Bernard Placidus Johann Nepomuk Bolzano (October 5, 1781 – December 18, 1848) was a Czech mathematician, theologian, philosopher and logician. He was innate within Prague.

Bolzano entered a University of Prague in 1796 & studied maths, philosophy and physics. Starting inside 1800, he also began researching theology, & was appointed to the chair of religion around 1805. He proved to exist as the popular lecturer non only inside religion however as well philosophy, & was elective head of the department of philosophy around 1818. Notwithstanding, his political convictions (which he was inclined to part by owning others by having a few frequency) one of these days proved to exist as as well liberal for the conservative institution, and within 1819 he was dismissed from his positions & exiled to the countryside for the remainder of his life.

Although forbidden to publish inside mainstream journals as a trouble of his exile, Bolzano continued to produce his ideas & publish the two either around his have or even in obscure Eastern European journals. Bolzano's early function Paradoxien des Unendlichen (The Paradoxes of the Infinite) was greatly admired by many of the eminent logistician of the day, including Charles Peirce, Georg Cantor, and Richard Dedekind. Despite such ground-innovative contributions to the foundations of mathematical analysis as the introduction of the fully rigorous ε-δ definition of a mathematical limit and the first purely analytic proof of the Intermediate Value Theorem (also known as Bolzano's theorem), much of Bolzano's work remained virtually unknown until Otto Stolz rediscovered many of his lost journal articles and republished them in 1881.

Now he is mostly remembered for the Bolzano-Weierstrass theorem, which Karl Weierstrass developed independently and published years when Bolzano's number one proof & which was at a start known as the Weierstrass theorem until historiographer of math found Bolzano's sooner act.

Around his philosophy, Bolzano developed an ontology in which the world consisted of actual and non-actual objects. Actual objects were farther divided into substances such as tables or mortal beings & a disciple to substances like colors or even mental states. Non-actual objects consisted of non-material things such as numbers and what Bolzano known as "Sätze-an-sich" ("Ideas-as-such"). A Sätze-an-sich involved what come au fond logical axioms and abstract truths, which Bolzano believed to exist independently of the man mind.

Within his 1837 "Theory of Science" he attempted to provide logical foundations for all sciences, building in abstractions rather section-relation, abstract objects, attributes, phrase-shapes, idewhen-as-such, propositions, sums & sets, collections, substances, adherences, subjective ideas, judgments, & phrase-occurrences. These tries were in essence an extension of his earliest thoughts in the philosophy of math, e.g. his 1810 Beiträge where he emphasized a distinction between a objective relationship between logical results & my subjective recognition one modems. For Bolzano, it was non enough that i personally only stand confirmation of natural or even mathematical truths, however like it was a proper role of the sciences (both pure and applied) to seek out justification in terms of the fundamental truths that may or may not appear to be obvious to our intuitions.