Pietro Mengoli

Pietro Mengoli (1626 to 1686) was an Italian mathematician and clergyman from Bologna, where he studied with Bonaventura Cavalieri at the University of Bologna and succeeded him in 1647, remaining a professor there for the rest of his life. He was a pivotal figure in the development of calculus: he established the divergence of the harmonic series nearly forty years before Jacob Bernoulli, gave a series development of logarithms thirteen years before Nicholas Mercator's Logarithmotechnia, and defined the definite integral in a way close to the one Cauchy gave more than a century later. In 1650 he first posed the Basel problem, solved by Euler in 1735, and proved that the alternating harmonic series sums to the natural logarithm of 2. His early books Novae quadraturae arithmeticae, Via regia ad mathematicas and Geometria won him a wide reputation, especially among academics in London. Ordained a Catholic priest in 1660, he later turned to music theory, cosmology, logic and metaphysics, and his Speculationi di musica was reviewed by Henry Oldenburg in the Philosophical Transactions.