|A Mathematician’s Apology by G. H. Hardy |
(with a Foreword by C. P. Snow).
Cambridge University Press,
1940, 1967; 23rdPrinting 2016.
|Godfrey Harold Hardy 1887-1947. |
Hardy is eloquent, making a strong case for his field of theoretical mathematics as having greater value than applied mathematics. He begins by laying out four theorems. The first is Euclid’s proof that no end exists for prime numbers, that an infinity of prime numbers exists. The second is Pythagoras’s proof that the square root of two is irrational. Those he proves for the reader.
Two others are left unfinished. The Fundamental Theorem of Arithmetic says that any integer can be resolved in only one way into a product of primes. Hardy shows some examples, but says that the proof might be tedious for the general reader. Similarly, he tells us of Fermat’s “Two Square” Theorem which says that all prime numbers can be divided by 4 with a remainder of either 1 or 3; and that all of the first class and none of the second can be written as the sum of two squares. Again, he lists some examples, but leaves the proof for the reader.