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+-------- Thread: The Story of Proof [Stillwell] (/showthread.php?tid=1989)
The Story of Proof [Stillwell] - mklabgr - 09-15-2026
Adhemar Bultheel’s review of John Stillwell’s The Story of Proof presents the book as a history of mathematics viewed through the evolution of mathematical proof. Stillwell traces the transformation from the visually intuitive geometry of Euclid to increasingly abstract systems involving algebra, calculus, topology, set theory and formal logic.
The review emphasizes that developments in proof techniques and mathematical disciplines continually influenced one another: algebra led to new number systems and structures, calculus required rigorous treatment of limits and infinity, and geometry expanded through projective, hyperbolic and Riemannian ideas.
The later chapters follow mathematics toward its foundations and the formalization of logic, culminating in the profound limitations revealed by Gödel’s incompleteness theorems and Turing’s work. The reviewer stresses that the book is neither a conventional historical survey nor a popular mathematics introduction: it contains many actual proofs and gradually demands greater mathematical maturity.
Its central message is that proof is not merely a way of verifying that a statement is true—it explains why it is true and reveals how mathematical thought itself has evolved. Bultheel considers the book an entertaining and valuable account that should appeal particularly to readers interested in the foundations and historical development of mathematics.
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