Paul du Bois-Reymond (nonfiction): Difference between revisions
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[[File:Paul_Du_Bois-Reymond_Heidelberg.jpg|thumb|Paul David Gustav du Bois-Reymond.]]'''Paul David Gustav du Bois-Reymond''' (2 December 1831 – 7 April 1889) was a German mathematician who was born in Berlin and died in Freiburg | [[File:Paul_Du_Bois-Reymond_Heidelberg.jpg|thumb|Paul David Gustav du Bois-Reymond.]]'''Paul David Gustav du Bois-Reymond''' (2 December 1831 – 7 April 1889) was a German mathematician who was born in Berlin and died in Freiburg. | ||
His thesis was concerned with the mechanical equilibrium of fluids. He worked on the theory of functions and in mathematical physics. His interests included Sturm–Liouville theory, integral equations, variational calculus, and [[Fourier series (nonfiction)|Fourier series]]. In this latter field, he was able in 1873 to construct a continuous function whose Fourier series is not convergent. His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere. | His thesis was concerned with the mechanical equilibrium of fluids. He worked on the theory of functions and in mathematical physics. His interests included Sturm–Liouville theory, integral equations, variational calculus, and [[Fourier series (nonfiction)|Fourier series]]. In this latter field, he was able in 1873 to construct a continuous function whose Fourier series is not convergent. His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere. | ||
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Du Bois-Reymond also established that a trigonometric series that converges to a continuous function at every point is the Fourier series of this function. He also discovered a proof method that later became known as the [[Cantor's diagonal argument (nonfiction)|Cantor's diagonal argument]]. | Du Bois-Reymond also established that a trigonometric series that converges to a continuous function at every point is the Fourier series of this function. He also discovered a proof method that later became known as the [[Cantor's diagonal argument (nonfiction)|Cantor's diagonal argument]]. | ||
His name is also associated with the fundamental lemma of calculus of variations of which he proved a refined version based on that of Lagrange. | His name is also associated with the fundamental lemma of calculus of variations of which he proved a refined version based on that of [[Joseph-Louis Lagrange (nonfiction)|Joseph-Louis Lagrange]]. | ||
He developed a theory of infinitesimals, observing: | |||
<blockquote>The infinitely small is a mathematical quantity and has all its properties in common with the finite […] A belief in the infinitely small does not triumph easily. Yet when one thinks boldly and freely, the initial distrust will soon mellow into a pleasant certainty ... A majority of educated people will admit an infinite in space and time, and not just an "unboundedly large". But they will only with difficulty believe in the infinitely small, despite the fact that the infinitely small has the same right to existence as the infinitely large. […] | |||
</blockquote> | |||
— Paul du Bois-Reymond, ''Über die Paradoxen des Infinitär-Calcüls'' ("On the paradoxes of the infinitary calculus"), 1877. | |||
He was the brother of physician and physiologist [[Emil du Bois-Reymond (nonfiction)|Emil du Bois-Reymond]]. | |||
== In the News == | == In the News == | ||
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* [[Cantor's diagonal argument (nonfiction)]] | * [[Cantor's diagonal argument (nonfiction)]] | ||
* [[Emil du Bois-Reymond (nonfiction)]] | |||
* [[Fourier series (nonfiction)]] | * [[Fourier series (nonfiction)]] | ||
* [[Joseph-Louis Lagrange (nonfiction)]] | |||
* [[Mathematician (nonfiction)]] | * [[Mathematician (nonfiction)]] | ||
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* [https://en.wikipedia.org/wiki/Paul_du_Bois-Reymond Paul du Bois-Reymond] @ Wikipedia | * [https://en.wikipedia.org/wiki/Paul_du_Bois-Reymond Paul du Bois-Reymond] @ Wikipedia | ||
[[Category:Nonfiction (nonfiction)]] | [[Category:Nonfiction (nonfiction)]] | ||
[[Category:Mathematicians (nonfiction)]] | [[Category:Mathematicians (nonfiction)]] | ||
[[Category:People (nonfiction)]] | [[Category:People (nonfiction)]] | ||
[[Category:Portraits (nonfiction)]] | |||
Latest revision as of 09:56, 15 November 2017
Paul David Gustav du Bois-Reymond (2 December 1831 – 7 April 1889) was a German mathematician who was born in Berlin and died in Freiburg.
His thesis was concerned with the mechanical equilibrium of fluids. He worked on the theory of functions and in mathematical physics. His interests included Sturm–Liouville theory, integral equations, variational calculus, and Fourier series. In this latter field, he was able in 1873 to construct a continuous function whose Fourier series is not convergent. His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere.
Du Bois-Reymond also established that a trigonometric series that converges to a continuous function at every point is the Fourier series of this function. He also discovered a proof method that later became known as the Cantor's diagonal argument.
His name is also associated with the fundamental lemma of calculus of variations of which he proved a refined version based on that of Joseph-Louis Lagrange.
He developed a theory of infinitesimals, observing:
The infinitely small is a mathematical quantity and has all its properties in common with the finite […] A belief in the infinitely small does not triumph easily. Yet when one thinks boldly and freely, the initial distrust will soon mellow into a pleasant certainty ... A majority of educated people will admit an infinite in space and time, and not just an "unboundedly large". But they will only with difficulty believe in the infinitely small, despite the fact that the infinitely small has the same right to existence as the infinitely large. […]
— Paul du Bois-Reymond, Über die Paradoxen des Infinitär-Calcüls ("On the paradoxes of the infinitary calculus"), 1877.
He was the brother of physician and physiologist Emil du Bois-Reymond.
In the News
Fiction cross-reference
Nonfiction cross-reference
- Cantor's diagonal argument (nonfiction)
- Emil du Bois-Reymond (nonfiction)
- Fourier series (nonfiction)
- Joseph-Louis Lagrange (nonfiction)
- Mathematician (nonfiction)
External links:
- Paul du Bois-Reymond @ Wikipedia