Examples of counterexamples: a book conspectus

Abstract

A counterexample is any exception to a generalization. Counterexamples are often used in science (and philosophy), as a means to setting boundaries. In mathematics at large, well-chosen counterexamples may bound possible theorems, disprove certain conjectures. Recent breakthroughs show that artificial intelligence tools are becoming able to generate counterexamples, disproving long-standing math conjectures. This challenges human assumptions about machine reasoning limitations. This conspectus is (mostly) meant to gather and share counterexample book references in relation to mathematics (on algebra, analysis,computer science, calculus, logic, philosophy, probability, statistics, topology) and related topics (computer science, philosophy).