A stringent criterion for a public intellectual is proposed: persons who are simultaneously major creative intellectuals, and successful political leaders. Using data from the careers of 2700 philosophers throughout world history, and social scientists in recent centuries, the article concludes that three kinds of political failure by intellectuals are prominent: (1) failure to attain political office; (2) failure while in office; and (3) failure of political influence from adoption of one’s ideas. On the whole, major intellectuals are not good at politics; and politicians do not make outstanding intellectuals. The skills and pressures of the two spheres are too different.