Evolution or Revolution in Mathematics: The Case of Leibniz

There is a conventional interpretation of Leibniz's mathematical achievements, specifically his discovery of the calculus, found in histories of mathematics like Boyer (1959), Burton (1985), or the more technical monographs by Baron (1969), Edwards (1979), or Hofmann (1974a). It goes roughly as follows: Leibniz's contribution was a predictable synthesis–mainly through improvements in notation–of earlier results of many seventeenth-century mathematicians such as Fermat (1601–1665), Cavalieri, Descartes, Barrow, Sluse (1625–1685), and others. Calculus in the form of contemporary investigation of tangent or quadrature problems was "in the air":…