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The Mathematical Works of Bolzano

Bernard Bolzano (active in the first half of the 19th century) made outstanding conceptual and technical contributions to logic and mathematics, foreshadowing Tarski's semantic notions of truth and consequence, Cauchy's concepts of convergence and continuity, Weierstrass' insights into highly pathological (fractal) functions, and Cantor's establishment of a theory of infinite sets. A major series of translations (of 9 German publications or manuscripts) appears in The Mathematical Works of Bernard Bolzano published by Oxford University Press.

Bolzano's insights were founded on the very clear separation of objective meanings from psychological events, linguistic expressions and real-world objects (if any). This was at a time prior to the domination of mathematics and logic by methods of abstraction and formalism. Modern computing was born, and developed, under the influence (perhaps undue influence) of a mathematical and formal perspective. Current research on Bolzano is part of a larger enquiry into the principles underlying the accommodation of formal and informal elements in both 19th century mathematics and modern computing.