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This is an offshoot of the question on Fun math outreach/social activities. I have listed a few videos/documentaries I have seen. I would appreciate if people could add on to this list.

$1.$ Story of maths Part1 Part2 Part3 Part4

$2.$ Dangerous Knowledge Part1 Part2

$3.$ Fermat's Last Theorem

$4.$ The Importance of Mathematics

$5.$ To Infinity and Beyond

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    $\begingroup$ for [big-list] questions, please remember to flag for moderator attention to convert to a Wiki. $\endgroup$ Jan 25, 2011 at 12:36
  • $\begingroup$ @Willie Wong: Ok. $\endgroup$
    – user17762
    Jan 25, 2011 at 16:07
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    $\begingroup$ @Nick: You... limit your upvotes? This is a CW thread - so upvotes don't even give a reputation boost. We get 30 or 40 votes a day. I encourage you to use more of them. A while ago, SE sites actively tried to ward off this type of voting behavior, including math. But I would understand holding back on upvoting 'low level' content if you find that you hit the vote limit. Anyhow, I encourage you to read those meta posts. $\endgroup$
    – davidlowryduda
    May 23, 2012 at 8:41
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    $\begingroup$ @Nick: You're of course welcome to vote as you want to, but I'd like to also encourage you to vote more liberally. In general, if I feel that a question is the sort of thing I want to see on the site, I give it an upvote. And as mixedmath points out, this particular question has been marked "CW" (community wiki), which means the person who posted it isn't even getting any reputation points from it, so when you upvote you're only expressing your interest in the question. Like you I'm also liberal with my favorites - pretty much anything I think I might want to look at more closely later :) $\endgroup$ May 23, 2012 at 8:55
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    $\begingroup$ @ZevChonoles: It's not about reputation to me and the vote of questions isn't even so problematic. But if someone gives a new answer to an old question, which already contains another (not as good) answer with 15 votes, the new and better answer will stay low forever. So I don't think it's a good thing if answers have too many upvotes. If an answer has a two-digit number of votes, it's clear enought that it's worth reading. E.g. there are about ten posts in this thread. Even if someone posts the most important video of math history, it can't climb up if the other posts are voteworthy too. $\endgroup$
    – Nikolaj-K
    May 23, 2012 at 9:12

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Chaos: A Mathematical Adventure* (2010) and Dimensions** (2008) by Jos Leys, Étienne Ghys, Aurélien Alvarez, et al. are excellent, CC BY-NC-ND 3.0-licensed (i.e., free) movies about math.

Chaos introduces determinism vs. indeterminism, the butterfly effect, and Lorenz attractors. Dimensions does a very good job introducing stereographic projection, fourth dimensional geometry, complex numbers, fibrations, and proofs.

Both films are dubbed and subtitled in various languages.

*downloadable from Archive.org, HD720p torrent, or HD1080 torrent
**on YouTube

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Möbius transformations revealed is pretty amazing. Also, anything by Vi Hart.

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    $\begingroup$ I second your recommendation of Vi Hart! $\endgroup$ Jan 25, 2011 at 4:36
  • $\begingroup$ Vi Hart has now joined the Khan Academy so you can find them there as well. $\endgroup$
    – Brad
    May 2, 2012 at 14:41
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Documentary of Paul Erdos "N is a Number" is another good documentary. Also there is a documentary of Srinivasa Ramanujan called God, Zero and Infinity was released by TIFR in 2009.

Another documentary named Hard Problems was released by MAA which shows how US students performed in the IMO.

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When I was a kid we used to watch "Donald in Mathmagic land" starring Donald Duck. While in undergrad we all gathered to watch and it was still enjoyable.

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Here's a really excellent video, Finite Simple Group (of Order Two), that's definitely more towards the fun side than educational, although if you're not getting some of the jokes it may inspire you to look up a thing or two.

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Should this be a community wiki? I really liked Beautiful Young Minds about the British IMO team.

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A Russian documentary about Grigori Perelman and the Poincare conjecture. Now with English subtitles!

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Bob Gardner's page is a treasure trove.:)

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There were some great answers to this post, however, I preferred to share my answer too.

Dimensions videos are really nice but they can be boring at the same time due to their slow rhythm.

enter image description here

In addition The Story of 1 $($BBC documentary narrated by Terry Jones$)$, Paul Erdos - N is a number are very interesting. You can find some awesome videos about fractals.

Also, there are some movies about math which can be helpful such as "a beautiful mind", "the man who knew infinity", "Fermat's room", ...

But what I highly recommend:

$1)$ some movies like flatland, futurama, and some stand-up comedies by Matt Parker, etc...

enter image description here

$2)$ some youtube channel about math like

STP

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Here is a (not well-known, it seems) video containing a lecture and interview with Richard Courant, former student of David Hilbert:

Göttingen and New York : reflections on a life in mathematics

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Nova's Mathematical Mystery Tour is still on youtube (let's hope it stays there): (link to first part): http://www.youtube.com/watch?v=vPSx2CkKE3c

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I enjoyed Between the Folds, which gives a rather high-level view of the mathematics behind origami and how they provide means for constructing incredibly complex shapes.

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Fractals - Hunting the Hidden Dimension by PBS: Nova.

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you all may want to see BBC: Code Breakers Bletchley Parks lost Heroes http://www.youtube.com/watch?v=JF48sl15OCg

Documentary about the story behind the German cryptography systems used in World War II that gave birth to the digital age i am not talking about Enigma but an even tougher system, which Hitler called his 'secrets writer'.

Its story of and Bill Tutt and Tommy flowers whom i believe to be the inventors of worlds first computer.as the transcript goes "This Is the story of a secret war , and how two men changed the world and then disappeared from history"

If you are interested in cryptography this documentary clearly explains how ciphers works, XOR ciphers in particular .

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A few years back the NHK made a documentary called "The Spell of Poincare Conjecture". (You can find a possibly non permanent link here to part 1 of 4 [with also links to the rest of the video].)

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    $\begingroup$ A shame I can't understand a word... There's no way around it then: I'll have to learn japanese and come back! $\endgroup$
    – Sam
    Jan 25, 2011 at 15:33
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    $\begingroup$ @S.L. Oh, I linked to the Japanese version? Darn. There is an English version, which I think was shown on PBS in the States. You may be able to find it if you Google the title of the documentary. $\endgroup$ Jan 25, 2011 at 17:02
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While it's been a while since I've seen it, the old Geometry Center videos - especially Not Knot - are personal favorites. The Geometry Center's video page is at http://www.geom.uiuc.edu/video/ - as for Not Knot itself, I'm sure it should be findable easily enough...

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For youngsters, there is Donald in Mathmagic Land.

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On Srinivasa ramanujan the genius mathematician from India. I believe a hollywood movie based on his life is being made, with Madhavan playing the role of Ramanujan.

Ramanujan:Letters from an Indian Clerk http://www.youtube.com/watch?v=OARGZ1xXCxs

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I found this talk about the life and work of Évariste Galois Superb: here is a link

The Memoirs and legacy of Évariste Galois-Dr Peter Neumann

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Flatland: Have you ever imagined if all of us live in a 1-dimension world? And after a long live in this one, the surprise to see the 3-dimension world in the first time?

Sphereland: the same as the flatland movie, but now, you live in a sphere

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May not be fundamental maths videos, but I like the teaching style of Shai Simonson and his lectures in Discrete Mathematics and Theory of Computation are entertaining as well as enlightening.

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These are some introductory videos from an 'old' (mid-80's) series co-produced by Caltech called Mechanical Universe. One on derivation and another one on integration. Features some nice Newton-Leibniz cosplay if nothing else. If you're into that sort of thing.

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  • $\begingroup$ These videos no longer exist $\endgroup$
    – LCarvalho
    Jun 10, 2017 at 0:18
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A very nice TED talk by Robert Lang about the mathematics of origami: http://www.ted.com/talks/robert_lang_folds_way_new_origami.html. It goes very well with this Wikipedia article: http://en.wikipedia.org/wiki/Mathematics_of_paper_folding. The talk itself isn't heavy mathematics, but the mathematics behind the talk is very interesting.

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A very nice video is the public lecture of Terence Tao on Structure and Randomness in the Prime Numbers.

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Seems like Richard Borcherds is making good use of the extra time we're all spending inside.

Just recently he started a youtube channel. So far he has given at home lectures on group theory, algebraic geometry, commutative algebra, and representation theory, as well as some interesting talks on assorted topics like monstrous moonshine, among other things.

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I found a lecture "A tribute to Euler" from CMI, about the biography and a some mathematical results of Euler. Here is the link! "The music of the prime" by Marcus is also very good mathematical material. Watch here!

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I just found this amazing website Mathtube.org. Here is excerpt from the site's About page:

"What is mathtube.org? mathtube.org is a new multimedia resource hosted by the Pacific Institute for the Mathematical Sciences. mathtube.org gives users easy access to mathematical seminar and lecture materials including videos notes and slides. mathube.org allows users to view slides and video simultaneously, making it convenient to follow a lecture at your own pace and review anything you have missed."

Mathtube.org has dozens of lectures, for example there is a lecture by Ben Green titled On the Sylvester-Gallai Theorem.

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MyWhyU's 3 part cartoon series on Topology videos were a pretty neat and fun intro:

Topology Part 1

Topology Part 2

Topology Part 3

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I am surprised no-one seems to have mentioned the Numberphile youtube channel.

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