Juggling has advanced enormously in recent decades, since mathematicians began systematically investigating the possible patterns of non-colliding throws. As part of this research, many new possibilities have been discovered for jugglers to attempt. In addition, the connections between juggling and the algebra of braids provide another view of juggling.
For much more about juggling, including a proof of the Average Theorem mentioned in the video, see Burkard Polster, The Mathematics of Juggling (Springer, 2003).
More videos from the Mathematical Impressions series.