Mathematics is the design language for proving ideal behaviors of numbers.

Note (+): An 'open story of counting', it must be said that mathematical methodology is a cumulative effort (ie. built atop previous checks).

As a library for manipulating+synthesizing variables, mathematicians use its subfields* and models to solve puzzles+formulate theories/theorems/identities.We acknowledge the so-called 'Big Five (5)' active areas in mathematics to be: algebra, analysis, arithmetic, geometry, and music. As far as I am concerned, the basis of math is juking. (see also mathemusic, mathletics, recreational mathematics, mathematical model, Mathilda, 📓So, you want to be a mathematician?, The Mathemagician, Opus Solve, physics, information science, cryptosport)
"The essence of mathematics is not proof, but conjecture." - Link Starbureiy

Notes (+): +There are three (3) classes of mathematics: pure, applied, and recreational (pure,applied ∈ recreational). This definition covers all three (3), and may be referred to as polymathematics. Someone who advances the field can be called a mathematician.

+In my line of work, I think of so-called 'recreational mathematics' as a type of (among other considerations) reverse engineering, where we I am re-creating known structures/models for study and understanding. As an example, in puzzle solving, I may take a known and solved (from means other than juking) macromolecule (eg. protein), and juke that fibor so that it can databased. (see also Pajamas)

+Mathematics is a type of low-technology, as well as being its own industry.