I love learning about history, as evidenced by my work annotating James Burke's documentaries. My favorite of James Burke's show would have to be Infinitely Reasonable, as it actually discussed the history development of science and mathematical thought.
I always thought a longer discussion of the history of math would be interesting. It seems that the BBC and Oxford Mathematics Professor Marcus du Sautoy agree, as they produced and aired a 4-part documentary back in 2008, called The Story of Maths.
In this post, you can watch all 4 complete episodes, as long as they're available on YouTube. If you have any trouble viewing the videos below, you can still probably find the episodes on YouTube, or via a Google video search.
The first episode, The Language of the Universe, begins with the importance of math in our modern life, before going on to explore the origin and development of math in the ancient western countries of Egypt, Mesopotamia, and then Greece.
After the fall of Greece, scientific and mathematical development came to an unfortunate halt. However, in the eastern countries, math continued to expand and develop. In The Genius of the East, we learn about the influence of China, India, and the Middle East. It also discusses the effect of these developments on western countries as the Renaissance began.
With a renewed European interest in mathematics, we see great gains over the next few centuries in modeling and analysis from Minds like Descartes, Leibniz, Newton, Euler, and many others. In the third episode, we see how the work of men long ago helped take us to The Frontiers of Space.
What could possibly be left? Not only does mathematics itself continue to develop, but there are still numerous problems from the past that still haven't been solved. The effect these have on the current state of math, and their future potential, is the subject of the final episode, To Infinity and Beyond.