Given how awfully complicated the work of mathematicians appears to other people, and how much explanation must be given to help people to understand the work, the author’s statement about the allure of simplicity is puzzling. A little elaboration about how simplicity leads to the development of poorly understood financial instruments or how it is seen in multiple-page proofs, these being products of the work of mathematicians, would be informative.
The author gives a good introduction to some of the underlying philosophy of math and its consideration of objects of the mind. A trend in math instruction has been to try to move away from abstraction and instead concentrate on solving practical problems, and to deal with what can be manipulated by the hands, leading to excesses such as overuse of things called algebra tiles. So, the author’s describing the intangible as something that can be enjoyed is welcome. It would be helpful, however, to avoid any implication of a false dichotomy that math must only concern itself with the world of the imagination. Also, the typical work of mathematicians isn’t figuring out geometrical relationships that might well have been figured out by the ancient Greeks already. I must assume that he would not have students actually attempt to deal directly with a current mathematical problem, while somehow having them do what mathematicians do on some level, to follow his desire.