A while ago I was reading an interview with the actress Cameron Diaz in a movie magazine. At the end the interviewer asked her if there was anything she wanted to know, and she said she'd like to know what E=mc^2 really means. They both laughed, then Diaz mumbled that she'd meant it, and then the interview ended.

"You think she did mean it?" one of my friends asked, after I read it aloud. I shrugged, but everyone else in the room -- architects, two programmers, and even one historian (my wife!) -- was adamant. They knew exactly what she intended: They wouldn't mind understanding what the famous equation meant too.

It got me thinking. Everyone knows that E=mc^2 is really important, but they usually don't know what it means, and that's frustrating, because the equation is so short that you'd think it would be understandable.

There are plenty of books that try to explain it, but who can honestly say they understand them? To most readers they contain just a mass of odd diagrams -- those little trains or rocketships or flashlights that are utterly mystifying. Even firsthand instruction doesn't always help, as Chaim Weizmann found when he took a long Atlantic crossing with Einstein in 1921: "Einstein explained his theory to me every day," Weizmann said, "and soon I was fully convinced that he understood it."

I realized there could be a different approach. The overall surveys of relativity fail not because they're poorly written, but because they take on too much. Instead of writing yet another account of all of relativity, let alone another biography of Einstein -- those are interesting topics, but have been done to death -- I could simply write about E=mc^2. That's possible, for it's just one part of Einstein's wider work. To a large extent, it stands on its own.

The moment I started thinking this way, it became clear how to go ahead. Instead of using the rocketship-and-flashlight approach, I could write the biography of E=mc^2. Everyone knows that a biography entails stories of the ancestors, childhood, adolescence, and adulthood of your subject. It's the same with the equation.

The book begins, accordingly, with the history of each part of the equation -- the symbols E, m, c,=, and . For each of these -- the equation's "ancestors"--I focus on a single person or research group whose work was especially important in creating our modern understanding of the terms.

Once the nature of those symbols is clear, it's time to turn to the equation's "birth." This is where Einstein enters the book: his life as a patent clerk in 1905; what he'd been reading, and what he'd been thinking about, which led to all those symbols he wove together in the equation hurtling into place in his mind.

If the equation and its operations had stayed solely in Einstein's hands, our book would simply have continued with Einstein's life after 1905. But pretty quickly after this great discovery his interests shifted to other topics; his personal story fades from the book, and instead we pick up with other physicists: more empirical ones now, such as the booming, rugby-playing Ernest Rutherford, and the quiet, ex-POW James Chadwick, who together helped reveal the detailed structures within the atom that could -- in principle -- be manipulated to allow the great power the equation spoke of to come out.

In any other century those theoretical discoveries might have taken a long time to be turned into practical reality, but the details of how Einstein's equation might be used became clear early in 1939, just as the twentieth century's greatest war was beginning. A long, central section of the book homes in on the equation's coming of age here, in the furious race between scientists based in the United States and those in Nazi Germany to see who could build a deathly, planet-controlling bomb first. The history is often presented as if America's victory were inevitable, due to the country's industrial superiority, but it turns out that Germany came dangerously closer to success than is often realized. Even as late as D Day in June 1944, Army Chief of Staff George Marshall saw to it that several of the U.S. units landing in France were supplied with Geiger counters as a precaution against a possible Nazi attack with radioactive weapons.

In the final sections of the book we switch away from war; the equation's "adulthood" has begun. We'll see how E=mc^2 is at the heart of many medical devices, such as the PET scanners used for finding tumors; its effects are also widespread in our ordinary household devices, including televisions and smoke alarms. But even more significant is how its power stretches far out into the universe, helping to explain how stars ignite, and our planet keeps warm; how black holes are created, and how our world will end. At the very end of the book, there are detailed notes, for readers interested in more mathematical or historical depth; further background explanations are available at the Web site davidbodanis.com.

The stories along the way are as much about passion, love, and revenge as they are about cool scientific discovery. There will be Michael Faraday, a boy from a poor London family desperate for a mentor to lift him to a better life, and Emilie du Châtelet, a woman trapped in the wrong century, trying to carve out a space where she wouldn't be mocked for using her mind. There are accounts of Knut Haukelid and a team of fellow young Norwegians, forced to attack their own countrymen to avert a greater Nazi evil; Cecilia Payne, an Englishwoman who finds her career destroyed after daring to glimpse the sun's fate in the year A.D. 6 billion; and a nineteen-year-old Brahmin, Subrahmanyan Chandrasekhar, who discovers something even more fearful, out in the beating heat of the Arabian Sea in midsummer. Through all their stories -- as well as highlights from those of Isaac Newton, Werner Heisenberg, and other researchers -- the meaning of each part of the equation becomes clear.