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I know of two good mathematics videos available online, namely:

  1. Sphere inside out (part I and part II)
  2. Moebius transformation revealed

Do you know of any other good math videos? Share.

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    $\begingroup$ The sphere eversion video is available in one part on Google Videos: bit.ly/2Bmj3Z $\endgroup$
    – Harrison Brown
    Commented Oct 21, 2009 at 20:33
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    $\begingroup$ The sphere eversion video is great, and it seems like a really good way to explain topology and the idea of an invariant to a non-mathematician. On the other hand, I wouldn't expect someone to sit for 20 minutes just to find out what I care about. Does anyone have recommendations of shorter videos that achieve similar goals? $\endgroup$
    – Aaron Mazel-Gee
    Commented Oct 22, 2009 at 6:26
  • $\begingroup$ I protected this one as it seems a clear candidate for this and as it just got reactivated and thus I noticed it. If you see a problem with this please let me know, or bring it up on meta. $\endgroup$
    – user9072
    Commented Dec 7, 2013 at 12:58
  • $\begingroup$ You missed to specify for which group / level of knowledge you are searching the "best mathematics videos". This makes it hard to answer. If you have 10 to 18 years old, you find great video material here (in German, all Youtube videos are with subtitles, thus translatable to English): matheretter.de/mathe-videos $\endgroup$
    – Avatar
    Commented Oct 7, 2015 at 7:32
  • $\begingroup$ @HarrisonBrown: The link you give appears to be broken in the meantime. Probably you mean youtube.com/watch?v=R_w4HYXuo9M. $\endgroup$
    – Stefan Kohl ♦
    Commented Oct 25, 2015 at 18:06

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The "Touching Soap Films" series by Springer. about minimal surfaces. Some excerpts of the video are available here: http://page.mi.fu-berlin.de/polthier/video/Touching/Scenes.html

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This video is less about mathematics, but about a fascinating mathematician in two bodies who helped saving medieval unicorns - students liked it.

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  • $\begingroup$ This is a very cute story! For people who'd prefer a slightly less cryptic description: the video is about two brothers, both professional mathematicians, who helped the Metropolitan Museum of Art construct a high-resolution digital image of a medieval tapestry. The tapestry had been photographed in thirty or so overlapping chunks, but the chunks didn't fit together into a consistent image. With the help of a graduate student, the brothers tracked down the source of the mysterious inconsistencies, and then figured out how to correct them. A nifty application of math---well worth watching! $\endgroup$
    – Vectornaut
    Commented Apr 19, 2010 at 5:36
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My good friend Professor Elvis Zap has the "Calculus Rap," the "Quantum Gravity Topological Quantum Field Theory Blues," a vid on constructing "Boy's Surface," "Drawing the hypercube (yes he knows there is a line missing in part 1)," A few things on quandles, and a bunch of precalculus and calculus videos. In order to embarrass all involved, he posted the series "Dehn's Dilemma" that was recorded in Italy last summer.

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Elvis's youtube link

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    $\begingroup$ Hey, that guy looks awfully familiar. $\endgroup$
    – Jim Conant
    Commented Mar 9, 2011 at 1:21
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On this page of sample animations using the k3d program there's a short animation of a "flower" blooming which is actually the first part of the sphere eversion.

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For a course on cluster algebras (by S. Fomin): http://qgm.au.dk/video/mc/cluster/

EDIT: Some graduate short-courses in FCEyN, UBA, Buenos Aires, Argentina:

  • J. Harris, Intersection Theory
  • R. Hartshorne, Introduction to Deformation Theory
  • D. Maclagan, Introduction to Tropical Algebraic Geometry
  • P. Beelen, Algebraic Geometric Codes

Here are the links to the videos of these 4 lectures.

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Among the best math videos can be found here: http://www.khanacademy.org/

(or the youtube-channel: http://www.youtube.com/khanacademy )

There is everything from counting to solving differential equations with Laplace transforms - nearly 1.000 videos altogether (and the guy is funny :-)

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Ken Ribet's introductory lecture on Serre's modularity conjecture. Useful and quite easy to follow and understand. http://fora.tv/2007/10/25/Kenneth_Ribet_Serre_s_Modularity_Conjecture

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Hitler learns topology

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Richard Feynman gave the 1964 Messenger Lectures at Cornell University --- this is an endowed lecture series to which a number of famous scholars have been invited, including several physicists. His lectures were recorded, and Bill Gates bought the rights to them and has provided them to the public for free.

http://research.microsoft.com/apps/tools/tuva/index.html

The content is mostly designed for a general audience, so if you have never learned physics you will learn something. And if you have studied plenty of physics already, you will be pleased to see the master at work in his prime. I very much enjoyed watching it.

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Timothy Gowers' "The Importance of Mathematics" never fails to instill a sense of purpose in my work, even when I feel I'm doing "useless" mathematics.

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Sir Michael Atiyah: Beauty in Mathematics.

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An excellent (and very lively) overview of basic one-variable calculus: Calculus I in 20 minutes: Part I, Part II.

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The Abdus Salam International Centre for Theoretical Physics has lots of lectures in mathematics and physics.Some of them are difficult to find in other places(Complex Analysis,Abstract Algebra,Topology,Functional Analysis,Algebraic Geometry..).For the same topic(ex:Complex Analysis)there are lectures by 2 ore more lecturers so you can choose. http://www.ictp.it/ http://www.ictp.tv/diploma/index07-08.php?activityid=MTH http://www.ictp.tv/diploma/index08-09.php?activityid=MTH

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A nice introduction to representation theory of compact lie groups, sl2(R) and other topics: http://www.math.utah.edu/vigre/minicourses/sl2/schedule.html

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A few talks under the heading "What is ..." (",,," could be "Morse Theory", for example) given at the Freie Universität Berlin can be found here:

http://www.scivee.tv/user/5216

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I found the Graduate weekend repository of lectures at the Mathematics Department of Duke's University very entertaining. There is more in the other folders(G.Tian, Langlands, just to name a few )$\ldots$

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David Cox's lectures in toric varieties at MSRI

Something really good to end the evening with :)

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I am quite surprised to see Dan Freed's lecture of Hodge Conjecture has not been mentioned. (Although it is an old thread I believe this should be in here. Before there was a QuickTime video but I am grateful to find that it has been youtubed.)

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As of today, the digitized tapes of CBMS Lectures on Probability Theory and Combinatorial by Michael Steele are online. I heartily recommend them — the style is informal, but educating: there are jokes, juggling lessons, speculations about the stock market, and all of these amidst beautiful mathematics.

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The first Minerva Lecture by Jean-Pierre Serre at Princeton in Fall 2012 is online. There were two other lectures, and they did videotape them, but I can't find them online.

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Any video on

Jos Leys "Mathematical Imagery"

is a true masterpiece, and has a non-trivial mathematical content...

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At the time of writing, Rutgers experimental mathematics seminar has over 200 videos up on youtube. I wish more seminars would do this!

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The complete introductory course on Algebraic Geometry by Miles Reid is very interesting (28 lectures following and extending his own undergraduate book on the subject), and his other set of lectures on Algebraic Surfaces.

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Marcus du-Sautoy's lecture - Music of The Prime Numbers, is a very nice popular talk about prime numbers

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I'd like to think that my math art is awesome, and start here.

the mapping behind that video is $(x,y,z)\rightarrow(2*cos(z-y),2*sin(x-z),7*cos(y-x))$, and has a singular Jacobian -- the immediate ramification of which is that there is overlap in the video.

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http://www.youtube.com/watch?v=VdPrCWr9Ruk&feature=player_embedded#!

is a video made by a student in the school of arichitecture using pov-ray is about algebraic surfaces and how they "deform"

there are a few more animations at the following url

http://www.formulas.it/animazioni.php

they are part of on-going project about the visualization of mathematics (being developed by group of mathematicians and architects)

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