Mathematics - Good films about maths are rare... yet director George Csicsery (pronounced "Chi-cherry") has produced 13 elegant films about mathematicians & mathematics.  (List below.)  In his own words "Working with mathematicians is a great source of pleasure. It is the only group I know, where the answer 'I don't know' is met with excitement and motivation rather than with irritation. I hope that some of this excitement and passion filters through the film to audiences." [a]
    
Just watching the trailers is rewarding.  If you've never met a mathematician, these should give you a personal look into the very diverse worlds of some great modern mathematicians and to see the humanity behind the thinking.  If you're a mathematician or love mathematics, these are inspiring.

And now, the list of 13 films, courtesy of Csicery's studio Zala Films:

[1]  Counting from Infinity: Yitang Zhang & the Twin Prime Conjecture (2015)
    The central challenge of the film was finding a way to depict Yitang Zhang's dedication to working in isolation. The qualities he embraces-solitude, quiet, concentration-are the opposites of those valued in the media. Fortunately, it is a conundrum Csicsery had faced before in other films about mathematicians. He had learned that contrary to the rules, it is okay to shoot long scenes of "the grass growing," or in this case, shots of "a person just sitting with pencil and paper and thinking. The longer the scene, the more you realize that you really can see someone thinking. The human face is very expressive. Give it time and it speaks volumes."  - George Csicsery
    About: http://www.zalafilms.com/films/countingabout.html
    Trailer: http://www.zalafilms.com/films/countingtrailer.html

    
[2]  Porridge Pulleys & Pi: Two Mathematical Journeys (Hendrik Lenstra, Number Theory, Elliptic Curves & Cryptography) & (Vaughan Jones: Quantum Mechanics, Knot Theory, and DNA Protein Folding) (2004)
    Trailer: http://www.imdb.com/video/wab/vi1773798425/     About: http://www.zalafilms.com/films/pppdirector.html
    "There are several stereotypes and beliefs about mathematicians that Porridge pulleys and Pi aims to dispel. First, I wanted to show that there is no single type of person who can become a mathematician. ... given the right training, any child with the aptitude can turn into a mathematician. ... Jones and Lenstra are the opposites of the eccentric nerdy type who has come to characterize the popular conception of what mathematicians are like. Another cliche I hope to debunk is that of the tortured genius. This film contains clear evidence that mathematicians derive a great deal of pleasure from their work." - George Csiscery
    http://www.zalafilms.com/films/pppdirector.html
    

[3]  Taking the Long View: The Life of Shiing-shen Chern (one of the fathers of modern differential geometry) (2011)
    View Short: http://zalafilms.com/takingthelongviewfilm/viewfilm.html
    Synopsis: http://zalafilms.com/takingthelongviewfilm/synopsis.html
    There’s a quotation from Lao Tzu, an ancient Chinese philosopher, that could have been written about Chern. ‘The master does his job and then stops. He understands that the universe is forever out of control, and that trying to dominate events goes against the current of the Tao. Because he believes in himself, he doesn’t try to convince others. Because he is content with himself, he doesn’t need other’s approval. Because he accepts himself, the whole world accepts him.’ - Alan Weinstein, UC Berkeley
    
    The true importance of Shiing-shen Chern’s role in the development of mathematics ... His influence with Chinese government leaders helped bring Western mathematicians to China and send Chinese students to study abroad. Today’s leaders in Chinese mathematics were all beneficiaries of Chern’s vision. His greatest contribution to the restoration of Chinese mathematics, however, is the establishment of the Nankai Institute of Mathematics, today known as the Chern Institute of Mathematics. The Chern Institute provided a base for these international interactions which often led to collaborations, reciprocal visits, and joint papers.
    About: http://www.takingthelongviewfilm.com/


    He said, ‘my policy to operate this institute is very simple. Three words in Chinese. First, no meetings. Second, no plan. Third, do more.’ That means, just do your research work.
    Molin Ge, Theoretical Physicist, Chern Institute of Mathematics


[4] Invitation to Discover: An Introduction to the MSRI (Mathematical Sciences Research Institute) (2002)
    Watch: http://www.msri.org/web/msri/online-videos/special-productions-events/invitation-to-discover     
    
[5] I Want to Be a Mathematician: A Conversation with Paul Halmos (2009)
    Trailer: http://www.zalafilms.com/films/halmostrailer.mov
    About: http://www.zalafilms.com/films/halmossynopsis.html
    "When an engineer knocks at your door with a mathematical question, you should not try to get rid of him or her as quickly as possible. You are likely to make a mistake I myself made for many years: to believe that the engineer wants you to solve his or her problem. This is a kind of over simplification for which mathematicians are notorious. Believe me, the engineer does not want you to solve his or her problem. Once I did so by mistake (actually I had read the solution in the library two hours previously, quite by accident) and he got quite furious, as if I were taking away his livelihood. What an engineer wants is to be treated with respect and consideration, like the human being he is, and most of all to be listened to with rapt attention. If you do this, he will be likely to hit upon a clever idea as he explains the problem to you, and you will get some of the credit. Listening to engineers and other scientists is our duty. You may learn some interesting mathematics while doing so." - Gian-Carlo Rota, Indiscreet Thoughts 1979


[6]  Julia Robinson and Hilbert's 10th Problem (2008)
    Trailer: http://www.zalafilms.com/films/julia.html
    About: http://www.zalafilms.com/films/jrbackground.html

    
[7]  Navajo Math Circles (in production)
    "Open-ended questions are totally new to most of the kids. Usually you have to have an answer within 20 seconds, 30 seconds, that’s what math is. Math circles are the opposite. We start with some simple questions, and we ask more questions and more questions. We get some answers along the way. The answers actually don’t matter. The more and more questions… we’re opening whole research problems, and that is something totally new to the kids. And once they like it, it’s just amazing, it’s transformative." - Matthias Kawski, Arizona State University
    Trailer: http://www.zalafilms.com/navajo/trailer.html
    About: http://www.zalafilms.com/navajo/about.html

    
[8]  Hard Problems: The Road to World's Toughest Math Contest, covering the story of the 2006 US IMO team (2008)
    *Trailer: http://www.hardproblemsmovie.com/trailer.html
    About: http://www.hardproblemsmovie.com/synopsis.html


[9]  N is a Number: A Portrait of Paul Erdos (1993)
    Trailer: https://www.simonsfoundation.org/multimedia/n-is-a-number-a-portrait-of-paul-erdos/     About: http://www.zalafilms.com/films/nisfilm.html
    Full: https://www.youtube.com/watch?v=wN4yLPPvRBgs


[10]  Erdos 100 (2013)
    Trailer: http://www.zalafilms.com/films/erdostrailer.html    
    About: http://www.zalafilms.com/films/erdos.html


[11]  To Prove and Conjecture: Excerpts from Three Lectures by Paul Erdos (1993)
    About: http://www.zalafilms.com/films/prove.html

        
[12]  The Right Spin: How to fly a broken space craft (Mir), the Story of a Dramatic Rescue in Space and the Mathematics Behind It (2005)
    About: http://plus.maths.org/content/right-spin-how-fly-broken-space-craft            http://archive.msri.org/specials/rightspin     Alternate documentary: https://www.youtube.com/watch?v=tM7fTLLmgbk


[13]  On Mathematical Grounds: A Refresh of an Introduction to the Mathematical Sciences Research Institute (MSRI) (2009)
    About: http://www.zalafilms.com/films/omg.html
    YouTube: https://www.youtube.com/watch?v=MO-JRzTiSNo     
    
References:
[a] George Csicsery, Producer & Director, Zala Films, in his own words:   http://zalafilms.com/takingthelongviewfilm/directors_statement.html

[b] The Films: http://www.zalafilms.com/films/index.html

[c] The story of George Csicsery: Math Films, Yes - But So Much More:  http://cinesourcemagazine.com/index.php?/site/comments/csicsery_math_films_yes_but_so_much_more/

[d] Science Lives, Simon Foundation & Zala Films, videos of interviews with living mathematicians  https://www.simonsfoundation.org/category/multimedia/science-lives/alphabetical-listing/