Martin Gardner and Mathematics and Pleasure
In the delightful and generously illustrated 32-page booklet that accompanies the CD-Rom Martin Gardner’s Mathematical Games: The Entire Collection of His Scientific American Columns (MAA, 2006), Martin gave an interesting response to the challenge "Complete the following: 'I enjoy mathematics so much...'" from interviewer Don Albers. He said,
"Because it has a strange kind of unearthly beauty. There is a strong feeling of pleasure, hard to describe, in thinking through an elegant proof, and even greater pleasure in discovering a proof not previously known."Martin continued with characteristic modesty,
"On a low level I have experienced such a pleasure four times:
(1) I discovered the minimal number of acute triangles into which a square can be dissected. (Coxeter includes the dissection in his classic Introduction to Geometry.)
(2) I found a minimal network of Steiner trees that join all the corners of a chessboard.
(3) I constructed a bicolor proof that every serial isogon of 90 degrees–a polygon with all right angles, and sides in 1, 2, 3, ... sequence–must have a number of sides that is a multiple of 8.
(4) I devised a novel way to diagram the propositional calculus."
Charles Aschbacher, writing in the Journal of Recreational Mathematics, concluded, "Gardner himself downplays his mathematical ability, arguing that he is 'strictly a journalist.' Which is about the only piece of unintentional nonsense he has ever written. Gardner will go down in history as one of the most significant mathematicians of all time."