Mathesis universalis

John Wallis invokes the name as title in his Opera Mathematica, a textbook on arithmetic, algebra, and Cartesian geometry.

[1] Leibniz attempted to work out the possible connections between mathematical logic, algebra, infinitesimal calculus, combinatorics, and universal characteristics in an incomplete treatise titled "Mathesis Universalis" in 1695.

More generally, mathesis universalis, along with perhaps François Viète's algebra, represents one of the earliest attempts to construct a formal system.

[1] In the discussion of Rule Four, Descartes' provides his clearest description of mathesis universalis:[...] I began my investigation by inquiring what exactly is generally meant by the term 'mathematics' and why it is that, in addition to arithmetic and geometry, sciences such as astronomy, music, optics, mechanics, among others, are called branches of mathematics.

[5][6] Leibniz also identified synthesis with the ars combinatoria, viewing it in terms of the recombination of symbols or human thoughts.