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Axiomatics: Mathematical thought and high modernism

The author states, in the note to readers, “This book is a history of mathematical thought rather than of mathematics per se” and also “… I have tried to limit to a minimum the mathematical content in the book.” Both statements are true, yet still this book will be of great interest to many mathematicians. The author follows several important intellectual threads in mathematics from the end of the 19th century up to around 1980, including the conflict between pure and applied mathematics, and provides a deep attempt to explain the ideas that steered the direction mathematics took.

A particularly interesting thread is the connection between the Modernist movement in art and the pull towards abstraction among professional mathematicians, even those doing “applied” work. Steingart tells interesting stories of mathematicians, historians, artists, setting the scene for many of the conflicts and disagreements that occurred, and also highlights the importance of mathematical approaches in a variety fields. Finally, Steingart describes the rise in interest in the history of mathematics among mathematicians, leading to major philosophical and historiographical disputes, such as those involving Sabetai Unguru and André Weil.

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