I'm making my way through Charles Seife's Zero. It is a very lucid and well-illustrated little book. It is also much more than I anticipated, in that it is a complete primer on the history of mathematics, rather just a "cultural compendium" on the notion and uses of zero. Seife, who holds an MA in mathematics from Yale, does a very good job demystifying calculus. Unlike some pop-science writers, Seife does not convey a chummy, conspiratorial tone, as if every reader should find the intricacies and mystique of arcane thinkers' thought processes as fascinating as… well, as those thinkers did. You won't find Seife writing sentences that sound like "Now, to REALLY grasp what Leibniz was after, you need to take a step back and look at blah blah blah." Instead, Seife just says what Leibniz did with calculus (and Newton with his fluxions). For example, need it be any more difficult to explain calculus than to say, as Seife does, that differential equations are the tangent-by-tangent analysis of a curve, while integrals are the area under that curve? I think not, and hence, I found Seife's brutally pellucid definitions invaluable.
It's the first time I have been on such copacetic terms with calculus since I took calc my freshmen year at U of C. In that course, once I saw that calculus is just a formalized way to talk about real objects and events, I could see not only its obvious utility, but also, more important, its basically narrative nature. Each problem is a story and each value is a character with its own ends and means. The solution is simply the tale that is told about their competing goals on a common slice of the Cartesian-plane world. A differential equation is a snapshot of the action at one point on the story arc, while an integral is a summary of the entire tale from a higher vantage point (at which one can see the whole surface area, or plot, under the story curve). Seeing calculus "again for the first time" re-inspires me to approach it as just something learned with much practice; hopefully someday this side of the veil I can get to my Big Book of Calculus Problems. And through my various Latin and Greek textbooks. Sigh.
Having said all that in favor of Seife's book, I will note just a couple weak points in it. First, in one single paragraph he does manage to condense the standard religion-is-opposed-to-science canards, specifically by conscripting Giordano and Galileo as alleged martyrs of science at the hands of religious obscurantists. He gets it right by saying an attack on Aristotle [and his denial of a cosmic void] was considered an attack on the church", but then fails to explicate how Aristotelian cosmology was no more the church's philosophy than anyone else's; it was simply the default cosmology. Only when Galileo insisted his findings demanded the church subject its dogmatic autonomy to the transient, private competence of science––and thus ceding ground to the Reformers' view of Scripture and Tradition––did he, a lifelong pious Catholic, raise the ire of leading clerics for more than intellectual reasons. Prior to that, he had been warmly accepted and supported by the pope and numerous clerics. Because his views challenged the hegemony of both secular and religious Aristotelian scholars, they collaborated to sully his reputation, and then force him into a more combative, reckless position, whereupon he did draw censure from the Church. As for Bruno, well, to call him a martyr of science is more or less equal to hallowing Deepak-Chopraism as "science". Not only was Bruno's grasp of science apparently quite mediocre, but also Kepler and Galileo wrote disapprovingly of Bruno's claims, largely because he was hijacking their already controversial science for his own literally esoteric homiletic (and rabble-rousing) purposes. For more about these issues, I recommend Thomas Lessl's "The Galileo Legend" and Stanley Jaki's "Giordano Bruno: Martyr for Science?" and "Galileo Lessons".
One other glaring problem Seife ignores has to do with the incredible correspondence between our mathematical reasoning and spatiotemporal reality. Seife glides by this matter thus: "Nature speaks in equations. It is an odd coincidence." That is an understatement of enormous magnitude. The conformability between our ability to perform formal mathematical operations, even if removed from physical reality, and the ability of those operations to describe reality, point strongly to an immanent validity in mathematics. Mark Steiner, in The Applicability of Mathematics as a Philosophical Problem, and Russell Howell in "Does Mathematical Beauty Pose Problems for Naturalism?" both elucidate this point better than I can. For someone who loves math as much as Seife does, it was disappointing to see him trivialize the implicitly transcendent link between "mere math" and the beauty of physical reality. If man's mind were not created to grasp such physical reality in the language of math, it is hard to explain how, on purely Darwinian terms, Homo sapiens sapiens can make the mental leap from crude anthropocentric physics and geometry to such abstract vision, considering that grand metamathematical insight has no value for the sheer transmission of genes.