# Mathematician:Bernhard Placidus Johann Nepomuk Bolzano

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## Contents

## Mathematician

Bohemian priest who was also a mathematician, logician, theologian and philosopher.

A major precursor of the wave of development of analysis in the late $19$th century.

Proved the Bolzano-Weierstrass Theorem, independently of (and earlier than) Karl Weierstrass.

Gave the first analytical proof of the Intermediate Value Theorem (which is also known as Bolzano's Theorem).

## Nationality

Bohemian

## History

- Born: 5 Oct 1781 in Prague, Bohemia, Austrian Habsburg domain (now Czech Republic)
- 1791 to 1796: Attended Piarist Gymnasium in Prague
- 1796: Entered faculty of Philosophy at Charles University of Prague, studying philosophy, physics and mathematics
- 1799 to 1800: undertook research in mathematics with František Josef Gerstner
- 1800: Began three years of theological study at Charles University, at the same time preparing a doctoral thesis in geometry
- 1804: Received doctorate in mathematics and ordained as a Roman Catholic priest
- 1807: Granted a chair at University of Prague in the philosophy of religion
- 1815: Elected to the Royal Bohemian Society of Sciences
- 1816: Charges brought against him at the court of Vienna
- 1818: Elected Dean of Faculty of Philosophy at Charles University
- December 1819: Dismissed from his position, placed under house arrest and forbidden to publish.
- 1821 to 1825: Tried by the Church, required to recant his supposed heresies
- 1823 to 1830: Lived during the summer near Techobuz, with his friends Josef and Anna Hoffmann; during the winter lived in Prague with his brother Johann
- 1830 to 1841: Lived throughout the year with the Hoffmanns
- 1841: Move with the Hoffmanns to Prague, became active in Royal Bohemian Society of Sciences
- 1842 to 1843: President of Royal Bohemian Society of Sciences
- Died: 18 Dec 1848 in Prague, Bohemia (now Czech Republic)

## Theorems and Definitions

- Intermediate Value Theorem, also known as Bolzano's Theorem
- Bolzano-Weierstrass Theorem (independently of Karl Weierstrass)

Results named for **Bernhard Placidus Johann Nepomuk Bolzano** can be found here.

## Pulications

- 1810:
*Beyträge zu einer begründeteren Darstellung der Mathematik. Erste Lieferung* - 1816:
*Der binomische Lehrsatz* - 1816:
*On the Condition of the Two Nationalities in Bohemia* - 1817:
*Rein analytischer Beweis*(Pure Analytical Proof) - 1837:
*Wissenschaftslehre*(Theory of Science) - 1851:
*Paradoxien des Unendlichen*(The Paradoxes of the Infinite) (contains the first instance in mathematical literature of the term*Set*)

## Also known as

Some sources render his name as **Bernard Bolzano**.

## Critical View

*Weierstrass and Bolzano march arm-in-arm together through the history of mathematics, but not nearly enough seems to be known about Bolzano.*- -- George F. Simmons:
*Calculus Gems*($1992$)

- -- George F. Simmons:

## Sources

- John J. O'Connor and Edmund F. Robertson: "Bernhard Placidus Johann Nepomuk Bolzano": MacTutor History of Mathematics archive

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($\text {1815}$ – $\text {1897}$): Footnote $5$ - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next): Entry:**Bolzano, Bernhard Placidus**(1781-1848) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**Bolzano, Bernhard Placidus**(1781-1848)