Every mathematician will rank other mathematicians linearly according to past accomplishments while he rates himself on the promise of his future publications. Unlike most mathematicians Halmos has taken the unusual step of printing the results of his lifelong ratings. He is pretty fair to everyone included in his lists (from first-rate [Hilbert] to fifth-rate [almost everybody else]), except to himself, to whom he is merciless (even in the choice of the title to the book:¹ "I Want to be a Mathematician," as if there were any question in anybody's mind as to his professional qualifications).