“I am a biologist,” writes Jeffrey C. Hall, a professor at Brandeis, at the beginning of The Stand of the U.S. Army at Gettysburg (Indiana, 415 pages, $49.95), “but I claim to know as much history as biology on one subject: The Battle of Gettysburg.” Unless he’s an amazingly good biologist, he’s being modest. His book is a fascinating, detailed account of the battle with more than a hundred maps. The author has several main points to make: that the Union’s strong position at the end of the first day was no accident; that Sickles’s big blunder on day two actually did the Union much good; that Union artillery and one little-known Ohio regiment were the main players in the defeat of Pickett’s Charge. He also proves himself broadly enough informed about history to reflect on how Meade’s performance after the battle compares with Spruance’s after Midway and how similar the action at Little Round Top was to the 1941 Battle of Crete.

The title of “America’s greatest playwright,” like that of “America’s greatest portrait painter,” is unlikely to change hands in the future, since anyone capable of becoming the greatest in these fields can easily find a less archaic outlet for his or her talents. The drama crown may thus be held in perpetuity by Arthur Miller, whose first full-length biography was published last year: Arthur Miller: His Life and Work , by Martin Gottfried (Da Capo, 496 pages, $30.00). In a detailed and sympathetic account, the author narrates each decade’s crisis in Miller’s life—the Depression in the 1930s; World War II (in which he did not fight) and the failure of his first play in the 1940s; McCarthyism in the 1950s; the breakdown of his wife, Marilyn Monroe, and their divorce in the 1960s; and the decline of his reputation from the 1970s onward—all in the vigorous style Gottfried developed over decades as a theater critic.