Jørgen Pedersen Gram: Difference between revisions

Jørgen Pedersen Gram
Jørgen Pedersen Gram
Born	27 June 1850; Nustrup, Duchy of Schleswig, Denmark
Died	29 April 1916 (aged 65); Copenhagen, Denmark
Known for	Gram matrix; Gram points; Gram polynomials; Gram's theorem; Gram–Charlier A series; Gram–Euler theorem; Gram–Schmidt process

Browse history interactively

← Previous edit

Content deleted Content added

VisualWikitext

Inline

Latest revision as of 21:04, 20 November 2024

Jørgen Pedersen Gram (27 June 1850 – 29 April 1916) was a Danish actuary and mathematician who was born in Nustrup, Duchy of Schleswig, Denmark and died in Copenhagen, Denmark.

Important papers of his include On series expansions determined by the methods of least squares, and Investigations of the number of primes less than a given number. The mathematical method that bears his name, the Gram–Schmidt process, was first published in the former paper, in 1883.^[1]

For number theorists his main fame is the series for the Riemann zeta function (the leading function in Riemann's exact prime-counting function). Instead of using a series of logarithmic integrals, Gram's function uses logarithm powers and the zeta function of positive integers. It has recently been supplanted by a formula of Ramanujan that uses the Bernoulli numbers directly instead of the zeta function.

In control theory, the Gramian or Gram matrix is an important contribution named after him. The Controllability Gramian and Observability Gramian are both important in the analysis of the stability of control systems. The Gram matrix is also important in deep learning, where it is used to represent the distribution of features in style transfer.

Gram was the first mathematician to provide a systematic theory of the development of skew frequency curves, showing that the normal symmetric Gaussian error curve was but one special case of a more general class of frequency curves.^[2]

Gram's theorem, the Gram–Charlier series, and Gram points are also named after him.

He died on his way to a meeting of the Royal Danish Academy after being struck by a cyclist.^[3]

References

Notes

^ David Poole (2005). Linear Algebra. Thomson Brooks/Cole. p. 387. ISBN 0-534-99845-3.
^ Helen Mary Walker (1929). Studies in the History of Statistical Method: With Special Reference to Certain Educational Problems. The Williams & Wilkins Company. pp. 77, 81.
^ O'Connor, John J.; Robertson, Edmund F., "Jørgen Pedersen Gram", MacTutor History of Mathematics Archive, University of St Andrews

Bibliography

Gram, J. P. (1884). "Undersøgelser angaaende Maengden af Primtal under en given Graeense". Det K. Videnskabernes Selskab. 2: 183–308.

This article about a European mathematician is a stub. You can help Wikipedia by expanding it.

This article about a Danish scientist is a stub. You can help Wikipedia by expanding it.

[1] David Poole (2005). Linear Algebra. Thomson Brooks/Cole. p. 387. ISBN 0-534-99845-3.

[2] Helen Mary Walker (1929). Studies in the History of Statistical Method: With Special Reference to Certain Educational Problems. The Williams & Wilkins Company. pp. 77, 81.

[3] O'Connor, John J.; Robertson, Edmund F., "Jørgen Pedersen Gram", MacTutor History of Mathematics Archive, University of St Andrews

[1]

[2]

[3]

@@ Line 1: / Line 1: @@
+{{Short description|Danish actuary and mathematician (1850–1916)}}
-{{Refimprove|date=October 2008}}
+{{Infobox scientist
-[[File:Jorgen Gram.jpg|thumb|Jørgen Pedersen Gram in an undated photo]]
+| name         = Jørgen Pedersen Gram
-'''Jørgen Pedersen Gram''' (June 27, 1850 – April 29, 1916) was a [[Denmark|Danish]] [[actuary]] and [[mathematician]] who was born in [[Nustrup]], Duchy of [[Schleswig]], [[Denmark]] and died in [[Copenhagen]], Denmark.
+| image        = Jørgen Pedersen Gram by Johannes Hauerslev.jpg
+|birth_date        = {{birth date|1850|06|27|df=y}}
+|birth_place       = [[Nustrup]], [[Duchy of Schleswig]], [[Denmark]]
+|death_date        = {{death date and age|1916|04|29|1850|06|27|df=y}}
+|death_place       = [[Copenhagen]], [[Denmark]]
+|known_for = [[Gram matrix]]<br>[[Riemann–Siegel theta function#Gram points|Gram points]]<br>[[Discrete Chebyshev polynomials|Gram polynomials]]<br>[[Gram's theorem]]<br>[[Gram–Charlier A series]]<br>[[Gram–Euler theorem]]<br>[[Gram–Schmidt process]]
+}}
+'''Jørgen Pedersen Gram''' (27 June 1850 – 29 April 1916) was a [[Denmark|Danish]] [[actuary]] and [[mathematician]] who was born in [[Nustrup]], Duchy of [[Schleswig]], [[Denmark]] and died in [[Copenhagen]], Denmark.
-Important papers of his include ''On series expansions determined by the methods of least squares'', and ''Investigations of the number of primes less than a given number''.  The mathematical method that bears his name, the [[Gram–Schmidt process]], was first published in the former paper, in 1883.<ref>{{cite book|title=Linear Algebra|author=David Poole|pages=387|publisher=Thomson Brooks/Cole|date=2005|isbn=0-534-99845-3}}</ref>  The [[Gramian matrix]] is also named after him.
+Important papers of his include ''On series expansions determined by the methods of least squares'', and ''Investigations of the number of [[Prime number|primes]] less than a given number''.  The mathematical method that bears his name, the [[Gram–Schmidt process]], was first published in the former paper, in 1883.<ref>{{cite book|title=Linear Algebra|author=David Poole|pages=387|publisher=Thomson Brooks/Cole|year=2005|isbn=0-534-99845-3}}</ref>
-For number theorists his main fame is the series for the [[Riemann zeta function]] (the leading function in [[Riemann]]'s exact [[prime-counting function]]). Instead of using a series of logarithmic integrals, Gram's function uses logarithm powers and the zeta function of positive integers. It has recently been supplanted by a formula of [[Ramanujan]] that uses the [[Bernoulli number]]s directly instead of the zeta function.
+For number theorists his main fame is the series for the [[Riemann zeta function]] (the leading function in [[Riemann]]'s exact [[prime-counting function]]). Instead of using a series of [[Logarithmic integral function|logarithmic integrals]], Gram's function uses logarithm powers and the [[zeta function]] of positive integers. It has recently been supplanted by a formula of [[Ramanujan]] that uses the [[Bernoulli number]]s directly instead of the zeta function.
-Gram was the first mathematician to provide a systematic theory of the development of skew frequency curves, showing that the normal symmetric Gaussian [[error curve]] was but one special case of a more general class of frequency curves.<ref>{{cite book|title=Studies in the History of Statistical Method: With Special Reference to Certain Educational Problems|author=Helen Mary Walker|publisher=The Williams &amp; Wilkins Company|date=1929|pages=77, 81}}</ref>
+In control theory, the Gramian or [[Gram matrix]] is an important contribution named after him.  The [[Controllability Gramian]] and [[Observability Gramian]] are both important in the analysis of the stability of [[control systems]].  The Gram matrix is also important in [[deep learning]], where it is used to represent the distribution of features in [[style transfer]].
-He died after being struck by a bicycle.<ref>{{MacTutor Biography|id=Gram}}</ref>
+Gram was the first mathematician to provide a systematic theory of the development of skew frequency curves, showing that the normal symmetric Gaussian [[error curve]] was but one special case of a more general class of frequency curves.<ref>{{cite book|title=Studies in the History of Statistical Method: With Special Reference to Certain Educational Problems|url=https://archive.org/details/in.ernet.dli.2015.264023|author=Helen Mary Walker|publisher=The Williams & Wilkins Company|year=1929|pages=[https://archive.org/details/in.ernet.dli.2015.264023/page/n94 77], 81}}</ref>
-==See also==
-* [[Logarithmic integral function]]
+[[Gram's theorem]], the [[Edgeworth series#Gram–Charlier A series|Gram–Charlier series]], and [[Riemann–Siegel theta function#Gram points|Gram points]] are also named after him.
-* [[Prime number]]
-* [[Riemann-Siegel theta function]] which contain Gram points.
+He died on his way to a meeting of the [[Royal Danish Academy of Sciences and Letters|Royal Danish Academy]] after being struck by a cyclist.<ref>{{MacTutor Biography|id=Gram}}</ref>
 ==References==
+'''Notes'''
 {{reflist}}
-==Bibliography==
+'''Bibliography'''
-* {{cite journal|author=Gram, J. P.|title=Undersøgelser angaaende Maengden af Primtal under en given Graeense.|journal=Det K. Videnskabernes Selskab|volume=2|pages=183&ndash;308|date=1884}}
+* {{cite journal|author=Gram, J. P.|title=Undersøgelser angaaende Maengden af Primtal under en given Graeense.|journal=Det K. Videnskabernes Selskab|volume=2|pages=183&ndash;308|year=1884}}
+<!--spacing-->
-{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
-| NAME              = Gram, Jorgen Pedersen
+{{Authority control}}
-| ALTERNATIVE NAMES =
-| SHORT DESCRIPTION =
-| DATE OF BIRTH     = June 27, 1850
-| PLACE OF BIRTH    =
-| DATE OF DEATH     = April 29, 1916
-| PLACE OF DEATH    =
-}}
 {{DEFAULTSORT:Gram, Jorgen Pedersen}}
-[[Category:Danish mathematicians]]
+[[Category:19th-century Danish mathematicians]]
-[[Category:19th-century mathematicians]]
+[[Category:20th-century Danish mathematicians]]
-[[Category:20th-century mathematicians]]
 [[Category:1850 births]]
 [[Category:1916 deaths]]
+[[Category:Cycling road incident deaths]]
+[[Category:Linear algebraists]]
+[[Category:Pedestrian road incident deaths]]
+[[Category:Road incident deaths in Denmark]]
+[[Category:People from the Duchy of Schleswig]]
-{{euro-mathematician-stub}}
+{{europe-mathematician-stub}}
 {{denmark-scientist-stub}}
-[[da:Jørgen Pedersen Gram]]
-[[de:Jørgen Pedersen Gram]]
-[[fr:Jørgen Pedersen Gram]]
-[[it:Jørgen Pedersen Gram]]
-[[nl:Jørgen Pedersen Gram]]
-[[pt:Jørgen Pedersen Gram]]
-[[sk:Jørgen Pedersen Gram]]
-[[sl:Jørgen Pedersen Gram]]
-[[sv:Jørgen Pedersen Gram]]

Authority control databases
International	ISNI VIAF WorldCat
National	Germany Netherlands
Academics	Scopus zbMATH MathSciNet
Other	IdRef