Abstract:In the 17th century the cycloid was known as the "Helen of Mathematics."This intrinsically beautiful curve was greatly appreciated for the new and  difficult concepts of the calculus she so effectively illustrated.

Homotopies are incredibly difficult to imagine geometrically. No wonder  topologists prefer to work algebraically. The sphere eversion has been  a favorite subject of illustration for half a century. This talk will  provide a brief and illustrated history of mathematical illustration as  exhibited in the sphere eversion.