Jørgen Pedersen Gram: Difference between revisions
wlnk |
Inline the see-also section, ensuring all terms are mentioned and linked somewhere in the text. |
||
| Line 11: | Line 11: | ||
'''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. |
'''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|year=2005|isbn=0-534-99845-3}}</ref> [[Gram's theorem]] and the [[ |
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> [[Gram's theorem]] and the Gramian or [[Gram matrix]] are also named after him. |
||
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|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> |
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> |
||
Other mathematical achievements that bear his name include the [[Gram–Charlier A series|Gram–Charlier series]], [[Riemann–Siegel theta function#Gram points|Gram points]]. |
|||
| ⚫ | |||
| ⚫ | |||
==See also== |
|||
* [[Logarithmic integral function]] |
|||
* [[Prime number]] |
|||
* [[Gram–Charlier A series|Gram–Charlier series]] |
|||
* [[Riemann–Siegel theta function#Gram points|Gram points]] |
|||
* [[Gram–Schmidt process]] |
|||
==References== |
==References== |
||
Revision as of 20:09, 13 April 2022
Jørgen Pedersen Gram | |
|---|---|
 | |
| Born | 27 June 1850 |
| Died | 29 April 1916 (aged 65) |
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] Gram's theorem and the Gramian or Gram matrix are also named after him.
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.
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]
Other mathematical achievements that bear his name include the Gram–Charlier series, Gram points.
He died on his way to a meeting of the Royal Danish Academy after being struck by a bicycle.[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.
| International | |
|---|---|
| National | |
| Academics | |
| Other | |
 | 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. |