When I was a senior in college, I took two upper level math courses to satisfy a degree requirement for General Science. I was in way over my head in Number Theory. But I survived. Two of us were enrolled in Math 226, otherwise known as Geometry.
Those two courses taught me how to think like a mathematician: take nothing for granted; prove everything; build an edifice by small and careful steps. If only I had been thinking like a mathematician before I took four semesters of calculus and statistics.
We did not study the historical (?) Euclid. We didn’t directly study his seminal work Elements, either. But this book by David Berlinski dips into the man (what we can deduce or guess from those who wrote about him) and about some of the elements of his work in mathematics.
This book gets off to a difficult start. It’s not written like most popular science books, though there are elements of personal interest from great mathematicians. The author tries, maybe a bit too hard, to be literary. I do like his prose. But he takes too long to say what he needs to say.
Dr Berlinski doesn’t say everything. He doesn’t distill all of Euclidean geometry into 156 pages. He spends a lot of ink on interesting things like analytical geometry and the parallel postulate. By Chapter IX he gets to the advent of non-Euclidean geometry–things like how lines and two-dimensinoal shapes behave on something like a sphere. The earth’s surface, for example.
So we come to a final question about the title. Is Euclid still king in a scientific culture that stands with one foot in the fantastic? Elements was a geometry textbook for more than two millennia, but no longer. Forget space; does Euclid have any authority in human time?
I’m probably not thinking like a mathematician any more. So this book was a bit difficult for me, though not in the concepts it presents. Can I recommend it? Sure: if you like geometry.