BOLZANO, Bernhard

B. was born on the 5th of October 1781 in Prague as a son of an art dealer Bernard Pompeius B (1737-1816) and Mary Cecile Maurer (1796-1821). From 1796, after attending a piarystic gymnasium, he studied philosophy, mathematic and logic at University of Prague and, from 1800 onwards, a theology. While still a student he published his first work Deliberations regarding certain subjects of elementary geometry (1804). While competing for a position of the professor of elementary mathematic as well as for the position of a recently introduced university catechist, he managed to occupy a second place on both occasions. In March 1805 he was appointed catechist with the duty of teaching religious education and obligation to influence the students affected by the French revolution. His lectures about religious morality had drawn an attention of a broader intellectual public in Prague. Simultaneously he prepared his second mathematical work Contributions to elementary interpretation of mathematics (1810). While in his first work he tried to alter the traditional interpretation of Euclid’s elements – enabling merely approximate results by using vector algebra - his second work stressed the forms of basic rules of mathematical logic and the construction of mathematical theory.
In 1815 he became a dean of the Faculty of Arts in Prague as well as a member of the Royal Czech Academy of Sciences. Acute tuberculosis between 1815/16 thwarted the fulfillment of his teaching obligations. Nevertheless two of his minor papers were published in 1816/17: Die Binomische Lehrsatz und als Folgerung aus ihm der polynomische, und die Reihen, die zur Berechnung der Logarithmen und Exponentialgrößen dienen, genauer als bisher erwiesen (1816) in Rein analytischer Beweis des Lehrsatzes, dass zwischen je zwei Werthen die ein entgegengesetzes Resultat gewähren, wenigstens eine reelle Wurzel der Gleichung liege (1817). In these papers he offered a new principal concept of mathematical analysis, a few years before the manual of August L. Cauchy (1789-1875) Cours d’analyse (1820) was published. He suggested a new concept of mathematical analysis by defining terms such as marginal limit, continuity, derivate, interval and infinity. B has replaced Euler’s congruity of the function with analytical finding with today normative coordination of two elements. It was here that he also offered a standard for Cauchy’s convergent criteria.
In his work from 1817 B. defined ‘three problems of rectification, complanation and cubation’ the basic conceptions which were leading towards topological understanding of geometrical concepts (continuum, dimension, accumulation point, interval as well as defining the concept of closed curve which is in accordance with contemporary Jordan law) and were generally accepted in the field of mathematic only a century later. These concepts brought B to the serious mathematical interpretation of existence by constructing the first law of Euclidean elements. After resuming his lectures, B was charged by some stranger as ‘a person known all over Czech lands by his unconventional manner of teaching the religious doctrines as well as sophist plotting… and that he is an example of a blasphemous renunciation of reliable and insuperable doctrine’. The accusations have reached Rome and on the 24. of December 1819 B was discharged from his position. The process which dragged for five odd years should force B to renounce his manner of interpreting the religion through ethics. B had also struggled against feudalism, advocated an abolition of aristocratic titles and emphasized equality among people. Intervention from Josef Dobrovský and a threat to publish B’s replication finally concluded the process. B had left Prague and had been living and working on the tenure of his friends in Radič and Jirny but for the most of the time by the Hoffmann family in Tĕchobuz, not far from Pacov (app. 100 km south of Prague). In an effort to prove the proper truth B published eleven works in 1830s within the field of ethnic, social and religious themes. They were published outside the boundaries of the Hapsburg monarchy. His mathematical works, however, remained unpublished. The only exceptions being in 1837 published Wissenschaftshlehre (Theory of Science) that was discussing various conceptions of predicative functions, probable conclusions of implications, and a like. The major part of his mathematical works was published only after his death: Mengentheorie (The Theory of Multitudes, 1851), Theorie der Funktion (The Theory of Function, 1860), Theorie der reellen Zahlen (The Theory of Real Numbers, 1862). Incited from the side of Mrs. Hoffmann, B wrote his autobiography in 1863, and published it along with brief essay about the thoughts Von dem besten Staate (The Best in the State). The autobiography was dedicated to the students and had been circulating within the intellectual parish of Prague.
At the beginning of 1840s B returned to Prague where he actively occupied himself with the work on the Royal Czech Society of Sciences. In the same year in the month of December he succumbed to pneumonia.