List of interesting math videos / documentaries 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
 A: A Russian documentary about Grigori Perelman and the Poincare conjecture. Now with English subtitles!
A: Bob Gardner's page is a treasure trove.:)
A: 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.

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...

$2)$ some youtube channel about math like

*

*Numberphile [my favorite sections are choosing toilets, elliptical pool, shapes and hooks, How they found the World's Biggest Prime Number, ...]

*Vihart [my favorites are Doodling in Math Class Connecting Dots, Hexaflexagons, Möbius Music Box, Wind and Mr.Ug,...]

*Mathologer [my favorites are Always WIN with math, Rubik's cubes, gyroscopes , ...]


*$3$Blue$1$Brown [my favorites are Euler's formula with introductory group theory  , Visualizing the Riemann zeta function ,...]

*Henry Segerman's videos [my favorites are Stereographic projection, Illuminating hyperbolic geometry ,... ]


A: 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

A: 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
A: 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.
A: Fractals - Hunting the Hidden Dimension by PBS: Nova.
A: 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 .
A: 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].)
A: 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...
A: For youngsters, there is Donald in Mathmagic Land.
A: 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 
A: 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
A: 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
A: 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
A: Möbius transformations revealed is pretty amazing.  Also, anything by Vi Hart.
A: 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.
A: 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.
A: 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.
A: A very nice video is the public lecture of Terence Tao on Structure and Randomness in the Prime Numbers.
A: 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.


*

*http://www.youtube.com/watch?v=plohsYdD9LY
Another documentary named Hard Problems was released by MAA which shows how US students performed in the IMO.
A: 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.
A: 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. 
A: Should this be a community wiki? I really liked Beautiful Young Minds about the British IMO team.
A: 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!
A: 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.
A: 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
A: I am surprised no-one seems to have mentioned the Numberphile youtube channel.
A: High Anxieties- The Mathematics of Chaos (2008)
Professor Avi Wigderson on the "P vs. NP" problem 
Professor Avi Wigderson on a computational theory of randomness
Professor Avi Wigderson on cryptography 
The Limits of Understanding 
epic conway's game of life
John Von Neumann
A: 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.
A: One interesting documentary that I haven't seen mentioned is "the code" by Prof Marcus du Sautoy (available on netflix-https://www.netflix.com/gb/title/80063658)
A: Meant for kids, I watched it as a kid, but I still love it as an adult:
Mathnet, here's an example:  https://www.youtube.com/watch?v=FngBiPt7yRU
It's like a math version of the police show Dragnet.  Lots basic math, deadpan humor, and bad puns.  It's a few decades old though, so don't expect any great filming.  Just a great show though.
A: Jos Leys's Mathematical Imagery is plainly amazing.

A: Socratica's youtube Abstract Algebra series is the best! Of the playlist, simple groups was my favorite.
I also like mathew salomone, mathdrbob and Michael Penn and everyone likes blackpenredpen.
