Book Review: A Mathematician's Apology

 

Godfrey Harold Hardy was a prominent 20th century mathematician. He was most known for his long-time collaboration with John Edensor Littlewood and for his mentorship of the Indian mathematical prodigy, Srinivasa Ramanujan.

The forward to the book was written by his friend from Cambridge, C. P. Snow. It may be one of the longest book forwards I have read - 58 pages. However, Snow's forward also serves as a brief biography of Hardy, so it is worth reading.

Hardy was in his early sixties when he wrote the Apology. It is his acknowledgement that most great mathematical works are produced by much younger mathematicians. I enjoyed Hardy description of how mathematics differs from science and his observations of what people's talent. He does include two brief descriptions of mathematical proofs for the purpose explaining how such proofs work. The two are Euclid's proof of the existence of an infinite number of prime numbers and Pythagoras's proof of irrationality of the square root of 2.

Clever Hans, the mathematical horse

In 1907 William von Osten toured around Germany with a horse, Clever Hans, that he claimed could perform various math problems. His story is found here: Clever Hans. While the feats of Clever Hans were debunked as an elaborate palor trick, scientists have found that many animals do have a sense for numbers. More recently, an article in Quantamagazine, highlights many true animal feats in recognizing different number of objects and even having a sense for zero.