1.
Bernard Bolzano
–
Bernard Bolzano was a Bohemian mathematician, logician, philosopher, theologian and Catholic priest of Italian extraction, also known for his antimilitarist views. Bolzano wrote in German, his mother tongue, for the most part, his work came to prominence posthumously. Bolzano was the son of two pious Catholics and his father, Bernard Pompeius Bolzano, was an Italian who had moved to Prague, where he married Maria Cecilia Maurer who came from Pragues German-speaking family Maurer. Only two of their children lived to adulthood. Bolzano entered the University of Prague in 1796 and studied mathematics, philosophy, starting in 1800, he also began studying theology, becoming a Catholic priest in 1804. He was appointed to the newly created chair of philosophy of religion at Prague University in 1805. He proved to be a popular lecturer not just in religion but also in philosophy, Bolzano alienated many faculty and church leaders with his teachings of the social waste of militarism and the needlessness of war. He urged a total reform of the educational, social, upon his refusal to recant his beliefs, Bolzano was dismissed from the university in 1819. His political convictions eventually proved to be too liberal for the Austrian authorities and he was exiled to the countryside and at that point devoted his energies to his writings on social, religious, philosophical, and mathematical matters. Although forbidden to publish in journals as a condition of his exile, Bolzano continued to develop his ideas. In 1842 he moved back to Prague, where he died in 1848, Bolzano made several original contributions to mathematics. His overall philosophical stance was that, contrary to much of the mathematics of the era, it was better not to introduce intuitive ideas such as time. These works presented. a sample of a new way of developing analysis, to the foundations of mathematical analysis he contributed the introduction of a fully rigorous ε–δ definition of a mathematical limit. Bolzano was the first to recognize the greatest lower bound property of the real numbers, like several others of his day, he was skeptical of the possibility of Gottfried Leibnizs infinitesimals, that had been the earliest putative foundation for differential calculus. Bolzano also gave the first purely analytic proof of the theorem of algebra. He also gave the first purely analytic proof of the intermediate value theorem, the logical theory that Bolzano developed in this work has come to be acknowledged as ground-breaking. Other works are a four-volume Lehrbuch der Religionswissenschaft and the metaphysical work Athanasia, Bolzano also did valuable work in mathematics, which remained virtually unknown until Otto Stolz rediscovered many of his lost journal articles and republished them in 1881. Bolzano begins his work by explaining what he means by theory of science, human knowledge, he states, is made of all truths that men know or have known