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Students of mathematics at the calculus level and beyond are usually made vaguely aware that, despite some minor historical contention, Isaac Newton is credited for the discovery of calculus. Fewer in number are those who learn the name Gottfried Wilhelm Liebniz as Newton's rival claimant for that honor, and still fewer are those who are informed that Newton's methods of fluxions and fluents were almost immediately abandoned in favor of Liebniz's differentials and his superior mathematical notation (essentially that still in use today).
Author Jason Bardi aims to correct that knowledge shortfall in THE CALCULUS WARS: NEWTON, LIEBNIZ, AND THE GREATEST MATHEMATICAL CLASH OF ALL TIME. The use of the word "wars" and the hyperbolic phrasing "greatest clash of all time" set the expectations stage for an epic battle of intellectual giants as potentially juicy as 20-year-old Evariste Galois's fatally romantic duel with pistols. The historical facts are rather less sensational, however, consisting largely of letters and journal articles (most submitted anonymously at the time) hurling nationalistic accusations, often petty or unfounded, from one side of the English Channel to the other. As a result, Mr. Bardi struggles to deliver the implicit drama: there is no critical face-off between the principals, no momentous debate (even the British Royal Society largely shrugs it off thanks to Newton's presidency of that august body), no climactic moment when the truth is laid bare.
Perhaps more disconcerting, the vast majority of Bardi's book is not about calculus at all, not about the battle over its discovery, its historical underpinnings, or its subsequent development along the lines of Liebniz's work. We never see a comparative representation of the Newtonian and Liebnizian models, their notational differences, or their intellectual geneses from the mathematical work of their predecessors (Archimedes' famous method of exhaustion, for example, receives just one passing mention). Instead, the author falls back on the more conventional approach of chronological biography, trailing the two men's parallel lives from 1642 to 1728. It could certainly be argued that their respective biographies give important background to their personalities and professional status when the "calculus wars" finally broke out in 1699 (175 pages into Bardi's 250-page book). However, Bardi writes extensively on Liebniz's silver mining schemes, invention of a leather folding chair and a new type of windmill, promotion of binary numbers, theories of planetary motion and theology, political machinations, court genealogical work, and studies of China, to name a few. Similarly with Newton, it is his optics, theories of universal gravitation, stewardship of the British Mint, dabblings in alchemy, psychological mood swings, even his sexual orientation.
In the end, Bardi sides with Liebniz as the more aggrieved party, clearly innocent of the charges of plagiarism. Newton is clearly the loser in this "war," both for hoarding his great discovery to the detriment of fellow scientists and mathematicians and for treating his Continental contemporaries with such disdain. Sadly, the entire affair did nothing to polish the honor of either man.
Bardi's storytelling prose is fluid and well suited to his task, with one significant exception. In a tale of dueling mathematical, scientific, and intellectual giants, one inserts oneself at the greatest of risks. Perhaps a Stephen Hawking could merit an occasional authorial "I" in this story, but decidedly not a Jason Bardi (despite his ostentatiously displayed middle name, Socrates, that ironically only emphasizes the disparity). Author Bardi is given to repeated, utterly trivial, and mostly parenthetical insertions of his own opinions that are presumptuous, irrelevant, and distracting: "When I was in London, I noticed..." , "...an event I like to call..." , "I get this picture when I think about it..." , "...as I recall from my encounter..." , "For my part, I can't help but wish..." , "a docent told me..." , "I examined..." , "...I have read..." , "I examined... [again]" , culminating with the irrepressible "I'm not surprised, really" and the exquisite "For me, what's really interesting... " Every one of these first person insertions should have been removed by a more exacting editorial pencil.
I approached this book hoping to discover a comparative treatment of the origins and development of Newton's and Liebniz's twin lines of calculus development, to learn how two intellectual giants of the 18th Century each separately made a conceptual mathematical leap nearly on a par with Einstein's leap to relativity. The similarities and differences in their developmental threads would surely be part and parcel of the historical argument over rights of discovery and accusations of plagiarism. Regrettably, I found instead seemingly endless pages of biographical minutiae about everything else in these two great men's lives.