Phyllotaxis, the arrangement of phylla (leaves, bracts, seeds) near the shoot apical meristems of plants has intrigued and mystified natural scientists for over two thousand years. It is surprising that only within the last two decades have quantitative explanations emerged that describe the wonderful architectures which are observed. I will give an overview of two types of explanation, teleological and mechanistic, one based on rules which posit that each new phyllo be placed according to some optimal packing principle and the other which uses plain old biophysics and biochemistry to build mechanistic models which lead to pattern forming pde's. One of the stunning new results is that, while the latter is richer, both approaches lead to completely consistent results. This may well have broader ramifications in that it suggests that nature may use instability driven patterns to achieve optimal outcomes.

The talk should be accessible to students and colleagues in other disciplines.