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Jan Peter Schäfermeyer
Jan Peter Schäfermeyer
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I think that by the end of the 19th and the beginning of the 20th century many mathematicians felt the need for a unified theory of "linear things" because they realized that they were doing the same things over and over again in different fields, e.g. Maxime Bocher writes in his Introduction to the study of Integral Equations that the notion of orthogonal functions was presented to him by Felix Klein in a lecture on the differential equations of mathematical physics in 1889.

The author of thisJean-Luc Dorier writes in the conclusion to his paper on "A general outline of the genesis of vector space theory" writes in his conclusion: "Many examples of implicit linear methods in different contexts in mathematics or physics can be traced from Antiquity, but, until the 19th century at least, they remained isolated methods; the same author could use the same idea twice (in terms of the theory of linear algebra) in different contexts without noticing the similarity of the methods. In this sense, linear algebra long remained implicit because of a lack of unification. Nevertheless, its origins can be found in various contexts, and linearity has always been a question which has penetrated nearly every branch of mathematics."

I think that by the end of the 19th and the beginning of the 20th century many mathematicians felt the need for a unified theory of "linear things" because they realized that they were doing the same things over and over again in different fields, e.g. Maxime Bocher writes in his Introduction to the study of Integral Equations that the notion of orthogonal functions was presented to him by Felix Klein in a lecture on the differential equations of mathematical physics in 1889.

The author of this paper on "A general outline of the genesis of vector space theory" writes in his conclusion: "Many examples of implicit linear methods in different contexts in mathematics or physics can be traced from Antiquity, but, until the 19th century at least, they remained isolated methods; the same author could use the same idea twice (in terms of the theory of linear algebra) in different contexts without noticing the similarity of the methods. In this sense, linear algebra long remained implicit because of a lack of unification. Nevertheless, its origins can be found in various contexts, and linearity has always been a question which has penetrated nearly every branch of mathematics."

I think that by the end of the 19th and the beginning of the 20th century many mathematicians felt the need for a unified theory of "linear things" because they realized that they were doing the same things over and over again in different fields, e.g. Maxime Bocher writes in his Introduction to the study of Integral Equations that the notion of orthogonal functions was presented to him by Felix Klein in a lecture on the differential equations of mathematical physics in 1889.

Jean-Luc Dorier writes in the conclusion to his paper on A general outline of the genesis of vector space theory: "Many examples of implicit linear methods in different contexts in mathematics or physics can be traced from Antiquity, but, until the 19th century at least, they remained isolated methods; the same author could use the same idea twice (in terms of the theory of linear algebra) in different contexts without noticing the similarity of the methods. In this sense, linear algebra long remained implicit because of a lack of unification. Nevertheless, its origins can be found in various contexts, and linearity has always been a question which has penetrated nearly every branch of mathematics."

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Jan Peter Schäfermeyer
Jan Peter Schäfermeyer
  • 1.4k
  • 9
  • 7

I think that by the end of the 19th and the beginning of the 20th century many mathematicians felt the need for a unified theory of "linear things" because they realized that they were doing the same things over and over again in different fields, e.g. Maxime Bocher writes in his Introduction to the study of Integral Equations that the notion of orthogonal functions was presented to him by Felix Klein in a lecture on the differential equations of mathematical physics in 1889.

The author of this paper on "A general outline of the genesis of vector space theory" writes in his conclusion: "Many examples of implicit linear methods in different contexts in mathematics or physics can be traced from Antiquity, but, until the 19th century at least, they remained isolated methods; the same author could use the same idea twice (in terms of the theory of linear algebra) in different contexts without noticing the similarity of the methods. In this sense, linear algebra long remained implicit because of a lack of unification. Nevertheless, its origins can be found in various contexts, and linearity has always been a question which has penetrated nearly every branch of mathematics."