The Role of Mathematics in the Copernican Revolution

The Copernican revolution can conveniently be divided into two, partly overlapping, phases. The first phase comprises the work of Copernicus and Kepler. The main focus was on improving the accuracy of planetary astronomy. This goal was successfully achieved and enabled much better astronomical tables to be produced. The Prutenic tables of 1551, compiled using Copernicus’ work, were much superior to any previous ones, and the Rudolphine tables, compiled by Kepler himself and published in 1627, were better still. The second phase began with Galileo’s telescopic discoveries, which were published in 1610. It resulted, principally through the work of Galileo, Descartes, Huyghens and Newton, in the creation of a new mathematical mechanics. The main thesis of this chapter is that the role of mathematics was significantly different in the two phases. The mathematical apparatus used by Copernicus and Kepler did not differ very much from that employed by the ancient Greeks. Kepler made a striking innovation by using ellipses rather than combinations of circles to describe planetary orbits, but this did not require mathematical innovation. The mathematics of ellipses had been worked out by Apollonius of Perga, and Kepler could take it ‘off the shelf’. This pattern is also to be found in the revolution in physics in the first three decades of the twentieth century. Though relativity and quantum mechanics transformed physics, they did not require any new mathematics. When Einstein was developing General Relativity, he was able, like Kepler, to take the necessary mathematics ‘off the shelf’. A quite different pattern is to be found in the second phase, for the development of a new mechanics brought into existence co-ordinate geometry and the differential and integral calculus. I will argue that the new mathematics was necessary for the new mechanics. Newtonian mechanics could not have satisfactorily developed using mathematics taken off the shelf. It required the creation of a new mathematics. Then I will argue that the creation of this new mathematics constituted a revolution in mathematics which should be considered as part of the Copernican revolution.