Theorem of the Day
The links below will bring you (in a new window) a superb collections of sites, blogs, online magazines etc, covering large parts of mathematics. Some subject-specific links are here.
This site draws inspiration from:
Pat Ballew's On This Day in Math
Nathan W. Kahl has posted a list Top 100 Theorems, attributed to Paul and Jack Abad but enhanced with many well-chosen links. The site appears now to exist only as an archive but the idea has been given new life by Freek Wiedijk whose list of formalised theorems I believe to be an important and forward-looking resource. A related effort (on an industrial scale!) is the Archive of Formal Proofs.
Neil Sloane's Online Encylopedia of Integer Sequences is a virtual theorem list. Not all it's >260K entries correspond to proved assertions but mostly there's at least one bona fide theorem involved somewhere! By the way, Quanta Magazine has an excellent interview with Sloane.
Another site offering infinitely many theorems ... named after you!
In case you are wondering about where the proofs are ... they are here!
Mathematics Compendia & Encyclopediae
Cut-the-knot: Alexander Bogomolny's cornucopia of maths applets and animations.
Mathpages by the admirable but elusive Kevin Brown
Numericana is an Aladdin's cave of answers to mathematical questions, basic and advanced, maintained by Gérard P. Michon. The Numericana Hall of Fame links to some of the best web resources in mathematics (I wrote that before Dr Michon was kind enough to include theoremoftheday.org in it!).
European Mathematical Society Newsletter, increasingly full of excellent expository material (but increasingly big: up to 9MB pdf downloads).
Fibonacci Quarterly a serious journal but with much that is accessible at all levels. Currently free online up to Volume 49 (2011) with some later special issues open access.
Function by Michael Deakin, published by Monash University's mathematics department from 1977 to 2004
The Feature Column of the AMS, currently edited by David Austin, Bill Casselman, Joe Malkevitch and Tony Phillips, has an brilliant archive going back ten years, with well over 100 authoritative articles
Gonit Sora, Indian (mostly English-language) magazine, with problems, interviews, book reviews etc etc
Journal of Humanistic Mathematics, serious journal but with much that is accessible to non-professionals
Bulletin of the Irish Mathematical Society, professional newsletter but with much of general interest
Kömal Hungarian-language magazine
London Mathematical Society Newsletter, professional newsletter but with much of general interest
MAA Focus, an excellent source of expository articles, book reviews etc. From the Mathematics Association of America whose range of wonderful magazines are not otherwise online but over a hundred award-winning articles from them are.
MATEMATICALIA Spanish-language magazine, from 2005 to 2012
Mathematical Chronicle published by the Mathematical Chronicle Committee, 1969-1991: more than 20 years of top quality articles, reviews etc
Mathematics Magazine Canadian magazine for high school students
Nautilus 'glossy' online science magazine with occasional mathematical interest
Nieuw Archief voor Wiskunde Dutch-language magazine (some English-language articles). A selection of material is open access
Pythagoras, Dutch-language magazine
Quadrature, French-language magazine
SIAM News, the newsletter of the Society of Industrial and Applied Mathematics
Solmu, Finnish-language magazine
The Aperiodical – home of Carnival of Mathematics, Puzzlebomb, Travels in a Mathematical World and tons more.
John Baez's Stuff – blogs, diaries, news; one of the greats!
Cameron Counts – a top professional gives an unusually wide-ranging view of the profession.
Carnival of Mathematics – showcasing mathematics blogs.
Combinatorics and More – a beautiful blog by Gil Kalai.
CSE Blog – fun place for puzzles, tricks, tips on quantitative methods by Pratik Poddar.
Tanya Khovanova's blog –"mathematics, applications of mathematics to life in general, and my life as a mathematician". Fun and sometimes funny and sometimes weird.
Let's Play Math (blog carnival used to be Math Teachers at Play)
Mathblogging: latest posts from hundreds of maths blogs.
Math by Matt: Matt Rosenzweig's blog
Terence Tao's What's New – groundbreaking research and top-class expository articles...
Tony's Maths Blog, aka the 14-15 Puzzle in Numberland, a professional mathematician browses, muses and amuses.
XOR's Hammer – a wonderful blog by Michael O'Connor, primarily about mathematical logic, but with lots and lots of other nice things
alwaysmath.com/ pre-kindergarten to college level math: a kind of online home tutor; lots of multiple-choice tests etc.
For Dutch speakers, Curiosa Mathematica, by Jens Bossaert, is a wonderful source of mathematical gems (currently 11.5MB).
goodcalculators.com offers a wide variety of calculation resources for everything from geometry to taxes
images.math.cnrs.fr, great blog-style collection of images and words (in French) — à ne pas manquer!
The International Mathematical Olympiad Foundation: news, interviews, problem sets and, of course, the big competition!
intmath, a great resource from Murray Bourne
Just The Maths, a superb teaching pack for 'mathematical methods' by A.J. Hobson. The distillation of a lifetime's thinking about how it should be done.
The M500 Society, one of the UK's great unsung mathematical resources, going from stength to strength after 35 years and the source of the beguiling M500 Magazine.
mangahigh.com, a commercial-quality computer games site for school-level maths. Very impressive!
Math Forum, an excellent resource for schools and colleges.
Math Insight, a tremendous collection of notes on mainly analysis-related topics.
Math Playground (used to be a blog called learninginmathland)
Maths et tigues great French language site, home of the online magazine Quadrature
NRICH brings mathematics alive for school students like nowhere else.
The Peoples Archive has film+transcript interviews with a galaxy of intellectual and artistic giants, including Miachael Atiyah, Freeman Dyson, Don Knuth, Benoit Mandelbrot.
Travels in a Mathematical World: podcast site, a great source of live interviews, bits of mathematical history etc. Peter Rowlett has moved on (see above) but the site will remain, and remains a valuable visit.
Virtual Maths Museum: a fine collection of images of curves, surfaces etc.