foundations
Low Dimensional Topology group blog by Ryan Budney, Nathan Dunfield, Jesse Johnson, Daniel Moskovich and Henry Wilton
mathbabe Blog on mathematical finance by former academic
Mathblogging.com A compilation of math blogs sorted according to genre including the “weekly pics” of the hosts: Felix Breuer, Frederik von Heymann, and Peter Krautzberger
math for love Blog of mathematics education consultants includes puzzles, teaching tips, and philosophical musings
Mathematics and Computation (Andrej Bauer, includes also topology and foundations–last update July 2011)
Mathematics Under the Microscope (Alexandre Borovik)
Mathematics without Apologies (Michael Harris)
mathlight’s blog (Zoran Škoda, noncommutative and derived geometry, mathematical physics, sci publishing)
Mathlinks / Art of Problem Solving community, math olympiad style problems discussed
Mathlog (in German, variety of topics from Open Access journals to Klein groups and geometry)
Math Vault (Everything higher mathematics: college math, calculus, linear algebra, logic, probability, statisitcs, proof-based math, educational technology and learning)
neverendingbooks (Lieven le Bruyn)
Noncommutative Geometry (Connes, Khalkhali…)
Nuit Blanche (data/imager/sensory compression, pattern recognition, networking, internet, AI/machine learning, neuroscience)
Oscar Cunningham’s Blog (Category theory, nontrivial trivialities)
Phd plus Epsilon Adriana Salerno reflects on her life as a junior faculty member at a Liberal Arts college
Proof Math is Beautiful Beautiful images of mathematical interest.
Quomodocumque University professor Jordan Ellenberg’s blog
Secret Blogging Seminar run by 8 recent Berkeley Ph.D. graduates. “Sort of like a seminar, but with (even) more rude commentary from the audience.”
Shadows of simplicity - algebraic combinatorics, umbral calculus
SymOmega (root systems, Weyl groups, buildings, algebraic groups…)
Tanya Khovanova’s math blog Light musings, puzzles and anecdotes concerning mathematics
The accidental mathematician (Izabella Laba: personal blog of a math professor, various topics, rarely even math)
The Math Less Travelled Expository writing aimed to expose the beauty of mathematics to a general audience
The n-Category Café A group blog on math, physics and philosophy written by (currently) seven people and affiliated with this wiki
The Polymath Blog (Tim Gowers “polymath” group projects: number theory, polynomials, algorithms, complexity, …–last updated July 2011)
Three-Toed Sloth (Cosma Shalizi: books, science, automata, complex networks, stochastic processes, numerics and simulation, arts, literature, politics)
Transcendence A math blog by whzecomjm covering Algebra, Number Theory etc. in Chinese.
Vi Hart’s blog Great videos and photos of mathematical art and story-telling
Victor Porton’s math blog (filters, posets, funcoids and reloids), abundant with self-centric claims of importance
What’s new (Terence Tao)
XOR’s hammer (logics and foundations–last updated July 2011)
Annoying Precision by Qiaochu Yuan (algebra, representation theory, combinatorics, abstract nonsense, arithmetics)
Ars Mathematica (analysis, probability…) - last updated in 2015
category theory at community.livejournal (in Russian)
Climbing Mount Bourbaki (Akhil Mathew: Lie algebras, differential and algebraic geometry…) - last updated in 2013
Concrete Nonsense A group blog on combinatorics, Lie algebras, representation theory, algebraic geometry – last update 2015
CSE Blog - quant, math, computer science puzzles ~ 250 Quant, Math & Computer Science Puzzles for Interview Preparation & Brain Teasing
Delta Epsilons A group blog focusing on algebra, representation theory, and Olympiad-style problem-solving –last update August 2010
degrees of freedom Math and Physics blog of Scientific American written by Davide Castelvecchi - last updated 2012
Embûches tissues (computational algebraic geometry, commutative algebra) – last update March 2010
Evolutionblog Mathematics and Politics blog by a college professor
FFF Forking, Forcing and back&Forthing – a blog by 10 model theorists - last updated in 2013
Geometric Group Theory (structured text with theorems, proofs and exercises in GGT) – last updated August 2009
Geometry and combinatorics (Konrad Swanepoel) - last updated 2014
Geometry and the Imagination (Danny Calegari: hyperbolic geometry, geometric group theory…)
God plays dice and previous location (probability, combinatorics, puzzles, financial math)
Höchste Zeit, unsern Kurs zu ändern – model theory of fields and commutative algebra
IMU - Journals blog on mathematical journals
Konrad Volkel blog (cohomology, geometry, topology); has also nice math resource list - blog last updated in 2015
Le Petit Chercheur Illustré (Signal processing and applied math, compressed sensing and inverse problems, random embeddings)
Martin’s Blog Martin Orr: algebraic geometry especially abelian varieties, Galois representations
Math-Blog (6 people blog: math books, university math, popular math etc.)
Mathcraft Math-inspired artwork and how-to info
Math Goes Pop! UCLA grad student writes about math in the media and pop culture
Math Monday The Museum of Mathematics will open in 2012 – this blog details its progress and fun math projects
Math Section ETH Zurich Master’s degree student writes about applications of mathematics in everyday life
Mathematical Formalities This blog is written by Sanath Devalapurkar, presenting some of his ideas and thoughts on (higher) category theory and $K$-theory.
Mathematical Musings (Interactions of probability, statistical physics, topology, and combinatorics. Matthew Kahle)
Maxwell’s Demon (Edmund Harriss: vizualizing math and math art, building math sculptures)
Misapplied Math (Math (mainly statistics, probability, and stochastic control), data science, and CS)
Motivic Stuff (Andreas Holmstrom writes on Cohomology, homotopy theory, and arithmetic geometry; see also the related Cohomology Theory Database by the same author)
Musings Mathematical and Otherwise (Edward Hughes - Algebraic Geometry and String Theory)
My research in geometry (Aleks Kleyn)
Nathaniel Johnston’s Blog (PhD student in quantum information – last update July 2011)
Nikita Markarian’s mathblog (derived algebraic geometry, dg-, $L_\infty, A_\infty, G_\infty$-algebras, operads, TQFT, BV formalism, Hochschild and cyclic (co)homology…–last updated July 2011)
Noncommutative geometry with point, by a grad student at Kansas–last updated September 2010
NUMBERPLAY A New York Times blog on math/numeric puzzles by Pradeep Mutalik
Paramanand’s Math Notes A math blog by Paramanand Singh covering Algebra, Number Theory, Mathematical Analysis, Geometry among other topics
Political Math Visualization of political information
Pronunciation of Mathematicians’ Names A blog about how to pronounce famous mathematicians’ names.
QED Insight (by Santo D’Agostino; mathematics, physics, education, pitched mainly to high school and undergraduate university students and teachers, with some material for lay people as well)
qrazydragon (math, books, internet, in Russian)
Reverberations in Mathematics (My Journey into Higher Mathematics - Julian Rachman
Rigorous Trivialities (a group blog - mainly algebraic geometry, including well-organized introductory notes algebraic geometry from the beginning – last updated 2015)
Sketches of Topology (colorful pictures, “visualizations of low dimensional topology”)
The Everything Seminar (“Geometry, topology, categories, groups, physics”; recently lots about experimental particle physics: LHC and CMS)
The Numbers Guy Wall Street Journal’s math/economics blog by Carl Bialik
The Unapologetic Mathematician (An expository “blath” by former academic John Armstrong) last updated in 2012
The Rising Sea (Daniel Murfet, previous blog moved to more of a homepage format, with arXiv of neat LaTeX notes on algebraic geometry, triangulated categories, sheaves…)
Theoretical atlas (Jeffrey Morton: groupoids, groupoidification, stacks, quantum physics, noncommutative geometry)
Things of interest (Mathematica visualisations, puzzles)
Todd and Vishal’s blog–last updated January 2011
Uncover a few New blog of problems and teaching ideas
Vivatsgasse 7 (Max Planck Bonn graduate students– last update November 2007)
Wiskundemeisjes (A blog about mathematics for a general audience, written by Jeanine Daems and Ionica Smeets, in Dutch)
Transient Dynamic (A blog on next-gen computational tools for mathematical modeling in complex systems, especially dynamical systems models)
Luca Trevisan’s LaTeX to Wordpress converter
This nifty script fixes the eyestrain caused by poorly designed blog contrasts. 15 seconds to install, works for Firefox only.
Detexify for finding LaTeX symbols by drawing them.