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Putting Newton and Leibniz on the Witness Stand

Those who have delved even briefly into the history of mathematics know that a famous quandary is determining who invented calculus. Is it Sir Isaac Newton, is it Gottfried Wilhelm Leibniz, or is it one of their predecessors such as Archimedes with his use of the infinite, Cavalieri with his idea of the indivisible, or Eudoxus with his method of exhaustion?

Jason Socrates Bardi attempts to clarify this quandary in his recent book, The Calculus Wars: Newton, Leibniz, and the Greatest Mathematical Clash of All Time, (Thunder's Mouth Press, 2006). His text focuses on the a careful examination of the evidence underlying the bitter ten-year dispute between England's Newton and Germany's Leibniz (and their respective advocates) as they lay claim to the title of "Father of Calculus." The result is "the greatest intellectual property debate of all time--one that, from beginning to end, revealed how these twin mathematical giants, these two elder statesmen of German and British mathematics, were brilliant, proud, at times mad---and in the end completely human" (p. viii).

The crux of the argument is:

  • In his work with physical laws, Newton had invented a system of calculus via his method of fluxions and fluents. But, he did not publish his ideas--in fact, he kept many of his ideas secret.
  • Approximately ten years after Newton's dicoveries, Leibniz expanded the notions of calculus beyond the physical laws, creating the system of symbols and notations used today. Plus, in contrast the secretive Newton, Leibniz published his ideas in two papers.
So who should get credit, especially when both men's ideas were built on the work of mathematician's who preceded them? Bardi's book is highly recommended for anyone who teaches secondary mathematics (especially calculus teachers), as it provides interesting information regarding how "new" mathematics is created (and credited). Bardi focuses more on the dispute than on the ideas of calculus, which makes the book more like a history text than a mathematics text.

To support the text and its use, Bardi has created a special website, surprisingly called the Official Site of the Calculus Wars. It includes an overview of the main characters (i.e. the dramatis personae), excerpts from the book, special chapter notes, means for ordering the test itself, and a pdf-based collection of "unfinished personal essays inspired by The Calculus Wars." The latter bear fascinating titles such as "Dan Brown Stole My Homework," "The Gift," "Sunspots, or How California Wildfires Showed Me the Beauty of Rare Italian Violins," and "Minor Characters Rule."

Is Bardi's book the "end-all" for discussions as to who is the Father of Calculus? No, but it does provide advocates of either side with more ammunition, while also being a fun read.