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Rosenhain went to the University of Vienna in 1851. Then, in 1857, he returned to Königsberg where he taught until he retired in 1886.
At Königsberg as a student Rosenhain became a close friend of Jacobi, editing some of Jacobi's lectures while he was still a student.
Rosenhain won the 1846 Paris Academy Prize (in 1851!) for work on elliptic functions with a beautiful piece of work. Göpel solved the problem too but he did not submit it for the prize. Rosenhain's methods are more closely linked to those of Jacobi than are the methods of Göpel.
Rosenhain never published anything other than his Academy Prize paper despite having shown outstanding mathematical abilities.
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