mathematics

Mathematics is an ambiguous way of proving ideal behaviors of objects.
An '`open` story of `counting`', it must be said that mathematical methodology is a cumulative effort (ie. rigorously `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 [1-5 labeled alphabetically]: algebra [1], analysis [2], arithmetic [3], geometry [4], and music [5]. 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, game, cryptosport)
"The essence of mathematics is not proof, but conjecture." - 🐨Link Starbureiy

+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. A mathematician is someone who advances `classical` mathematics.

+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 identified+`databased`. (see also Pajamas)

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

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#LEGEND
math.AG (algebraic geometry), math.AT (algebraic topology), math.AP (analysis of partial differential equations), math.CT (category theory), math.CA (classical analysis and ordinary differential equations), math.CO (combinatorics), math.AC (commutative algebra), math.CV (complex variables), math.DG (differential geometry), math.DS (dynamical systems), math.FA (functional analysis), math.GM (general mathematics), math.GN (general topology), math.GT (geometric topology), math.GR (group theory), math.HO (history and overview), math.IT (information theory), math.KT (k-theory and homology), math.LO (logic), math.MP (mathematical physics), math.MG (metic geometry), math.NT (number theory), math.NA (numerical analysis), math.OA (operator algebras), math.OC (optimization and control), math.PR (probability), math.QA (quantum algebra), math.RT (representation theory), math.RA (rings and algebras), math.SP (spectral theory), math.ST (statistics theory), math.SG (symplectic geometry)

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