Publisher Summary This chapter explores the relationship between God and the mathematics of Galileo. In the early modern era, the mathematical sciences began to produce potential instruments of power and to supply technically and socially valuable knowledge—for use in engineering, administration, and social control. This ability to produce useful knowledge and potential instruments of power became the critical basis for the existence of the mathematical sciences. In discussing Galileo's thoughts about mathematics and the mathematical sciences, it is necessary to keep in mind that he did not codify them and that he worked—as did many early modern scholars—with conflicting epistemologies. Furthermore, there is naturally a wide gap between his theoretical reflections on the nature of his scientific work and his actual procedures. However, Galileo considered mathematics in a rather monolithic way and did not distinguish among its diverse branches such as geometry, arithmetic, theory of proportions, and theory of indivisibles. To have an unequivocal conception of mathematics, he presented geometry alone as a model of mathematical rigor and exactness. This was, at the same time, to the convenience of the contemporary reader who might not have been at all familiar with more abstract mathematical concepts or with any kind of mathematics other than plane geometry.