Evangelista Torricelli (
October 15,
1608 -
October 25,
1647) was an
Italian physicist and
mathematician.
Born in Faenza , he was left fatherless at an early age. He was educated under the care of his uncle, a Camaldolese monk, who in 1627 sent him to Rome to study science under the Benedictine Benedetto Castelli (1577-1644), professor of mathematics at the Collegio della Sapienza in Pisa. Torricelli died a few days after having contracted typhoid fever.
Torricelli's work in physics
The perusal of Galileo's Two New Sciences (1638) inspired him with many developments of the mechanical principles there set forth, which he embodied in a treatise De motu (printed amongst his Opera geometrica, 1644). Its communication by Castelli to Galileo in 1641, with a proposal that Torricelli should reside with him, led to Torricelli repairing to Florence, where he met Galileo, and acted as his amanuensis during the three remaining months of his life.
After Galileo's death Torricelli was nominated grand-ducal mathematician and professor of mathematics in the Florentine academy . The discovery of the principle of the barometer which has perpetuated his fame ("Torricellian tube", "Torricellian vacuum") was made in 1643. The torr, a unit of pressure is named after him.
Torricelli's work in mathematics
Torricelli is also famous for the discovery of an infinitely long solid now called Gabriel's horn, whose surface area is infinite, but whose volume is finite. This was seen as an "incredible" paradox by many at the time (including Torricelli himself, who tried several alternative proofs), and prompted a fierce controversy about the nature of infinity, involving the philosopher Hobbes. It is supposed by some to have led to the idea of a "completed infinity".
Torricelli was also a pioneer in the area of infinite series. In his De dimensione parabolae of 1644, Toricelli considered a decreasing sequence of
positive terms 
and showed the corresponding
telescoping series 
necessarily converges to a0 - L, where L is the limit of the sequence, and in this way gives a proof of the formula for the sum of a geometric series.
References
Weil, André, Prehistory of the Zeta-Function, in Number Theory, Trace Formulas and Discrete Groups, Aubert, Bombieri and Goldfeld, eds., Academic Press, 1989
