Mathematics has the power to describe, predict and create patterns, a power that is very well demonstrated in the pattern-rich world of juggling. In this paper we examine a simple method of describing juggling patterns using mathematical notation, and then use this notation to predict new juggling patterns. We conclude with a demonstration of how mathematics has been used to create beautiful patterns that did not exist before these mathematical methods had been used, and how mathematical names are now used by jugglers worldwide — a powerful demonstration of mathematics advising the arts.