# Mathematician:Karl Theodor Wilhelm Weierstrass

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## Contents

## Mathematician

German mathematician whose main work concerned the rigorous foundations of calculus.

Known as "the father of modern analysis".

Champion beer-drinker and expert fencer.

## Nationality

German

## History

- Born: 31 Oct 1815, Ostenfelde, Westphalia (now Germany)
- Died: 19 Feb 1897, Berlin, Germany

## Achievements

- Pioneered the $\epsilon-\delta$ definition of continuity.
- Was able thereby to formulate proofs of the Bolzano-Weierstrass Theorem (which had been proved earlier, independently of Weierstrass, by Bernhard Bolzano), the Intermediate Value Theorem and the Heine-Borel Theorem.
- Made significant advancements in the field of calculus of variations.

## Theorems and Definitions

- Weierstrass's Theorem
- Weierstrass Approximation Theorem
- Weierstrass-Casorati Theorem (with Felice Casorati)
- Weierstrass E-Function
- Weierstrass Elementary Factor
- Weierstrass's Elliptic Function
- Weierstrass-Erdmann Corner Conditions
- Weierstrass Function
- Weierstrass M-Test
- Weierstrass's Necessary Condition
- Weierstrass Preparation Theorem
- Weierstrass Product Inequality
- Weierstrass Product Theorem
- Weierstrass Factorization Theorem
- Weierstrass Intermediate Value Theorem (also known as Bolzano's Theorem for Bernhard Bolzano)
- Weierstrass Extreme Value Theorem
- Weierstrass Substitution
- Bolzano-Weierstrass Theorem (independently of Bernhard Bolzano)
- Enneper-Weierstrass Parameterization (with Alfred Enneper)
- Hermite-Lindemann-Weierstrass Theorem (with Charles Hermite and Ferdinand von Lindemann)
- Sokhotski-Weierstrass Theorem (with Yulian Vasilievich Sokhotski)
- Stone-Weierstrass Theorem (with Marshall Harvey Stone) (a generalization of the Weierstrass Approximation Theorem)

Results named for **Karl Theodor Wilhelm Weierstrass** can be found here.

Definitions of concepts named for **Karl Theodor Wilhelm Weierstrass** can be found here.

## Publications

- 1854:
*Zur Theorie der Abelschen Funktionen*(*J. reine angew. Math.***Vol. 47**: 289 – 306) - 1856:
*Theorie der Abelschen Funktionen* - 1894:
*Abhandlungen-1* - 1897:
*Abhandlungen-2* - 1902:
*Vorl. ueber die Theorie der Abelschen Transcendenten* - 1915:
*Abhandlungen-3* - 1927:
*Vorl. ueber Variationsrechnung*

## Notable Quotes

*A mathematician who is not also something of a poet will never be a complete mathematician.*- -- Quoted in 1937: Eric Temple Bell:
*Men of Mathematics*:*They Say: What Say They? : Let Them Say*

- -- Quoted in 1937: Eric Temple Bell:

*The infinite emptiness and boredom of those years would have been unendurable without the hard work that made me a recluse -- even if I was rated rather a good fellow by the circle of my friends among the Junkers, lawyers, and young officers of the community ... The present offered nothing worth mentioning, and it was not my custom to speak of the future.*

## Critical View

*You should study with Weierstrass in Berlin; he is the master of us all.*

## Sources

- John J. O'Connor and Edmund F. Robertson: "Karl Theodor Wilhelm Weierstrass": MacTutor History of Mathematics archive

- 1937: Eric Temple Bell:
*Men of Mathematics*... (previous) ... (next):*They Say: What Say They? : Let Them Say* - 1937: Eric Temple Bell:
*Men of Mathematics*: Chapter $\text{XXII}$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($1815$ – $1897$)