nLab Bernard Bolzano

Bernard Bolzano (1789-1848) was a Bohemian mathematician, logician, and philosopher.

In his lifetime he was renowned perhaps mainly for his Wissenschaftslehre which puts forth an encompassing theory of science. In mathematics, much of his work became well known only after his death, but he can be regarded as an early proponent of epsilontic analysis and the introduction of rigor in analysis, as for example in the result that became to be known as the Bolzano-Weierstrass theorem.

• Wikipedia entry

• SEP: Bolzano, Bolzano’s Logic

• MacTutor biography

Selected writings

list of collected works: 10338.dmlcz/400001

Laying early foundations of modern analysis (epsilontic analysis) in an early rigorous proof of the intermediate value theorem via what is now called the Bolzano-Weierstrass theorem:

• Bernard Bolzano: Rein analytischer Beweis des Lehrsatzes, dass zwischen je zwey Werthen, die ein entgegengesetztes Resultat gewähren, wenigstens eine reelle Wurzel der Gleichung liege, Gottlieb Haase, Prague (1817) [eudml:202403, dml.cz:400016, pdf, pdf]

category: people