He taught in Lausanne, where he became a Calvinist, before moving to Utrecht in 1751, and then Berlin in 1763, where he remained for the rest of his life. In 1745, he married Elizabeth du Fresne with whom he had three children, the only surviving child was Maximilian Friedrich Gustav Adolf Salvemini (see below). In 1757, Elizabeth died, and he married Madeleine Raven two years later. In November 1787 he suffered a stroke. He met the Scottish diarist James Boswell in both Utrecht and Berlin, with Boswell recording several anecdotes and conversations.
In 1745, he was elected to the Royal Society. In 1765, Frederick the Great appointed him "Astronomer Royal", of the Observatory of Berlin. He received additional honors from foreign academies, was appointed a member of the Academy of Bologna in 1768, the Academy of Mannheim in 1777, the Academy of Padua in 1784, and the Academy of Prague in 1785. Succeeding Joseph-Louis Lagrange, he was appointed Director of the Mathematics Section of the Berlin Academy, a role he held until his death.
- Discours sur l'origine d'inegalite parmi les hommes. Pour servir de reponse au discours que M Rouseau (1756)
- Mémoire sur la règle de Cardan, et sur les equations cubique, avec Quelques Remarques sur les equations en général (1783)
- Examen philosophique de principes de quelque algebra 1790 and 1791 (memoirs)
- * Otto Spiess (1957), "Castillon, Jean", Neue Deutsche Biographie (NDB) (in German), 3, Berlin: Duncker & Humblot, pp. 174–174; (full text online)
- Monarchisms in the Age of Enlightenment: liberty, patriotism, and the common good, Editors John Christian Laursen, H. W. Blom, Luisa Simonutti, University of Toronto Press, 2007, ISBN 978-0-8020-9177-2
- St Andrews
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- Mémoires de l’Académie de Berlin, année 1804, p. 319.
- François-Joseph Fétis, Biographie universelle des musiciens et bibliographie générale de la musique, Paris, Firmin-Didot, t., 1883, p. 208.
- St Andrews
- "Archived copy" (PDF). Archived from the original (PDF) on 2011-07-06. Retrieved 2010-04-13. Cite uses deprecated parameter
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- "St Andrews", Biography from St Andrews University
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- Dall'età dell'Arcadia al "Conciliatore": aspetti teorici, elaborazioni testuali, percorsi europei, Author Giuseppe Antonio Camerino, Liguori Editore Srl, 2006, ISBN 978-88-207-3983-6
- Biblioteca matematica italiana dalla origine della stampa ai primi anni del secolo XIX Author Pietro Riccardi, Società tipografica, 1893
- "Discours sur l'origine d'inegalite parmi les hommes." French Wikipedia