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From here to infinity: Germs, math, and the beauty of discovery

In book reviews, the currency of superlatives is easily exhausted. ''The Hulk," for crying out loud, was alternately deemed ''beautiful," ''brilliant," and ''moving," along with a host of other adjectives not worth transcribing.

In the short life of this column I have tried to find first-rate, interesting science books and tell you the truth about them, all the while keeping puffery at a minimum.

Well, all that is out the window now. At the risk of squandering my already lean critical reserve, I must tell you that David Foster Wallace's ''Everything and More: A Compact History of Infinity" is marvelous. It's extraordinary. It's a book about transfinite math, loaded with symbols and shorthand and functions, and when you page through it, you may seriously consider putting it down because, as usual, he's not too generous with paragraph breaks, he's fond as heck of footnotes, and on nearly every page, there's some line like ''x = 0.a{-1}a{-2}a{-3}a{-4}a{-5}a{-6}a{-7} . . . ."

It can also, at times, make your brain feel as if a carrot peeler is being slowly dragged across its surface.

I expect you have heard that mathematics is beautiful. It's a language of pure abstraction, ''consecrated to the ideal of precision," (which means that math itself is a kind of infinite paradox -- how can precision be leveled upon abstraction?) and before reading Wallace's book, I understood this in a Learning Channel sort of way. But, to be honest, calculus and even algebra were things I left behind in college, subjects I had to ''get through," sort of like nasty but necessary surgeries. What I retain from those hours of my life is more about little shreds of pencil eraser. That's why ''Everything" is, in nearly every way, a gift. It's a thoughtful and witty 300-page testimonial to the qualities I never fully understood that mathematics possessed: Math is astonishing and full of ''shadowlands," and -- ultimately -- stunning beauty.

You won't need graph paper or a math consultant beside you as you read, although both may help. Wallace goes to great lengths to make the arguments comprehensible no matter how pitiable your foundation in mathematics. ''Your author," he tells us early on, ''did poorly in every math course he ever took, save one." So, the reasoning goes, if he can do it, so can you. And if you've had enough sleep, I promise you can make it through this book and understand a great deal of it.

Wallace mainly addresses the question: What is infinity? It has the corollary intention of helping us appreciate the mathematician Georg Cantor's extraordinary answers to that question. As Wallace points out, ''The whole issue here is of course incredibly hairy . . . because not only is the question abstract but everything it's concerned with is an abstraction -- existence, reality, number . . . ."

''Everything" is part of the new science series headily titled ''Great Discoveries." In it, popular writers will tackle some of the more fascinating and fundamental scientific achievements, such as relativity, the atom, the computer, etc. Released alongside Wallace's sparkling effort is Sherwin B. Nuland's ''The Doctors' Plague: Germs, Childbed Fever, and the Strange Story of Ignac Semmelweis."

After Wallace's book, you can fall into this biography of Semmelweis like a cozy beanbag chair. ''The Doctors' Plague" is a cleanly -- and clearly -- written biography of Semmelweis, the 19th-century doctor who discovered that obstetricians (including himself) were killing thousands of puerperal women by examining them, both before and after giving birth, with hands and tools covered with ''putrid cadaver particles," a.k.a bacteria.

Semmelweis's discovery, though, is only part of the story. The meat of the narrative is in the various ways Semmelweis tried, and failed, to get his contemporaries to wash their hands. Some of his failures were due to cultural resistance -- what doctor would want to believe he was the cause of so many deaths? -- but much was due to Semmelweis's own psychological failures and ''greater sense of unworthiness." He was quick-tempered, afraid to publish, indisposed to simple but vindicating experiments, and mostly uninterested in microscopy. ''It would remain," Nuland writes, ''for others to identify the nature of lethal microorganisms, while [Semmelweis] lay moldering in an unvisited grave."

Like the best biographers, Nuland is careful to offer a balanced portrait, diagnosing Semmelweis with the exactitude of a good clinician and avoiding the ''hero destroyed . . . by forces beyond his control" archetype. Both books are lessons in how discovery is pyramidal, based on a combination of circumstance, obsession, and the work of one's predecessors. At the same time these stories, especially Semmelweis's, demonstrate how difficult it is -- once a monumental discovery has been made -- to get human beings to question their basic assumptions.

If dunking your hands and forceps in a basin of chloride solution can save hundreds of thousands of lives, you can't help but wonder what simple, fundamental truths we are still missing. Books about great discoveries remind us how much there is left to discover, how we are only doing our best, fumbling through the darkness, toward an inaccessible infinity of understanding.

Anthony Doerr is the author of ''The Shell Collector."

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