The AMS Public Awareness Office recommends these mathematics websites which have extensive links to a wide range of resources on various mathematical topics at all levels, including: the history of mathematics, mathematicians, current research, and video collections.

The Euler Archive

An online resource for Leonhard Euler's original works and modern Euler scholarship.

Mathematics Matters: Case studies at the UK's Institute of Mathematics & its Applications, showing how modern math research affects people's lives.

MacTutor History of Mathematics Archive

A comprehensive site for mathematics history.

MathForum

Math education, resources, issues, and Ask Dr. Math.

Math in Daily Life

Examples of mathematics' ubiquity, and links to other sites.

Math on the Web

Links to departments, journals, and more.

MathWorld

Detailed descriptions of many mathematics subjects and news, by Eric Weisstein

Museum of Mathematics

A new project that includes a traveling exhibit. Schedule opening date is this December!

*Plus*

This online journal sponsored by Cambridge University introduces readers to the beauty and applications of mathematics. The monthly includes feature articles, games and puzzles, reviews, news, and interviews.

2014 Breakthrough Prize Videos

The above links to a panel discussion among the five winners of the 2014 Breakthrough Prizes in Mathematics that was part of a symposium held at Stanford University. Also see videos of presentations by each winner: Jacob Lurie, Simon Donaldson, Maxim Kontsevich, Terence Tao, and Richard Taylor.

Beautiful Math. MoMath presents “What do mathematicians think is beautiful about mathematics?” videos.

BIRS Workshop Lecture Videos

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) and the University of British Columbia's (UBC) Library have collaborated on a project to preserve, archive and disseminate the lecture videos from BIRS' weekly workshops at UBC Library's digital repository, cIRcle.

CIRM Audiovisual Mathematics Library

Browse, search and view videos of talks by mathematicians during their stay at CIRM (Centre International de Rencontres Mathématiques International), special events, interviews and outreach activities. The videos are in French and English.

Dimensions

Nine videos of stereographic projections in 3 and 4 dimensions, complex numbers, Hopf fibration, and proof.

GVSU Math Videos

Videos from the Mathematics Department at Grand Valley State University in Allendale/Grand Rapids, MI.

Institute for Advanced Study - School of Mathematics Videos

Lectures by mathematicians hosted at the IAS, Princeton, NJ.

Khan Academy videos

Instructional videos in arithmetic and pre-algebra, algebra, geometry, trigonometry, probability, statistics, precalculus, calculus, differential equations,lLinear algebra, brain teasers, and a collection of recreational mathematics and inspirational videos by resident mathemusician Vi Hart.

Levi L. Conant Lecture Series

Videos of lectures given at Worcester Polytechnic Institute (WPI) since 2008 by the winners of the Levi L. Conant Prize. Conant spent most of his career as a faculty member at the institute.

MathBytes@ICERM

Aimed at a general audience, ICERM's "MathBytes@ICERM" series introduces math topics in unique 15-30 minute clips. The videos feature ICERM public lecturers or program visitors who are able to communicate their research interests in concise and often fun ways.

Math Mornings at Yale

Math Mornings is a series of public lectures aimed at bringing the joy and variety of mathematics to students and their families. Speakers from Yale and elsewhere talk about aspects of mathematics that they find fascinating or useful. The talks will usually be accessible to students from 7th grade and up, although occasionally some familiarity with high-school subjects will be helpful.

Mathematical Impressions videos by George Hart for the Simons Foundation

Any of these videos could be the starting point for a personal math project or a group activity at a math club, and Hart lists some open-ended ideas of things to do that could go along with each video, along with some references to help get started.

Mathematical Society of Japan Video Collection (in English)

Free online videos of lectures delivered at MSJ meetings.

Mathematics in Movies

An extensive collection of movie and TV clips in which mathematics appears, posted by Oliver Knill of Harvard University.

Mathologer

Burkard Polster, School of Mathematical Sciences at Monash University, Victoria, Australia, presents videos explaining math in movies and other topics of popular interest.

Mathtube.org

Mathtube.org is a project of the Pacific Institute for the Mathematical Sciences (PIMS) to make mathematical seminar and lecture materials easily available online.

MIT Online Math Courses

Free online course videos from the Massachusetts Institute of Technology.

MSRI Online Videos

VMath - The Next Generation for Math Lectures, is a program of the Mathematical Sciences Research Institute in Berkeley, CA. Videos include workshops, seminars, and special productions.

Numberphile

Videos about numbers, by Brady Haran, supported by MSRI. Videos include speed solving Rubik's Cube, the Fields Medal, and calculating pi with real pies.

Open Culture

Videos of free online mathematics courses at MIT, Harvard, UCLA, UC berkeley, IIT, Carnegie Mellon, Johns Hopkins, Princeton.

PBS Infinite Series

Mathematician Kelsey Houston-Edwards offers ambitious content for viewers that are eager to attain a greater understanding of the world around them. Math is pervasive - a robust yet precise language - and with each episode you’ll begin to see the math that underpins everything in this puzzling, yet fascinating, universe.

SIAM Presents

Synchronized audio and slide presentations of invited lectures, prize lectures, and selected minisymposia from SIAM conferences, and video clips from SIAM's Annual Meeting.

Simons Foundation - Science Lives

The Simons Foundation presents a series of extended interviews with some of the giants of 20th-century mathematics and science. This collection, organized in collaboration with Hugo Rossi of the University of Utah, provides an opportunity to watch these great men and women discuss their lives and their thinking about science and our world.

UTM MCS Math Videos

The Mathematical and Computational Sciences Department at the University of Toronto Mississauga created these helpful videos for understanding First Year University Math Concepts. Each concept is explained through the use of examples.

Videolectures.net

There is a treasure trove of video lectures on mathematics on videolectures.net. The many topics include Algebra, Analysis, Game Theory, Graph Theory, Optimization, and Statistics.

Video Lectures in Mathematics

Links to a broad range of math videos on Pinterest, on a range of topics, and including some student lectures, instruction, videos from meetings, interviewsand even math humor.

Webcast Berkeley

Webcast videos of mathematics courses at UC Berkeley.

*The AMS also provides these websites for further explorations:*

What's Happening in the Mathematical Sciences

A series of books about recent developments in math research. Each chapter--including some available free online--brings readers the exciting world of modern mathematics and applications.

High School Students and Teachers

Links to online magazines, information on careers, posters and tools.

Math in the Media

A centralized tracker of articles about mathematics that appear in newspapers and science magazines. The collection--"Tony Phillips' Take on Math in the Media," "Math Digest" (summaries of mathematics in the news), and "Reviews" of books, plays and films with mathematical themes--is a great way to keep abreast of math resarch and news as reported in the general media.

Feature Column

A series of essays on a wide range of topics, such as voting, bin-packing and networks. Math in the Media and the Feature Column offer a wealth of information about current mathematics and its applications.