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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.

Randomblue
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    The sphere eversion video is available in one part on Google Videos: http://bit.ly/2Bmj3Z – Harrison Brown Oct 21 '09 at 20:33
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    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? – Aaron Mazel-Gee Oct 22 '09 at 06:26
  • 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. –  Dec 07 '13 at 12:58
  • 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): http://www.matheretter.de/mathe-videos – Avatar Oct 07 '15 at 07:32
  • @HarrisonBrown: The link you give appears to be broken in the meantime. Probably you mean https://www.youtube.com/watch?v=R_w4HYXuo9M. – Stefan Kohl Oct 25 '15 at 18:06
  • If I had more videos like this I would post as an answer. Here are some review solutions for my students in the United States for Finite Mathematics. I was able to find a way to write on the slides. https://www.youtube.com/watch?v=aDoqbx4zO2E&t=7s –  Dec 18 '20 at 22:27

80 Answers80

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77 instructional videos on category theory:

https://www.youtube.com/TheCatsters

I know you said "only one video per post", but I'm not posting 77 times...

Tom Leinster
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I have compiled a list (1500+) of math videos at http://pinterest.com/mathematicsprof/ . If anyone is aware of others, please send them to me.

jfm314
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Most of the talks at MSRI are videotaped and placed on the web here:

http://www.msri.org/communications/vmath/index_html

Andy Putman
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My personal all-time favorite is the Klein Four with their song "Finite Simple Group (of Order Two)"... it has lots of puns on topology in it, but I guess it doesn't teach anything.

Here's the link to the "Finite Simple Group" song

Konrad Voelkel
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    The song may not teach anything, but I think it's contributed positively to my education! Listening to it every once in a while gives me evidence that I'm actually learning stuff, because the song keeps getting funnier. ^_^ – Vectornaut Apr 19 '10 at 04:55
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I believe this was mentioned elsewhere, but for completeness, here's Serre on writing.

Stefan Kohl
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  • My favorite quote from this video (among many great quotes): "I'm sure that if this happened with Bourbaki, some member of Bourbaki, he would tell the other one, "It is because you are stupide and you have not found the correct statement, which would give both of them!"" – Harry Gindi Apr 23 '10 at 14:56
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Dimensions

Möbius Transformations Revealed

Gerald Edgar
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This video about Andrew Wiles and the proof of Fermat's Last Theorem is the only time I've seen the real excitement of mathematics presented accurately.

Stefan Kohl
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JoeG
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  • Thanks! I just watched the video! I can't even imagine the pressure Wiles got when the proof was Almost there, but just almost, after having announced the result! –  Feb 20 '11 at 23:38
  • I am unable to watch the video, please help. – random Jun 10 '21 at 05:32
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'Not Knot' is also a nice vid

http://www.youtube.com/watch?v=AGLPbSMxSUM

Any
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The Newton institute in Cambridge tapes alot (all?) of it's lectures, and they can be found on the Institutes webpage. High quality for videos of lectures.

GMRA
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At the accessible end of the scale, Vi Hart's "doodling in math class" series and subsequent videos are a delight.

Gray Taylor
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MIT's OpenCourseWare has a few math courses up:

http://ocw.mit.edu/OcwWeb/web/courses/av/index.htm#Mathematics

Matt
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GRASP is a new lecture series at the University of Texas at Austin, which is aimed at bringing some of the fundamental concepts and big picture of the GRASP areas (Geometry, Representation, and Some Physics) to a wider audience (the intended target audience are beginning graduate students).

http://www.ma.utexas.edu/users/benzvi/GRASP.html

Paolo
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The Institute for Advanced Study tapes some of its lectures. They tend to be very good.

Mitch
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You probably won't learn much actual math from it, but One Geometry is funnier and catchier than a Snoop Dogg parody about 3-manifolds has any right to be.

10

Along the sphere eversion lines, there is also the energy-minimizing sphere eversion constructed by Rob Kusner. I think there is a video of it at https://www.youtube.com/watch?v=I6cgca4Mmcc, though it isn't labelled as such.

Rob also has written a paper about the history of the minimax eversion.

Matt Noonan
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I guess all of John Conway's lectures are great. Some of those can be found here : http://www.math.princeton.edu/facultypapers/Conway/

Somnath Basu
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My personal favorite in Dimensions, that was mentioned before by Gerald Edgar. For a neat and clear exposition the Geom.of 3 manifolds, Poincaré conjecture, etc I recommend this lecture by C.McMullen. Or Das Schöne denken (hosted at the HIM in Bonn), for a good "glimpse in the world of the mathematician". Jos Leys' mathematical imagery contains some (interesting) videos and (a lot of beautiful) images.

Ferran V.
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There are Stephen Boyd's lecture videos on convex optimization:

http://www.stanford.edu/class/ee364a/videos.html

AgCl
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The series of videos from IAS School of Mathematics

Kelly Davis
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The IHES also has a lot of on-line videos. In particular, I like very much the ones from the "Colloque Grothendieck".

DamienC
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Dror Bar-Natan has begin putting many of his lectures and talks online in video format. I'm not claiming that these are the 'best' online maths videos, but they're certainly interesting, and in particular he's come up with some neat tricks to associate publicly editable annotations with particular moments in the video.

6

Not lecture videos or anything, but the stuff from Oliver Labs is very good for just illustrating geometric stuff, like blowups and dual curves.

6

I am surprised that nobody mentioned the four-week workshop at Göttingen on arithmetic geometry in 2006 summer. Almost all of the videos are still available. Wonderful videos.

Anweshi
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Videos recorded at IMPA:

http://video.impa.br/index.php?page=download

(some in English, some in Portuguese)

expmat
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Stoney Brook math videos:

http://www.math.sunysb.edu/Videos/dfest/

http://www.math.sunysb.edu/html/videos.shtml

6

This is an old thread, but this video was recently posted to the Don Davis topology list, and I have to share it. It was created by Niles Johnson at UGA and it illustrates the Hopf fibration.

http://www.youtube.com/watch?v=AKotMPGFJYk

5

This isn't purely a math video, it's an interview with Peter Woit and it is something of a summary of the main issues discussed on his blog and in his book. He talks about math vs. physics culture, especially the string theory community.

edit: the link appears to have changed.

https://bigthink.com/u/peterwoit

Discussion here:

http://www.math.columbia.edu/~woit/wordpress/?p=2670

Ryan Budney
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This one is quite old but it was fun when I watched a few years ago. It's about Fermat's Last theorem.

http://www.archive.org/details/fermats_last_theorem

sanokun
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5

John Stillwell - ET Math: How different could it be? A nice talk given at the SETI Institute.

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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

javier
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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.

Thomas Riepe
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  • 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! – Vectornaut Apr 19 '10 at 05:36
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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.

Scott Carter
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Elvis's youtube link

Scott Carter
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4

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.

Andrew Stacey
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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.

Stefan Kohl
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3

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 :-)

vonjd
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3

Sir Michael Atiyah: Beauty in Mathematics.

Spinorbundle
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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

T.B.
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NMU(https://en.wikipedia.org/wiki/Independent_University_of_Moscow) and MIAN lectures 2009-2010 (in Russian)

http://erb-files.narod.ru/

3

Hitler learns topology

Vivek Shende
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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.

3

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.

Peter Luthy
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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.

David Corwin
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Any video on

Jos Leys "Mathematical Imagery"

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

2

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

bhwang
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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

pi2000
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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

Jan Weidner
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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

2

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 )$\ldots$

Unknown
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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.

Alex M.
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David Cox's lectures in toric varieties at MSRI

Something really good to end the evening with :)

2

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

Gil Kalai
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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!

Stefan Kohl
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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.)

2

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.

Boris Bukh
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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.

1

https://www.youtube.com/watch?v=iSNsgj1OCLA

This video is far better than I expected. Show it to any discrete math course you teach. (With the possible exception of one of those courses that exist only to prepare students for a computer science course they take later.)

Michael Hardy
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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)

1

Some talks on history by some leading mathematicians (mostly in French):

http://www.archivesaudiovisuelles.fr/FR/_LibraryThemas.asp?thema=541

1

Searching for a video relating to another question, I found this: My Calculus Project

Gerald Edgar
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Documentary about infinite and its implications in mathematics (BBC)
http://www.youtube.com/watch?v=Cw-zNRNcF90

As usual, Gregory Chaitin on the history of logic
http://www.youtube.com/watch?v=HLPO-RTFU2o

Another one about logic and artificial intelligence
http://www.youtube.com/watch?v=nA3m9jgMp3U

zzzbbx
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All the talks of Atiyah 80+

1

http://www.youtube.com/user/njwildberger

Excellent lectures by Norman Wildberger on topics including: Geometry, Algebraic Topology, Linear Algebra, Foundations of Mathematics, and history of Mathematics

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    Watched a few Videos. But Wildberger is often trying to push his own views onto students, which he calls "Rational Trigonometry" (as in, Angles should be 0 to 1 instead of 0 to 2$\pi$. This makes the videos hard to watch, as they are not consistent with other books/lectures. – Michael Kissner Jul 20 '11 at 08:23
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The famous proof of the snake lemma in the 1980's movie It's my turn (can be found on utube).

euklid345
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'Selmer Ranks of Elliptic Curves in Families of Quadratic Twists' by Karl Rubin

http://research.microsoft.com/apps/video/default.aspx?id=140581

0

They filmed the FRG Conference on Topology and Field Theories and put the lectures on youtube.

0

So much maths video in http://nptel.ac.in/ National Programme on Technology Enhanced Learning

user48365
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I know of some youtube channels with good content. The last two link are not strictly pure math, but still worth a look.

Institut Henri Poincaré: https://www.youtube.com/channel/UCrKGv5WY5ryaIXEmnxKVxOQ

princetonmathematics https://www.youtube.com/channel/UCVKtRsfK1QPyHRP2QupyddQ

Institut des Hautes Études Scientifiques (IHÉS) https://www.youtube.com/channel/UC4R1IsRVKs_qlWKTm9pT82Q

StanfordCSTheory: https://www.youtube.com/channel/UCdZlxxfpEzQWwMvjVQ7gOJw

Simons Institute: https://www.youtube.com/channel/UCW1C2xOfXsIzPgjXyuhkw9g

rnegrinho
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Discrete Integrable Systems at Isaac Newton Institute for Mathematical Sciences

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I feel that I have something new to add. I sometimes make mathematical videos, and I should make more. Here is one about a 3D diagram that I made of the happy family, in group theory. There are a lot of other videos on my channel, however, not pertaining to mathematics such as singing and art, but I hope that in the future I will make more mathematical content.

https://www.youtube.com/watch?v=_4IjnIcECoQ&t=11s

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It's not a single video (and sadly there hasn't been any new content in a year!), but Richard Borcherds's channel has some of the best math content I've seen. If I have to pick one I'll go with this video from his Rings series about Burnside rings and differential operator rings as an illustration of his style; for me, at least, it's a source of excellent insight into fields (cough) I know very little about.

0

The University of New South Wales in Sydney has an eLearning channel on YouTube that contains lectures on a number of topics, including Algebraic Topology, Calculus, and Linear Algebra. Some computing and engineering topics are covered as well.

http://www.youtube.com/user/UNSWelearning#p/p

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I am surprised no one has mentioned that the Kavli Institute for Theoretical Physics, the Simons Center for Geometry and Physics, and the Perimeter Institute often tape conferences.

0

I am not sure if this will qualify as math exactly, but it's amazing nonetheless. It is a film with Richard Feynman called "Feynman: Take the wold from another point of view". Here is part 1

Feynman: Take the wold from another point ov view - Part 1/4

0

I make some maths videos at home,Here is an English video:Visible Fibre Bundle

maybe that can help some begginners.

All my maths vedios at my blog here,thirty courses of communtative algebra and I prepare to make much more in the future,but as you seen,most of them are Chinese(中文),because I can not say much English.

Strongart
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The amazing patterns that turn up in piece-wise isometries, like circles dancing in a rhomb:

http://vimeo.com/23772888

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The video that I am adding here is a new upload in Youtube. Here is the link: https://www.youtube.com/watch?v=aUl28Pjz89M

I have seen many videos on 21-card trick and also read many blogs on it. A very few of them has attempted to explain why this trick works. The ones give the proof, is pretty involved and requires some inclination towards the subject to understand this. But, this video has taken a totally different approach to explain the trick and why it works in a visual way. The approach is easy to understand for anyone. This is a great way of helping students get attracted towards Mathematics.