Philip J. Davis

Philip J. Davis (1923-2018) was an influential American mathematician who made significant contributions to numerical analysis and approximation theory. During his career spanning over six decades, he held positions at the National Bureau of Standards and Brown University, where he became Professor Emeritus in the Division of Applied Mathematics. At the National Bureau of Standards, Davis served as Chief of Numerical Analysis and contributed to the development of the widely-used Abramowitz and Stegun Handbook of Mathematical Functions. His work on numerical computation and approximation methods helped advance the field during the early days of computer-based mathematics. Davis authored numerous books and papers exploring both technical mathematics and broader mathematical themes. He received the Chauvenet Prize in 1963 and the Lester R. Ford Award in 1982 for his mathematical writings, which often examined the philosophical and historical aspects of mathematics alongside technical topics. His academic career began at Harvard University, where he completed both his undergraduate and doctoral studies in mathematics. After a brief period serving in Air Force aerodynamics research during World War II, he established himself as a prominent figure in applied mathematics through his work at major institutions and his extensive published research.

Readers appreciate Davis's ability to make complex mathematical concepts accessible while maintaining intellectual depth. His book "The Mathematical Experience" (co-authored with Reuben Hersh) stands out in reader reviews for blending philosophy, history, and mathematics in an engaging way. What readers liked: - Clear explanations of advanced mathematical concepts - Integration of historical context and philosophical perspectives - Engaging writing style that appeals to both mathematicians and general readers - Thoughtful examination of mathematics' role in society What readers disliked: - Some technical sections require advanced mathematical background - Occasional dated references and examples in older works - Dense writing in certain chapters that can be difficult to follow Ratings: - The Mathematical Experience: 4.2/5 on Goodreads (300+ ratings) - Mathematics and Common Sense: 3.9/5 on Goodreads (50+ ratings) - Amazon reviews average 4.3/5 across his works One reader noted: "Davis brings mathematics to life by showing how it connects to human culture and thought." Another mentioned: "The philosophical discussions sometimes overshadow the mathematical content."

The Mathematical Experience (1981) A comprehensive exploration of mathematics as a field of human endeavor, examining its nature, methods, applications and role in society through historical and philosophical perspectives.

Mathematics and Common Sense: A Case of Creative Tension (2006) An examination of the relationship between mathematical thinking and everyday reasoning, analyzing where these modes of thought align and diverge.

The Education of a Mathematician (2000) A memoir detailing Davis's personal journey through mathematics, including his experiences in academia and at the National Bureau of Standards.

Methods of Numerical Integration (1984) A technical treatise covering various methods and theories of numerical integration, including detailed mathematical procedures and applications.

Spirals: From Theodorus to Chaos (1993) A mathematical and historical investigation of spiral forms, from ancient Greek mathematics to modern chaos theory.

The Thread: A Mathematical Yarn (1983) An exploration of mathematical ideas through interconnected stories and historical narratives about mathematicians and their discoveries.

Descartes' Dream: The World According to Mathematics (1986) An analysis of how mathematical thinking has shaped our modern world and influenced various fields of human knowledge.

Mathematics: People, Problems, Results (1984) A collection of essays examining significant mathematical problems, the people who solved them, and their impact on mathematical development.

Keith Devlin combines mathematical expertise with accessible writing on the history and culture of mathematics, exploring how math interfaces with human society across his books "The Math Gene" and "The Language of Mathematics." His work, like Davis's, bridges technical concepts with broader cultural perspectives.

Morris Kline wrote extensively about mathematics education and the philosophical foundations of mathematics, including "Mathematics: The Loss of Certainty." His examination of how mathematics develops as a human endeavor parallels Davis's interest in the cultural aspects of mathematical thinking.

Reuben Hersh focuses on the nature of mathematics as a human activity and examines philosophical questions about mathematical reality. His work "What Is Mathematics, Really?" shares Davis's concern with understanding mathematics in its broader human context.

David Berlinski writes about mathematics and its history with attention to both technical detail and cultural significance. His books, including "A Tour of the Calculus," combine mathematical rigor with historical context in ways similar to Davis's approach.

William Dunham specializes in mathematical history and the evolution of mathematical ideas through time. His works, such as "Journey Through Genius," present mathematics through historical developments and the lives of mathematicians, reflecting Davis's interest in how mathematical ideas develop.