Bernard Bolzano

Bernardus Placidus Johann Nepomuk Bolzano ( born October 5, 1781 Prague, † December 18, 1848 ) was a Catholic priest, philosopher and mathematician. The theorem of Bolzano - Weierstrass is named after him.

Life

Bolzano's father was an art dealer from Nesso ( province of Como, Italy), his mother the daughter of a German Prague businessman. His younger brother was the Prague physician Peter Bolzano ( 1794-1818 ). In his childhood he was strongly influenced by the religion of his family. Already in his youth he worked on scientific and policy literature.

After he had from 1791 to 1796 attended the Gymnasium, he studied philosophy, mathematics and physics at Charles University in Prague. In the fall of 1801, he began the study of theology, which he received his doctorate in the winter semester 1804/ 05 and the degree of Dr. phil. obtained. From 1786 to 1872 only a test and not a thesis was required for at Austrian universities. In 1805 he was ordained a priest and temporary owner of the newly established chair of philosophy of religion. Although he tried to the chair of elementary mathematics, it has been otherwise occupied. On 2 October 1806, he was finally promoted to full professor.

He was born on February 19, 1815 Member of the Royal Bohemian Society of Sciences and in 1818 Dean of the Faculty of Arts of Charles University and director of the scientific department of the Royal Bohemian Society of Sciences.

Of his students, he was admired for his liberal and Bohemian- patriotic views. Bolzano, the son of an Italian and a Prague Germans wanted the nationalisms overcome in a cross- Bohemian patriotism. Josef Miihlberger writes in his History of German Literature in Bohemia ( Munich-Vienna 1981): "One of the barriers which divide he also scored nationalism. Bolzano was coined a founder and a pillar of the Bohemian, who felt obliged the two nations shared Bohemian country about the two nations out of the country in the same love and responsibility. " His lectures were of social criticism and analytical acumen. Bolzano criticized the Austrian constitution and represented pacifist and socialist views, so he was on 24 December 1819 founded by alleged heresies, relieved by Emperor Franz I. of his office. He was prohibited from continuing to accept public activities. The dismissal was the culmination of a 1816-1825 continuous investigation against Bolzano, in which he threatened the detention. The first volume of his speeches edification (1813 ) and his textbook of religious studies were 1828 and 1839, respectively set to the index. After Francis I had died in 1835, the monitoring Bolzano was mitigated and in the 1840s it has been approved, to be published in the Proceedings of the Royal Bohemian Society of Sciences work not theological content.

From 1823 he spent the summer months in the South Bohemian village of Těchobuz on the estate of the Hoffmann family. From 1830 on, he lived there all. In the 1830s he focused his studies on real numbers. He wrote a book on real functions and invented the first example of a continuous nowhere differentiable function ( Bolzanofunktion ).

Shortly before 1842 Anna Hoffmann died, he returned to his brother back to Prague. On December 18, 1848 Bolzano died in Prague and left an extensive handwritten estate.

In 1975, Bernard Bolzano- alley was named after him in Vienna Floridsdorf.

Work

As a mathematician, he pursued basic research in analysis. He constructed the first probably a function that is continuous everywhere but nowhere differentiable ( Bolzanofunktion ). He also dealt with large and infinitely small numbers.

In an essay of 1817 he proved the intermediate value theorem and introduced Cauchy sequences, four years before Augustin- Louis Cauchy. Bolzano's work to a more rigorous foundations of calculus were scarcely noticed by his contemporaries as opposed to those of Cauchy and appreciated only in the second half of the 19th century (for example, by Hermann Hankel, Hermann Amandus Schwarz, Otto Stolz ). Named after him is the mathematical theorem of Bolzano - Weierstrass.

Bolzano's philosophical work is of great importance. Especially in his four-volume science teaching, he makes numerous developments and trends of the later phenomenology and the subsequent analytic philosophy anticipated. Noteworthy is also the range of his philosophical work: it ranges from utilitarianism (ethics), on logic, ontology, epistemology and philosophy of science to the philosophy of religion into it, with Bolzano quite dealing aesthetics in his edifying speeches with general questions of social life (eg patriotism ).

Because of Bolzano's oppositional attitude to the imperial authority remained in his lifetime, many of his works in manuscript form and were only rediscovered long after his death. The following are some of his works are listed by year of publication.