The Beauty of Math
"Le savant n'étudie pas la nature parce que cela est utile; il l'étudie parce qu'il y prend plaisir et il y prend plaisir parce qu'elle est belle." (Henri Poincare)
Henri Poincare was just one among the leading mathematicians that pointed out the role of aesthetics in study of mathematics. Aesthetics is often cited as the driving subconscious force for mathematical creativity. The aesthetic aspects also play a central role in mathematical teaching, as one of the most important goals is to lead students to appreciate the power and beauty of mathematical thought. While we acknowledge the existence of beauty in mathematics, the notion of mathematical beauty raises some very interesting questions. When do we decide to say a certain math concept is beautiful? Is beauty subjective, or objective (or neither? or both?) Is beauty of math something that can be taught, or does it just come to be experienced over time? What is it, exactly, that makes the proof more attractive? In this talk, we will explore the aesthetic nature of mathematics and try to answer some of these questions.
Shape Modeling with Industry and Undergraduates
Have you ever wondered why you can't buy a robot to do your dishes? The main reason is that automated object recognition is incredibly challenging - the robot might wash your cat instead of your plates. This talk explores shape modeling, which is one formulation of the object recognition problem. We focus on a particular category of shape models, skeletal models, that represent an object as a collection of connected branches of curves and associated scalar function or functions. We will demonstrate how theoretical results relate to a collection of applied projects involving students and industrial/government partners, and discuss some benefits and challenges of collaborating with non-academic entities.