Paul R. Halmos
Hungarian-born American mathematician renowned for work in functional analysis, probability, and ergodic theory, and for influential expository books including Finite-Dimensional Vector Spaces, Measure Theory, Naive Set Theory, and A Hilbert Space Problem Book.
Books
This list of books are ONLY the books that have been ranked on the lists that are aggregated on this site. This is not a comprehensive list of all books by this author.
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1. Naive Set Theory
A concise, rigorous introduction to the foundations of axiomatic set theory, presenting the basic axioms and operations on sets, relations, and functions, and developing the ideas of cardinality and ordinal numbers. It explains countability and uncountability, transfinite induction and recursion, and the equivalence of the axiom of choice, Zorn’s lemma, and the well-ordering theorem, with clear proofs and informal commentary. Designed to equip readers with essential tools for modern mathematics, it emphasizes clarity and intuition while remaining mathematically precise.
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2. I Want To Be A Mathematician
An Automathography
A lively autobiographical account of a mathematician’s development from student to respected researcher and teacher, blending personal anecdotes and witty portraits of colleagues with reflections on problem-solving, proof, and exposition. The narrative chronicles work in functional analysis and related areas, conveys the joy and practical frustrations of mathematical life, and offers candid advice about teaching, writing, and building a career in mid-20th-century academia.
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