Early life and education Jacopo Riccati was born on May 28, 1676 to a noble family. His mother belonged to the
Colonna family, one of the most influential princely families in
Renaissance Rome. His father, a nobleman, died when he was still a boy. He was educated first at the
Jesuit school for the nobility in
Brescia, and in 1693 he entered the
University of Padua to study
law. He received a
doctorate in law (LL.D.) in 1696. Encouraged by
Stefano degli Angeli to pursue mathematics, he studied
mathematical analysis. By 1710 he was familiar with the ideas of
differential and
integral calculus. His main work was in the field of
differential equations, and he introduced new methods to solve them, such as the methods of separating variables and lowering the order of the equation. He corresponded with several European mathematicians, including
Leonhard Euler and
Daniel and
Nicholas Bernoulli. Riccati personally supervised the education of
Ramiro Rampinelli, the teacher of
Maria Gaetana Agnesi and
Paolo Frisi.
Career Riccati received various academic offers but declined them in order to devote his full attention to the study of
mathematical analysis on his own. In 1696 he married the countess Elisabetta Onigo, and established his residence in Treviso, refusing the invitation by
Peter the Great to become the president of the
St. Petersburg Academy of Sciences. He was also asked to
Vienna as an imperial councillor (
Consigliere Aulico) and offered a professorship as the University of Padua. He declined all these offers, preferring to stay in Italy and devote himself to his studies privately. Riccati played a pivotal role in the diffusion of
Newton's ideas in Italy. Most of his scientific work concerns mathematical analysis, especially differential equations. He is best known for introducing the
differential equation that bears his name: y'(x) = q_0(x) + q_1(x) \, y(x) + q_2(x) \, y^2(x) where q_0(x) \neq 0 and q_2(x) \neq 0. If q_0(x) = 0 This non-linear ordinary differential equation was to become of paramount importance in the centuries to come. Some of his work on
polynomials was included by
Maria Gaetana Agnesi, at Riccati's request, in the book on
integral calculus of her
Analytical Institutions. Riccati was very interested in
hydraulics as well, and was often consulted by the
Senate of Venice on the construction of canals and dikes along rivers. In addition, he studied
economics,
history,
theology,
ethics,
metaphysics, and
poetry. His works were collected and published in four volumes after his death (Lucca 1761-1765). ==Personal life==