The teaching of Mathematics in Bologna was first heard of in the fourteenth century, together with that of Astronomy (which had not then been distinguished from Astrology). Luca Pacioli, the great theorist of Divine Proportion, taught Mathematics. Scipione del Ferro and Ludovico Ferrari (a pupil of Cardano) found, respectively, the formulas for equations of the third and fourth degree. While studying the equation of the third degree, Raffaele Bombelli in his Algebra (1572) introduced imaginary numbers. Pietro Antonio Cataldi introduced the algorithm of continuous fraction (1613); Bonaventura Cavalieri wrote his Geometria indivisibilibus continuorum nova quadam ratione promota (1635) and the Exercitationes Geometricae Sex (1647 - a year after the birth of Leibniz) in which he already faced the problem of infinitesimal calculus. Gabriele Manfredi's De constructione aequationum differentialium primi gradus (1707), was studies and admired by Leibniz. After 1714 mathematical studies were continued at the Academy of Science and it is only in the nineteenth century that important mathematics are to be found again at the University.

Among these are: Luigi Cremona and Eugenio Beltrami (Algebraic Geometry and Differential Geometry), Federigo Enriques, Enrico Bompiani, Beniamino Segre, Cesare Arzelà, Salvatore Pincherle, Giuseppe Vitali, Beppo Levi, Luigi Fantappiè and Leonida Tonelli.

Medieval scholars of Law had faced the problems of property, exchange, price determination, the nature of monetary obligations and the justification of interest on loans. In the late thirteenth century Pietro de Crescenzi studied Farm Management and Agrarian Technology.

Luca Pacioli presented an early treatise of Mathematics applied to economic problems: in his Summa de arithmetica (1494), the first approach to double entry book-keeping can be found. In the seventeenth century Geminiano Montanari taught Mathematics and Astronomy and studied the foundations of monetary economy. During the eighteenth century, scientific interest shifted to the problem of the mathematical formulation of human feelings and beliefs. In the course of a debate between the supporters and opponents of Maupertuis, Giammaria Ortes dealt with a rigorous treatment of economic actions based upon the principle of sufficient reason; Gianbattista Vasco maintained that a careful balance of possible outcomes may provide a rational basis for decision making.

This tradition of economic research was continued in the nineteenth century by scholars such as Luigi Valeriani (a theory of natural price determination based on supply and demand), Pellegrino Rossi, Angelo Marescotti, Achille Loria, Tullio Martello, Antonio Graziadei and others.

In the period from the end of the nineteenth century to the first half of this century, scholars working at the University made outstanding contributions to fields such as the Theory of Money and Economic Dinamics (Del Vecchio), saving Formation and Capital Accumulation (Del Vecchio and Ricci), Inflation (Bresciani-Turroni), Public Finance (Puviani, Sensini, Flora), Statistics and Applied Economics (Gini, Del Vecchio, Vinci).