History
The theory of abelian integrals originated with the paper by Abel published in 1841. This paper was written during his stay in Paris in 1826 and presented to Cauchy in October of the same year. This theory, later fully developed by others, was one of the crowning achievements of nineteenth century mathematics and has had a major impact on the development of modern mathematics. In more abstract and geometric language, it is contained in the concept of abelian variety, or more precisely in the way an algebraic curve can be mapped into abelian varieties. The Abelian Integral was later connected to the prominent mathematician David Hilbert's 16th Problem and continues to be considered one of the foremost challenges to contemporary mathematical analysis.
Read more about this topic: Abelian Integral
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