G. H. Hardy (1877-1947) wrote **A Mathematician's Apology** in 1940, late in life, during wartime. It shows. The book is short, argumentative, often wrong. Hardy insists that the "pure" parts of mathematics and physics are irrelevant to ordinary life. How silly — increasingly, obviously so! His thesis that knowing "...a little chemistry, physics, or physiology has no value at all in ordinary life"? Ditto. His claim, "Real mathematics has no effects on war. No one has yet discovered any warlike purpose to be served by the theory of numbers or relativity, and it seems very unlikely that anyone will do so for many years ..."? Already wrong when he wrote them, more blatantly so now.

Wiser, perhaps, if Hardy had stood on his head, smiled, and said:

- deep patterns and relationships are beautiful, worth discovering
- mathematics, physics, and countless other abstractions have infinite relevance in non-obvious ways
- applications often happen far sooner than experts can anticipate

*(cf Strands of Truth (2000-11-02), Millennium Math (2002-12-05), The Unreasonable Effectiveness of Mathematics (2008-02-17), Progress in Math (2017-07-30), Ultimate Abstraction (2017-08-24), ...)* - * ^z* - 2019-02-13