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Software Engineer. Wannabe Mathematician. Itinerant Philosopher

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The history of the calculus and its conceptual development (Paperback, 1949, Dover Publications) 4 stars

Detailed and Well-Sourced History (Recommended)

4 stars

I'm enjoying this history quite a bit. Boyer has done a phenomenal job reviewing many centuries worth of mathematical research, and giving an intricate analysis about how each of the primary sources build upon a few common philosophies to eventually arrive at modern calculus.

I'm not able to assess Boyer's historical or philosophical accuracy in interpreting the contributions each source makes towards the development of calculus. In particular, Boyer insistently argues that various mathematicians fall short of expressing the limit concept. For instance, Archimedes sometimes gets credit for expressing an idea very similar to our modern concept of the limit in his quadrature of the parabola. Is Archimedes performing a limit, just in his own terminology, or is he not? Boyer convincingly says "no", given that Archimedes works from the method of exhaustion and ratios of geometric figures, rather than a numerical series. In fact, Archimedes could not have, explains …

John Napier (Hardcover, 2014, Princeton University Press) No rating

I skipped directly to chapter 3 on starting this book, since that's where Havil reconstructs the mathematics of Napier's Descriptio with modern typesetting. Havil does a wonderful job framing Napier's concerns - such as, why trigonometric functions form the backbone (no pun intended) of his method - as well as providing pseudo-code to reproduce all 45 pages of the Descriptio calculations.

I do feel the copy-editing could be tighter. It's as if Princeton merely converted the text to American spelling, while keeping British syntax. So some of the phrasing reads awkwardly, making me careful to double check the mathematics for errors that slipped into press.

Overall, a very valuable book in popular mathematics. I highly recommend for both teachers and students.