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Cohen was born in the Dutch capital of Amsterdam on April 21, 1806. Later in his life, he moved to Paris, where he worked as a music teacher and served as a curator of the Cabinet des Médailles at the Bibliothèque nationale de France.
He is perhaps best known for writing two fundamental works on ancient numismatics: the first, published in 1854, dealt with coinage of the Roman Republic, while the second, issued from 1859 to 1868 in eight volumes, focused on the coins of the Roman Empire.
Aside from his numismatic works, he is also known for writing Guide de l'amateur des livres à vignettes du XVIII Siècle, a bibliography of French 18th century illustrated books. He wrote several musical compositions during his life as well, one of which, the opera "l'Impératrice", was performed in Naples, Paris, and London around 1834. Moreover, Cohen published four tracts about music theory.