Then, depending on the degree of sanity on display, either conclude that the man rose above tremendous obstacles to become a great leader or was too ordinary to be anything but flummoxed by his life’s challenges. All the book’s subjects are men.

Some of these formulations are conveniently tidy: Dr. Ghaemi is able to call Gandhi and the Rev. Martin Luther King Jr. “the bookends of depressive activism.” And sometimes they are based on truly tenuous evidence; both the Gandhi and King families were able to maintain enough privacy to thwart Dr. Ghaemi’s research. Based on Gandhi’s depression and the self-destructive behavior of his son, Harilal, Dr. Ghaemi can go no further than this specious thought: “It is quite possible that others in the family have suffered the same illness.”

About the Kings: “Regarding genetics, King’s family is private, and the presence or absence of psychiatric diagnoses among family members is not publicly available knowledge.” That remark is more notable for redundancy than revelation. When Dr. Ghaemi does come up with anything remotely new, he is quick to congratulate himself for defying conventional wisdom.

This book would be shorter had its author ruled out ambiguous cases. But he is willing to speculate about those too. He states that although Richard M. Nixon was not a homoclite (or totally normal person), “he was not highly abnormal either.” He even navigates entirely around figures who do not fit any of his theories. Ronald Reagan is branded a homoclite, but “Reagan never faced a Cuban Missile Crisis.” Dr. Ghaemi drops his name, but can’t pigeonhole him at all.

As for Hitler and Kennedy, their pathologies actually are made to seem similar by “A First-Rate Madness.” Both were heavily medicated for illnesses that were kept from the public; both were fueled by combinations of steroids, amphetamines and barbiturates; both may have demonstrated great behavioral changes as a result of those drugs. But Kennedy, in the book’s estimation, rose to the challenges he faced. And Hitler — well, Dr. Ghaemi treads tenderly around him, because “the memory of those who perished is justifiably cherished,” as he puts it. Suffice it to say that Dr. Ghaemi thinks he has come up with important insights. He may, like some of our best-known leaders, be unrealistic in his beliefs.