This modern form of Stokes' theorem is a vast generalization of a classical result that Lord Kelvin communicated to George Stokes in a letter dated July 2, 1850.See: The letter from Thomson to Stokes appears in: Neither Thomson nor Stokes published a proof of the theorem. The first published proof appeared in 1861 in: Hankel doesn't mention the author of the theorem. In a footnote, Larmor mentions earlier researchers who had integrated, over a surface, the curl of a vector field. See: Spivak (1965), p. vii, Preface. Stokes set the theorem as a question on the 1854 Smith's Prize exam, which led to the result bearing his name. It was first published by Hermann Hankel in 1861.See: The 1854 Smith's Prize Examination is available online at: Clerk Maxwell Foundation. Maxwell took this examination and tied for first place with Edward John Routh. See: See also Smith's prize or the Clerk Maxwell Foundation. In a footnote on page 27, Maxwell mentions that Stokes used the theorem as question 8 in the Smith's Prize Examination of 1854. This footnote appears to have been the cause of the theorem's being known as "Stokes' theorem". This classical case relates the surface integral of the curl of a vector field over a surface (that is, the flux of ) in Euclidean three-space to the line integral of the vector field over the surface boundary.
This modern form of Stokes' theorem is a vast generalization of a classical result that Lord Kelvin communicated to George Stokes in a letter dated July 2, 1850.See: The letter from Thomson to Stokes appears in: Neither Thomson nor Stokes published a proof of the theorem. The first published proof appeared in 1861 in: Hankel doesn't mention the author of the theorem. In a footnote, Larmor mentions earlier researchers who had integrated, over a surface, the curl of a vector field. See: Spivak (1965), p vii, Preface. Stokes set the theorem as a question on the 1854 Smith's Prize exam, which led to the result bearing his name. It was first published by Hermann Hankel in 1861.See: The 1854 Smith's Prize Examination is available online at: Clerk Maxwell Foundation. Maxwell took this examination and tied for first place wi.th Edward John Routh. See: See also Smith's prize or the Clerk Maxwell Foundation. In a footnote on page 27, Maxwell mentions that Stokes used the theorem as question 8 in the Smith's Prize Examination of 1854. This footnote appears to have been the cause of the theorem's being known as "Stokes' theorem". This classical case relates the surface integral of the curl of a vector field over a surface (that is, the flux of ) in Euclidean three-space to the line integral of the vector field over the surface boundary.