Bernhard Bolzano Biography

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World of Mathematics on Bernhard Bolzano

Bernhard Placidus Johann Nepomuk Bolzano was a Czechoslovakian theologian, philosopher, and mathematician who wrote and published pioneering works on infinite set series and the infinitesimal.

Born in Prague, Bohemia in 1781, Bolzano entered the University of Prague at the age of 15 to study philosophy and mathematics. Four years later, he began theological studies at University, while simultaneously working on a doctoral thesis in geometry. In 1804, Bolzano was ordained a Roman Catholic priest, and received his doctorate in mathematics and an appointment to the chair of philosophy and religion at the University of Prague.

Over the next thirteen years, Bolzano published a number of mathematical works and papers. Rein analytischer Beweis (Pure Analytical Proof) published in 1817, contained a non-geometric, arithmetic proof of the location theorem in algebra. One of Bolzano's contemporaries, the French mathematician Augustin Cauchy, published a similar work several years later that received wider circulation and considerably more attention from the mathematical community. The similar mathematical concepts outlined by both men are thought to be a coincidental simultaneous discovery, as there is no written account of the two mathematicians ever meeting, nor of Cauchy having any familiarity with Bolzano's work.

Because of his pacifist views and his open criticism of the theology texts used at Prague, the Austrian government forced the suspension of Bolzano from his University position in 1819 under charges of heresy. Bolzano's work was largely censored in Austria from then on, but he managed to publish several more important mathematical papers over the next several decades. He was also active in the Royal Bohemian Society, and was named director in 1842.

Bolzano published Wissenschaftslehre, a comprehensive account of science and knowledge, in 1837. He continued his work with Paradoxien des Unendlichen (Paradoxes of the Infinite), an insightful work on infinite sets and theories of mathematical infinity that was published in 1850, several years after Bolzano's death. Bolzano left many unpublished manuscripts at the time of his death, some of which were published by students decades later. Although his ideas were revolutionary to the field of mathematics, they remained largely unnoticed until "rediscovered" by mathematicians and scholars that followed him. In some cases, Bolzano received posthumous recognition for his theories. The Bolzano-Weierstrass theorem, which states that a bounded set S containing infinitely many elements contains at least one limit point, was a mathematical concept originated by Bolzano, but rediscovered and reintroduced to the mathematical community by the University of Berlin's Karl Weierstrass some fifty years after Bolzano's original supposition.