Review: Infinitesimal

I think Amir Alexander’s Infinitesimal is better in principle than in execution.  However the principle is so good that it’s worth reading anyway.

The topic Alexander is exploring here is how the society of the 1500’s and 1600’s reacted to the fundamental ideas in geometry that became the basis for Netwon’s and Leibnitz’s calculus.  The mathematical ideas are compelling in their own right, but Alexander wisely focuses on their effect on thinking outside mathematics.  The result makes the forces driving philosophy and religion of these eras clearer and more vivid.

Infinitesimal shows us why the institutions of the day had any interest at all in an obscure mathematical movement and why that interest ebbed and flowed.  It’s quite fascinating to see the combinations of personality and politics that caused the interest.  I hadn’t realized the reach and vividness of the ideas until I explained what I’d learned from the book to a friend.  Quite powerful and surprising ideas.

There are some problems.  The book’s longer than it needs to be, partially because the chapters are somewhat repetitive and not so well integrated as one would hope.  I got the impression that they were individually composed and that the editing process was compartmentalized in such a way that the considerable overlap wasn’t spotted.  The resulting book is satisfying enough in the small and repetitive in the large.  Many parts benefit from skimming.

Overall an interesting discussion of a fascinating topic. Recommended.

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