People have been juggling for over 4000 years and creating new mathematics for much longer. Yet, it was not until the mid 1980's that people realized how much insight mathematics could lend to the process of discovering new patterns. In addition to describing this mathematical aspect of juggling, there will be demonstrations with up to 7 balls.

I will discuss my work in creating a computer system that plays the role of a sensitive and responsive musical accompanist in a piece of music for soloist and accompaniment. One important task is to create an algorithm that can track the soloist's progress through the musical score. To do this, the computer must somehow "hear" the soloist. My talk will relate sound, hearing and mathematics with several examples. I will also give a live demonstration of my accompaniment system. More detail on this work can be found at http://fafner.math.umass.edu/music_plus_one