Being a mathematician is a bit like being a manic depressive: you spend your life alternating between giddy elation and black despair.
A mathematician experiments, amasses information, makes a conjecture, finds out that it does not work, gets confused and then tries to recover. A good mathematician eventually does so - and proves a theorem.
This book reminds me of James Gleick's Chaos. The ideas and stories in Loving and Hating Mathematics are timely, interesting, and sometimes even profound. The authors, writing for nonspecialists, take pains to explain technical ideas in nontechnical language, and the book should interest general readers as well as a large mathematical audience.