Bolzano, Bernard

Bolzano, Bernard (bōltsä`nō), 1781–1848, Czech philosopher, mathematician, and theologian. Though as a Catholic priest he himself was primarily concerned with religious and ethical questions, he is known today for his work in philosophy, methodology of science, mathematics, and logic. Among his important works are Wissenschaftslehre (1837), an attempt at a complete theory of science and knowledge; Rein analytischer Beweis (1817), which contains an early successful attempt to free differential calculus from the concept of infinitesimals; and Theorie der reelen Zahlen, which laid the cornerstone of the theory of real numbers. He tried to devise a geometry without the use of Euclid's parallel postulate, developed a fairly complete theory of real functions, and worked at an ideal language. However, his work did not attract the attention of his contemporaries and thus did not influence the development of mathematics.