He is best known for his observation, made around 1667, that the second brightest star (called Algol as derived from its name in Arabic) in the constellation of Perseus varied in brightness. It is likely that others had observed this effect before, but Montanari was the first named astronomer to record it. The star's names in Arabic, Hebrew and other languages, all of which have a meaning of "ghoul" or "demon", imply that its unusual behaviour had long been recognised.
Montanari was born in Modena, studied law in Florence, and graduated from the University of Salzburg. In 1662 or 1663 he moved to Bologna, where he drew an accurate map of the Moon using an ocular micrometer of his own making. He also made observations on capillarity and other problems in statics, and suggested that the viscosity of a liquid depended on the shape of its molecules. In 1669 he succeeded Giovanni Cassini as astronomy teacher at the observatory of Panzano, near Modena, where one of his duties was to compile an astrological almanac. He did so in 1665, but perpetrated a deliberate hoax by writing the almanac entirely at random, to show that predictions made by chance were as likely to be fulfilled as those made by astrology. In the period shortly after Galileo Galilei, experimentalists like Montanari were engaged in a battle against the more mystical views of scientists such as Donato Rossetti.
In 1679 Montanari moved to a teaching post in Padua, but almost all records of this period of his life have been lost. A letter survives from 1682 recording a sighting of Halley's Comet. He also wrote on economics, observing that demand for a particular commodity was fixed, and making comments on coinage and the value of money (1683).
A crater on the Moon, at 45.8S, 20.6W, is named after him.
- De motionibus naturalibus a gravitate pendentibus (1667)
- Pensieri fisico-matematici (1667)
- La Livella Diottrica (The Spirit Level) (1674)
- Trattato mercantile delle monete (1680)
- L'Astrologia Convinta di Falso col Mezzo di Nuove Esperienze e Ragioni Fisico-Astronomiche o sia la Caccia del Frugnuolo (1685), in which Montanari describes his and his colleagues' random predictions intended to disprove astrology
- Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, edited by Bernard I. Cohen and Anne Whitman, Berkeley, University of California Press, 1999, pp. 913-915, 927.
- Gómez López, Susana, Le passioni degli atomi. Montanari e Rossetti: Una polemica tra galileiani, Florence, Leo S. Olschki, 1997.
- Rotta, Sergio, 'Scienza e "pubblica felicità" in G. Montanari', in Miscellanea Seicento, Florence, Le Monnier, 1971, vol. 2, pp. 65-208.
- Works by Geminiano Montanari at Project Gutenberg
- Works by or about Geminiano Montanari at Internet Archive
- "The impact of Galilean culture - From Bonaventura Cavalieri to Gian Domenico Cassini", Bologna University Department of Astronomy 2004-4-10