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.

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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