Bolzano, Bernardus Placidus Johann Nepomuk (1781–1848)

Czech mathematician and philosopher. Bolzano formulated a theory of real functions and introduced the nondifferentiable Bolzano function. He was also able to prove the existence and define the properties of infinite sets.

Bolzano was born and educated in Prague, where he became professor of mathematics in 1804 and of philosophy in 1805. For the next 14 years he lectured mainly on ethical and social questions, although also on the links between mathematics and philosophy. His liberal and Czech nationalist views brought him into disfavour with the Austro-Hungarian authorities and in 1819 he was suspended from his professorship and forbidden to publish. In 1824 Bolzano resigned his chair. Owing to the opposition of the imperial authorities, most of his work remained unpublished until 1962.

Bolzano formulated a proof of the binomial theorem and, in one of his few works published in his lifetime (1817), attempted to lay down a rigorous foundation of analysis. One of the most interesting parts of the book was his definition of continuous functions. During the 1830s Bolzano concentrated on the study of real numbers.