Is there another Mathematics?

Question

We all know of other languages, Spanish, English, Frensh, German...

...but is there another way to quantify and Analyse the world than Mathematics (in our age) ?

Answer 1

Maybe there is, maybe there isn't – but there are different areas of mathematics to quantify and analyse the world. There are even different systems of mathematics, ones different from that based on the axioms of Zermelo–Fraenkel set theory most commonly used in our age. One professor of mathematics has even attempted to redevelop the whole foundation of mathematics without conventional set theory, in particular the theory of infinite sets and real numbers, which he claims contain "logical flaws". His name is Norman J. Wildberger; he works at the University of New South Wales, Australia, and he even has a series of YouTube playlist of over 200 videos devoted to expounded his "rational mathematics".

Answer 2

Mathematics relies on axioms (propositions we start with) and rules of inference (which determine how we can expand the list of "proven" propositions), but there is variation in the axioms and inference rules adopted.

For example, mathematicians often take set theory as the base of the subject, but even if they do there are many set theories (ZFC, NBG, NF etc.). At a higher level there are multiple number systems, multiple geometries, multiple algebraic structures...

There are also many logics (classical, intuitionistic, dual-intuitionistic, quantum...), all with their own inference rules.

There is "one mathematics" in the sense of an umbrella over all the "this implies that" studies, but there are many different choices of "this".