Interesting mathematical documentaries I am looking for mathematical documentaries, both technical and non-technical. They should be "interesting" in that they present either actual mathematics, mathematicians or history of mathematics. I am in charge of nourishing our departmental math library (PUCV) and I would like to add this kind of material in order to attract undergraduates toward mathematics. For this reason, I am not looking for videos of conferences or seminar talks, but rather for introductory or "wide public" material.
Here are some good examples. 


*

*"Dimensions", by Leys, Ghys & Alvarez, http://www.dimensions-math.org/ which explains actual maths and is excellent.

*"Julia Robinson and Hilbert's tenth problem", https://www.vismath.eu/en/films/julia-robinson, about the life of some great mathematicians.

*BBC documentary on "Fermat's last theorem" (by the way, any information about how to purchase it would be welcome, it does not seem to be possible to do it from the BBC site http://www.bbc.co.uk/iplayer/episode/b0074rxx/horizon-19951996-fermats-last-theorem. Maybe http://vimeo.com/18216532 ?). 
Are there more examples? Thanks, Ricardo.
 A: Science Lives, made by the Simons Foundation, has nine very long interviews that essentially amount to miniature documentaries about the lives of a number of 20th/21st century mathematicians and physicists.
A: PBS documentary A Brilliant Madness that looks at the life of Nobel-prize winning mathematician, John Nash
http://www.youtube.com/watch?v=chXIfhJ36Iw
A: The man who saved Geometry is a documentary on D. Coxeter:
https://vimeo.com/120725835
A: "Achever l'inachevable" or "Achieving the Unachievable" features many mathematicians discussing M.C. Escher's Print Gallery, most of the material coming from the Notices article here.
A: The secret life of chaos. A BBC documentary.
A: The only documentary about Grigori Perelman has recently got English subtitles. (Perelman is the guy who proved the Poincare conjecture and then refused a million dollar prize.) It is for laymen, and very dramatic.
https://www.youtube.com/watch?v=Ng1W2KUHI2s
A: $N$ Is a Number: A Portrait of Paul Erdős. (Official site; Wikipedia link)

          
A: Try  Satyan Devadoss's "The shape of nature." 
A: My friend watched this in University of Waterloo: BBC: Code Breakers Bletchley Parks lost Heroes
This is not about the Enigma Machine, which is probably the more well known example in code breaking. Instead, this is about the Lorenz cipher.
This is a relatively new movie (october 2011) that talked about how a maths student and an engineer combined to hack into Hitler's personal super-code machine, named the secret writer, and helped win WWII. Also of historical significance, the movie described the decryption machine as the first programmable computer.
A: There is a new movie that just came out called Comment j'ai détesté les Maths (How I hated math). Cédric Villani, Jim Simons, and others are featured in the film.
A: A new documentary about Ramanujan just screened at the AMS meeting earlier this evening. It's called, The Genius of Srinivasa Ramanujan. It was claimed that it's already up on YouTube.
EDIT: All I was able to find on the web was a very short preview.
MORE EDIT: The full documentary went up here a few years later.
A: A very nice interview of László Lovász can be found here: https://www.simonsfoundation.org/science_lives_video/laszlo-lovasz/
A very wide variety of topics are covered (see the 'playlist' at the right hand side)!
A: The LMS commissioned a film "Thinking Space".

Through explorations of their various thought processes, the film portrays mathematicians who are grappling with advanced mathematical ideas. We are presented with the concepts of imagination, intuition, and wonder, as well as rigorous mathematical deduction.
The film features Kevin Buzzard, Peter Donnelly, Tim Gowers, Martin Hairer, Roger Penrose, Caroline Series, Richard Thomas, Reidun Twarock, and Karen Vogtmann.

There are some excerpts on the LMS website: Frames of mind.  However, you can also find the whole film on vimeo: Thinking Space by Heidi Morstang  (posted by the director of the film).
A: Recently a documentary on Maryam Mirzakhani was released called Secrets of the Surface: The Mathematical Vision of Maryam Mirzakhani. It both described her personal life/journey through mathematics, as well as an introduction to part of her research aimed at a general audience.
A: Nova's Mathematical Mystery Tour is a really nice one and is on youtube.
httpS://www.youtube.com/watch?v=MbOyXO-JFX8&feature=related
RAMANUJAN: Letters from an Indian Clerk again available on youtube.
httpS://www.youtube.com/watch?v=OARGZ1xXCxs
This question was also asked on math stackexchange sometime back and here is the link to it.
A: The Geometry Center (formerly of UMN, now apparently defunct) many years ago produced "Not Knot" (about hyperbolic space) and "Outside In" (about sphere eversion).  There is apparently a more recent third one "The Shape of Space" I'm not familiar with.  Apparently you can still order them here, although copies are now easily found on YouTube.
A: https://www.math.ru/lib/files/pdf/mehmat/mm3.pdf
Interviews and memories by leading Moscow mathematicians I.R. Shafarevich,
V.I. Arnold, S.P. Novikov, B.A. Sevostyanov, A.N. Shiryaev,
V.V. Golubev (major-general and dean of mexmat MSU at (1933-1935 и 1944-1952)).
Some of them are quite free-spoken.
PS
Sorry it is in Russian.
A: THE THINGS YOU DON'T UNDERSTAND, 2010, Peter and Petra Lataster
Mathematician Hendrik Lenstra has no car, no computer and no television. But he is the proud owner of numerous editions of Homer’s Odyssey. Directors Petra & Peter Lataster draw a portrait of Lenstra, a mathematician who thinks on the highest level. And also in daily life he is not interested in the superfluous and the fashionable. http://www.latasterfilms.nl/en/films/the-things-you-dont-understand/
A: This documentary on John Von Neumann produced by the MAA in 1966 is pretty good. Has interviews with Paul Halmos, Stanislaw Ulam, Eugene Wigner, among others.
https://www.youtube.com/watch?v=VTS9O0CoVng
A: Henri Cartan, une vie de mathématicien.
A: Au Bonheur des Maths  (it's in French but you can put English subtitles)     
Several short interviews of mathematicians around the IHES:
Alain Connes, Misha Gromov, Jean-Pierre Bourguignon, Cédric Villani, Sir Michael Atiyah, Giancarlo Servetto, Carolina Canales Gonzalez, Nicole El Karoui, Don Zagier.

A: 

"With striking images, some mathematical humor, a little drama, and a nice puzzle, this is again a very charming movie from director Ekaterina Eremenko."
  - John Rognes, Chairman of the Abel Committee

Trailer is here
A: Something new every day is a great short documentary about Ron Graham by George Csicsery.
A: In February of this year (2016), the Alfred P. Sloan Foundation
sponsored a workshop at the Fields Institute about the development of a new 'language' to represent mathematics in computerized/formalized form.
The participants were 40 mathematicians, logicians,
experts in computational mathematics and formalized mathematics. 
Because bringing the approximate 100 million pages
of peer-reviewed research mathematics into a modern,
computer-understandable form will be a long term
global effort (https://arxiv.org/abs/1404.1905),  the Alfred P. Sloan Foundation also sponsored the making  of a documentary-style video about the workshop; including 
participant interviews (e.g. with Ingrid Daubechies, Yuri Matiyasevich, 
Harvey Friedman, Stanislav Smirnov, Jeremy Avigad, Georges Gonthier) to foster a more global discussion on the subjects involved in 
developing such a new 'language'.
Topics such as: what is mathematics, why we need proofs, how to get more people involved in formal mathematics, what is the mechanized future of mathematics and others are discussed.
I was one of the workshop organizers, and we just finished editing a 90 min video 
("Towards a Semantic Language of Mathematics") and it is
now on Youtube:
https://www.youtube.com/watch?v=psSyM1zp82k
A: http://www.cosmolearning.com/mathematics/documentaries/
A: The youtube channel of Simons Foundation can be considered as a series of one-shot "documentaries" about puzzles and (auto)biographies of mathematicians:
https://www.youtube.com/channel/UCZVjCmJOQRpAQ_EruAIPqXg
There is also a (rare?) documentary on the life of Grothendieck in french, I saw a trailer here:
https://youtu.be/UO5KgnTY_fU
Unfortunately I haven't seen the movie but apparently they are working on an english translation of the movie as well.
A: I enjoyed watching "Great thinkers, great theorems" by William Dunham.
It is a great overview of the history, and still manages to get down to actually proving a lot of non-trivial stuff.
A: I really like this short documentary on Fermats Last Theorem and Andrew Wiles struggle and setbacks proving it.
A: La lettre scellée du soldat Doblin about Wolfgang Döblin / Vincent Doblin.
Here the synopsis from IMDB: "When France surrendered in 1940 and German soldiers showed up in the Vosgian village of Housseras, an unknown French foot soldier burned his papers and killed himself in a farmer's barn. Four years later he was identified as "soldat Doblin, Vincent". In fact, he was none other than the mathematician Wolfgang Doeblin, son of the famous German novelist Alfred Döblin ("Berlin Alexanderplatz") who was forced to flee Nazi Germany with his family in 1933. A French citizen since October 1936, Wolfgang Doeblin carried on his research into probability theory during his military service and even during the hardships of the "Phoney War" in the winter of 1939-40. In February 1940, four months before his death at the age of 25, he sent his most important manuscripts ("About the Kolmogoroff Equation") as a "sealed envelope" to the Academy of Science in Paris, where they were kept in safe custody for 60 years. Wolfgang Doeblin's short and dramatic life story, almost forgotten, was finally brought into the limelight when the "sealed envelope" was opened in May 2000. Far ahead of their time, his groundbreaking contributions to the theory of random processes place Wolfgang Doeblin among the major innovators of probability, the "mathematics of randomness". Mathematical models for evaluation of chances and risks went on to gain major importance in numerous domains of modern science, in everyday life and especially in contemporary financial mathematics."
A: "The Color of Math" (Wayback Machine) is a rather poetic documentary by Katia Eremenko that will have its premiere at the Moscow Film Festival (Wayback Machine) this upcoming Saturday, June 23, 2012. It features Cedric Villani, Anatoly Fomenko, Maxim Kontsevic, Jean-Michel Bismut, Aaditya V. Rangan (and myself).

(source: moscowfilmfestival.ru)
A: Something completely different, but I'm sure a lot of people here at MO would enjoy:
Beautiful young minds British documentary about International Mathematical Olympiad 2006 with focus on the UK team.
Hard problems American documentary about the same event with focus on the US team.
Documentaries contain analysis of that year's problems (although the focus is on the competition in general, team selection and contestants - which makes it more interesting to ex-contestants than to professional mathematicians or math enthusiasts).
A: Leys, Ghys & Alvarez have also made a video series in a similar style about dynamical systems called "Chaos". The nine chapters are all available under a Creative Commons license.
A: The Joy of Stats by Hans Rosling.
A: Marcus du Sautoy has a number of BBC math specials and short series dealing with concepts of zero, infinity, measurement. Some are done under the Horizon umbrella.
A: "Between The Folds" is another beautiful documentary about Math.
http://www.youtube.com/watch?v=tE4lqYzS2m0
A: Eugene B. Dynkin Collection of Mathematics Interviews
A: "Counting From Infinity" is a recent (nontechnical) documentary about Yitang Zhang's work on bounded gaps between primes:
http://www.zalafilms.com/films/countingindex.html
Some description of the documentary is also included in the New Yorker profile about Zhang:
https://www.newyorker.com/magazine/2015/02/02/pursuit-beauty
A: Apparently nobody mentioned Serre's "How to write mathematics badly".
A: The soundtrack is still in progress, so it's not yet fully available but Ester Dalvit made a very interesting movie about braids and knots. At the end it will be distributed under a Creative commons license.
A trailer and parts of the movie are available here. Up to now three (old versions of) chapters are available, explaining respectively through computer generated animations:


*

*the group structure of the braid group

*"combing" of braids and handle reduction (i.e. solutions to the world problem)

*Alexander and Markov theorems (i.e. the relation with knots).

A: Marcus du Sautoy's The Story of Maths is a total of four hours attempting to give an overview of the history of mathematics from ancient to modern time, spending 5-10 minutes each on the life and work of some of the most famous mathematicians.  While one could quibble with some of the selections, the project is overall a fantastic production.
A: "Taking the long view: The life of Shiing-Shen Chern"
http://takingthelongviewfilm.com/
This very nice documentary was produced recently on the occasion of the Chern Centennial Conference.
A: Alan Turing: Codebreaker and AI Pioneer (available here).

The code-breaking work at Bletchley Park, which helped save Britain from Nazi Germany, qualifies as one of the greatest stories of World War II, and the misunderstood genius, Alan Turing, stands at the center of this tale. Perhaps no one understands Turing's role during this period -- and his larger impact on mathematics and computing -- like B. Jack Copeland. In this lecture, Copeland contends that Turing should be celebrated as the father of artificial intelligence.

A: A short 2011 documentary on the life and mathematics of Évariste Galois, produced by the CNRS and available at the website CNRS Images:
Évariste Galois - Je n'ai pas le temps
A: "The Proof", from NOVA, presents Andrew Wiles and the story of Fermat's Last Theorem.
http://video.google.com/videoplay?docid=8269328330690408516
A: Dangerous Knowledge: https://topdocumentaryfilms.com/dangerous-knowledge/
Though this one is more about mathematicians, than mathematics.

In this one-off documentary, David
Malone looks at four brilliant
mathematicians – Georg Cantor, Ludwig
Boltzmann, Kurt Gödel and Alan Turing
– whose genius has profoundly affected
us, but which tragically drove them
insane and eventually led to them all
committing suicide.

A: I vote for 100年の難問はなぜ解けたのか
～天才数学者　失踪の謎 ("Why the difficult 100-year-old conjecture was proven- The mysterious disappearance of the genius mathematician"), about Grigory Perelman, Geometrization, and the proof of the Poincaré Conjecture, as the best mathematical documentary ever. It's non-technical, but it's really very well-made, and gives a good sense of what research mathematics is like, and why some people spend their lives searching for proofs of mathematical conjectures. The mathematics in it is mostly fairly solid. It inspired fashion design house Issey Miyake to design a fashion collection with Bill Thurston inspired by geometrization. 
A: Here is a short film on Paul Halmos.


*

*The 44-minute film contains a rare interview with Paul Halmos by Peter Renz, revealing his thoughts on mathematics, and how to teach it and write about it. Five bonus features include comments by mathematicians Robert Bekes, David Eisenbud, Jean Pedersen, and Donald Sarason about their experiences with Halmos. Interviews with Halmos by Don Albers and Halmos's own writings are included as PDF documents


A: Well, you may want to check out some short documentaries about beautiful minds. For example, my mathematical idol Kurt Gödel, here is the clip https://www.youtube.com/watch?v=i2KP1vWkQ6Y
There can be many more examples, just to give the students a taste of what it is like to be a mathematician.
A: There is a document "Banach spaces" about S.Banach and other polish mathematicians from Lviv ( S.Ulam, J.P.Schauder)
Unfortunetelly I don't know about any translation to english.
http://www.youtube.com/watch?v=EJgl_Z9Yz1Q
A: The best I have ever seen is "The Proof".  It is a Nova documentary on Sir Andrew Wiles and his proof of Fermat's last theorem.  I can always find something interesting to talk about with my students who range from algebra one level to calculus.
A: You can find a selection of open source maths films on the IMAGINARY platform:
http://www.imaginary.org/films
Many of the already mentioned films are there (like Dimensions, Chaos, Braids, etc.), but also some really good new ones, like "The Future of Glaciers", etc.
The platform is also open for contributions from outside, so you can come back and find a growing repository of free licensed maths films.
A: Although not a video series, the podcast series Relatively Prime by Samuel Hansen is a superbly produced series of 8 podcasts including interviews with eminent mathematicians and covering a wide range of topics. Perfect listening material for long commutes I've found.
A: Genius and villains: Kolmogorov (Russian)
A: PBS NOVA from April 15 2015 The Great Math Mystery
A: I can highly recommend MESH - A Journey Through Discrete Geometry by Beau Janzen and Konrad Polthier. Old and new are nicely linked together and the computer animations are great. The film won many prizes.
Then there is a feature about Yuri Manin by Agnes Handwerk and Harrie Willems called Late Style.
A: Two good ones that were recently uploaded to youtube:
Paul Halmos (teaching): https://www.youtube.com/watch?v=6KWaBikjnYw
Yitang Zhang (bounded gaps between primes): https://www.youtube.com/watch?v=XIIyKWxGhEA
A: Pits, Peaks, and Passes: A Lecture on Critical Point Theory about Marston Morse.
A: I recently knew of the film "Barry Mazur and the Infinite Cheese of Knowledge".
According to what we read in the website that was set up for the promotion of the film: "[this is] a compelling and intimate portrait of one of the world's most influential mathematicians, Barry Mazur... The film tells his surprising story and [captures] both his wit and profound approach to life, love and learning. From his early life as an ultra orthodox Jew in the Bronx during World War II, to his present status as one of the world's most admired and influential mathematical thinkers, this film tells the story of a man navigating the worlds of religion and science, fact and philosophy, love and loss. Surprising, witty, and often moving, this portrait of a polymath invites you to rejoice in curiosity in all its forms because ... we are all nibbling on the Infinite Cheese of Knowledge."

*

*Additional information about the film:

Duration: 35 min
Filmed and directed by: Oliver Ralfe
Producers: Michael Harris, Kobi Kremnitzer
Associate producers: James Bluemel, Minhyong Kim
A: NOVA's Hunting the Hidden Dimension
Mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature.   
Program Description
You may not know it, but fractals, like the air you breathe, are all around you. Their irregular, repeating shapes are found in cloud formations and tree limbs, in stalks of broccoli and craggy mountain ranges, even in the rhythm of the human heart. In this film, NOVA takes viewers on a fascinating quest with a group of maverick mathematicians determined to decipher the rules that govern fractal geometry.
For centuries, fractal-like irregular shapes were considered beyond the boundaries of mathematical understanding. Now, mathematicians have finally begun mapping this uncharted territory. Their remarkable findings are deepening our understanding of nature and stimulating a new wave of scientific, medical, and artistic innovation stretching from the ecology of the rain forest to fashion design. The documentary highlights a host of filmmakers, fashion designers, physicians, and researchers who are using fractal geometry to innovate and inspire.
Aired August 24, 2011 on PBS
See the following site for program information and to order the DVD: http://www.pbs.org/wgbh/nova/physics/hunting-hidden-dimension.html
A: Leon Henkin, an expert on mathematical logic and induction, made a movie on Mathematical Induction
A: There's Mathematics Illuminated, see https://www.learner.org/series/mathematics-illuminated/ These were intended as professional development for teachers.
A: The mathematics of love, by Hanna Fry
https://www.ted.com/talks/hannah_fry_the_mathematics_of_love/transcript#t-21495 
