What is Mathesis Universalis?

There are several interpretations of what mathesis universalis could have been. Some interpreters claim that mathesis universalis is a universal method of discovery; others understand it as coextensive with algebra as a fundamental discipline of mathematics; while still others identify it with the mathematical articulation of material reality. Each of these three interpretations is safe. We can find traces of all of them in Descartes’ work. However, each of them captures only one aspect of Descartes’ mathematical work, ignoring others. Also, they allow us to understand neither the unity of these three aspects of Descartes’ mathematical work nor the relationship between mathesis universalis and his method. The method, as Descartes presented it in the Regulae, was geometrical rather than algebraic, its aim was certainty rather than discovery, and it did not discriminate between material and non-material reality. I will show how Descartes gradually expanded and radicalized his mathesis universalis.