Carl Gustav Jacob Jacobi (10 December 1804 to 18 February 1851) was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants and number theory. He was born of Ashkenazi Jewish parentage in Potsdam, the second of four children of a banker, Simon Jacobi, and his elder brother Moritz also became known, as an engineer and physicist. He was first home schooled by his uncle Lehman and then attended the Potsdam Gymnasium, and in 1821 went to study at Berlin University, where he divided his attention between philology and mathematics and pursued private study of the works of Euler, Lagrange and Laplace.
Facts
Connections
Attributed Works
Source Theta function (Wikipedia)
Source Jacobi Triple Product (Wikipedia)
Source Jacobi's formula (Wikipedia)
In Branch
Source Wikipedia: Carl Gustav Jacob Jacobi
Mentored
Source Ludwig Otto Hesse (MacTutor)
Principal Result
Source Wikipedia: Carl Gustav Jacob Jacobi
Proofs Credited
Source Jacobi's four-square theorem (Wikipedia)
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Sources
1. Wikipedia: Carl Gustav Jacob Jacobi
Lead
He was the second of four children of a banker, Simon Jacobi.
Principal Result: Jacobi Triple Product, Article text
He discovered many of the fundamental properties of theta functions, including the functional equation and the Jacobi triple product formula, as well as many other results on q-series and hypergeometric series.
View the Source2. MacTutor History of Mathematics, University of St Andrews: Carl Gustav Jacob Jacobi
MacTutor History of Mathematics, University of St AndrewsQuick Info: BornQuote, Quick Info: Born
10 December 1804
Jacobi's formula (Wikipedia)
Attributed Works: Jacobi's formula, Lead sectionQuote, Attributed Works: Jacobi's formula, Lead section
The formula is named after the mathematician Carl Jacobi.
Ludwig Otto Hesse (MacTutor)
Mentored: Otto Hesse, Biography, doctorateQuote, Mentored: Otto Hesse, Biography, doctorate
Hesse had continued to study for his doctorate under Jacobi 's supervision
Jacobi's four-square theorem (Wikipedia)
Proofs Credited: Jacobi's Four-Square Theorem, LeadQuote, Proofs Credited: Jacobi's Four-Square Theorem, Lead
The theorem was proved in 1834 by Carl Gustav Jakob Jacobi.
Jacobi Triple Product (Wikipedia)
Attributed Works: Jacobi Triple Product, Lead paragraphQuote, Attributed Works: Jacobi Triple Product, Lead paragraph
It was introduced by Jacobi (1829) in his work Fundamenta Nova Theoriae Functionum Ellipticarum.
Theta function (Wikipedia)
Attributed Works: Jacobi Theta Function, Lead sectionQuote, Attributed Works: Jacobi Theta Function, Lead section
One Jacobi theta function (named after Carl Gustav Jacob Jacobi)
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