Evanston Public Library's Reviews > Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever

Great Feuds in Mathematics by Hal Hellman
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's review
May 31, 2012

bookshelves: nonfiction

My two middle-school kids are learning algebra and geometry, which I discovered I mostly remember. But they’re heading toward calculus, which I discovered I had mostly forgotten. So I started re-educating myself. While getting re-educated I learned the remarkable story behind calculus.

But first: What is calculus? In simple terms, it’s the mathematics of changing values. In less simple terms, it’s the set of tools for calculating “momentary” values like acceleration, deceleration, or slopes of curves (that’s differential calculus), and the related set of tools for calculating “cumulative” values like area, volume, or work (that’s integral calculus).

In metaphorical terms, it’s the song of the universe. I think of algebra as the words, and geometry as the music. Combine them and you get the song: the song of motion, engineering, physics, medicine, statistics, business, computers, even sports—any field in which problems can be mathematically modeled, and in which optimal solutions are desired.

So it matters who invented calculus. Was it the Englishman, Sir Isaac Newton (1642-1727)? Or the German, Gottfried Leibniz (1646-1716)? Probably the best answer is that it was both.

Newton came up with the basics first (building on predecessors’ work, of course—that’s another story). But Leibniz published first, independently, and did more to advance understanding. Neither saw it this way: each felt threatened by the other, perhaps even plagiarized by the other, and they battled bitterly. Their battle held back mathematical progress for decades, separating the English-speaking scientific world from the scientific world of continental Europe.

Ackroyd’s book highlights Newton’s personality, connecting it to his amazing insights not only into calculus, but also into gravitation and optics. It is a delight to read. Each sentence is a springboard for the next, and you gain keen insight into the character of the man voted by many the “scientist of the millennium.” Bardi writes more amateurishly, but explains the calculus battle in rich detail, exploring both Newton’s and Leibniz’s characters and linking them to the complex politics of their era. But if you don’t have the time (or the interest) to spend on a whole book, zero in on chapter three of Hellman—just twenty pages, almost as well-written as Ackroyd. (Jeff B., Reader's Services)


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