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DeadWolfe
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I know that th three dimensional case was discovered by William Thompson, but who discovered the general case?
Who discovered the general case of Stokes' Theorem?
In summary, while the three-dimensional case of Stokes' theorem was discovered by William Thompson (also known as Lord Kelvin), the general case was discovered by a number of mathematicians, including Ostrogradsky, Cauchy, Green, and Cartan. It is also referred to as the Stokes theorem and is considered one of the most beautiful and fundamental theorems in calculus, along with Noether's theorem and Euler's variational equation. The confusion surrounding its discovery and naming is a testament to its complexity and significance in mathematics.
- #2
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According to
http://maxwell.byu.edu/~spencerr/phys442/node4.html
which claim to refer to
E. T. Whittaker's A History of the Theories of Aether and Electricity...
says
"1850 - Stokes law is stated without proof by Lord Kelvin (William Thomson). Later Stokes assigns the proof of this theorem as part of the examination for the Smith's Prize. Presumably, he knows how to do the problem. Maxwell, who was a candidate for this prize, later remembers this problem, traces it back to Stokes and calls it Stokes theorem"
Some interesting reading
http://www.siam.org/siamnews/09-00/green.htm
How "general" do you want?
According to "[URL
"The History of Stokes' Theorem", Victor J. Katz
Mathematics Magazine, Vol. 52, No. 3. (May, 1979), pp. 146-156.[/URL] (available on JSTOR),
among those that worked on what would become the higher-dimensional "generalized Stokes theorem" is Ostrogradsky (1820s, 1836 for the generalized divergence theorem) and Volterra (1889 for including Green, Div, Stokes as special cases).
http://maxwell.byu.edu/~spencerr/phys442/node4.html
which claim to refer to
E. T. Whittaker's A History of the Theories of Aether and Electricity...
says
"1850 - Stokes law is stated without proof by Lord Kelvin (William Thomson). Later Stokes assigns the proof of this theorem as part of the examination for the Smith's Prize. Presumably, he knows how to do the problem. Maxwell, who was a candidate for this prize, later remembers this problem, traces it back to Stokes and calls it Stokes theorem"
Some interesting reading
http://www.siam.org/siamnews/09-00/green.htm
How "general" do you want?
According to "[URL
"The History of Stokes' Theorem", Victor J. Katz
Mathematics Magazine, Vol. 52, No. 3. (May, 1979), pp. 146-156.[/URL] (available on JSTOR),
among those that worked on what would become the higher-dimensional "generalized Stokes theorem" is Ostrogradsky (1820s, 1836 for the generalized divergence theorem) and Volterra (1889 for including Green, Div, Stokes as special cases).
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- #3
DeadWolfe
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Thank you for the article. Interesting stuff.
Aparently Ostrogadkssy discovered Gauss' theorem, Cauchy discovred Green's theorem, Kelvin discovered Stokes' theorem, and some guy named Cartan discovered the general case (which is also called stokes theorem). So none are named correctly. Hmm.
Aparently Ostrogadkssy discovered Gauss' theorem, Cauchy discovred Green's theorem, Kelvin discovered Stokes' theorem, and some guy named Cartan discovered the general case (which is also called stokes theorem). So none are named correctly. Hmm.
- #4
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If you read page #192 of Arnold's book on "Mathematical Methods of Classical Mechanics" you'll see just how big the confusion might be...
Daniel.
Daniel.
- #5
leach
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The general case of Stokes Theorem was the first great publication by Nicolas Bourbaki.
Trying http://www.google.com/search?hl=en&q=bourbaki+"stokes+theorem" with bourbaki and "stokes theorem" gives some good references.
Trying http://www.google.com/search?hl=en&q=bourbaki+"stokes+theorem" with bourbaki and "stokes theorem" gives some good references.
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- #6
DeadWolfe
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Wow. Things just keep getting curiouser and curiouser. Thanks all.
- #7
Perturbation
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DeadWolfe said:
Some guy called Cartan! Some guy! Blasphemy.
Stoke's theorem and Noether's are probably two of my favourite theorems.
[tex]\int_{U}d\tilde{\omega}=\int_{\partial U}\tilde{\omega}[/tex]
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- #8
masudr
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Hehe, that's what I was thinking!Perturbation said:
- #9
DeadWolfe
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My deepest apologies for my ignorance.
Who is Cartan?
Who is Cartan?
- #10
Cexy
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Elie Cartan lived in the first half of the 1900s, and made huge discoveries in the study of Lie groups, representation theory, differential geometry, topology and a whole host of others. He gave a complete classification of the simple Lie algebras, and he worked with Einstein on some problems in General Relativity with a non-zero Torsion field. He was also the first person to describe Newton's theory of gravity using the language of differential geometry, and you'll often see it called 'Newton-Cartan geometry' nowadays.
- #11
leach
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I read elsewhere that the discoverer of Stokes theorem was Henri Cartan, Elie's Cartan son. Henri Cartan was member of the Bourbaki group.Cexy said:
I agree. These two theorems enclose the true beauty of calculus. I think that the derivation of Euler's variational equation is other good example of that beauty: to obtain such a profound equation using high school math, and of course Euler's geniality.perturbation said:
FAQ: Who discovered the general case of Stokes' Theorem?
Who is credited with discovering Stokes' Theorem?
The general case of Stokes' Theorem was discovered by Irish mathematician George Gabriel Stokes in 1854. However, the concept of Stoke's Theorem has been studied and developed by multiple mathematicians, including Pierre-Simon Laplace and Lord Kelvin, prior to its formalization by Stokes.
What is the general case of Stokes' Theorem?
The general case of Stokes' Theorem is a fundamental theorem in vector calculus that relates the surface integral of a vector field over a closed surface to the line integral of the same vector field along the boundary of the surface.
What is the significance of Stokes' Theorem?
Stokes' Theorem is an important tool in the study of vector calculus and has many applications in mathematics, physics, and engineering. It allows for the simplification of complex surface integrals by relating them to simpler line integrals, making calculations and proofs more efficient.
How is Stokes' Theorem related to other theorems in mathematics?
Stokes' Theorem is closely related to other fundamental theorems in mathematics, such as the Divergence Theorem and Green's Theorem. These theorems all involve the relationship between surface and line integrals and are used to solve various problems in different fields of mathematics.
Is there a practical application of Stokes' Theorem?
Yes, Stokes' Theorem has many practical applications in physics and engineering, such as calculating the circulation of a fluid flow around a closed curve or determining the flow of electric and magnetic fields around a closed loop.