The first clue that Henri Poincaré: A Scientific Biography (ISBN 0691152713) is not going to be a typical biography is in the table of contents. It lists one appendix on elliptic and Abelian functions and another on Maxwell’s equations. This is a biography of a mathematician that doesn’t shy away from math.
The subtitle is “a scientific biography” because the book is primarily about the work of Poincaré rather than his personal life. It has more to say about the three-body problem and algebraic topology, for example, than about Poincaré’s parents.
I haven’t seen a book like this before. I’ve seen books that are essentially collections of scholarly papers with biographical footnotes. And at the other extreme I’ve seen biographies practically devoid of scientific details. But I don’t remember seeing a biography that unapologetically includes substantial scientific content in the course of telling the story of a scientist’s life.