What is Mathematics?

objective: an attempt at unpacking in layman's terms what mathematics is and how it is created.

def mathematics¹(Lockhart, 2009: 3): is an art like music and painting.

def mathematics²(Lockhart, 2009: 4): is about pure reason to get at the truth about something.

def side of Mathematics:(Hammack, 2018:viii):

• computation focused:

  • primary goals:
    • solve equations.
    • compute derivatives.
    • compute integrals.
    • multiply matrices.
    • find determinants.
    • ...
    • use the above-mentioned computations to answer practical questions about the real world.

  NB: Mathematical techniques and procedures used in this side, are founded in the theoretical side.

• theoretical focused:

  • primary goals:
    • understand Mathematical structures.
    • prove Mathematical statements.
    • invent or discover new Mathematical theorems and theories.

plain english:

• def mathematics: is a formal language. this means it has precise definitions for its words(+,-,*, π,e, etc) and grammar.
• the symbols are merely shorthands. symbols such as ∧, Σ, ∀, +, ×.
  • ∧ means: AND
  • Σ means: sum
  • ∀ means: for all
  • + means: add[which you know from Grade 1 Mathematics]
  • - means: subtract[which you know from Grade 1 Mathematics]

formal classification scheme:

• ZBMATH

def how is it created?:

• initialize mathematics from natural numbers
• initialize mathematics from axiomatic method

History:

• MoMath + Wolfram

Notation:

• Wumbo
• Glossary of mathematical symbols

Tools:

• The On-Line Encyclopedia of Integer Sequences (OEIS)
• LEAN
• mathlib4
• Mathematica

State of the art:

Quanta Magazine

Community:

• The South African Mathematical Society
• The African Mathematical Society
• Institute of Mathematics & its Applications
• Mathematical Association of America
• American Mathematical Society
• Clay Mathematics Institute
• Mathematical Logic
• Math Overflow
• Math Stackexchange

Mathematicians:

• Norman J Wildberger
• Richard Hammack
• Professor Loyiso G
• Terry Tao
• Asaf Karagila
• Index

References:

• Mathematics Subject Classification. 2020. https://zbmath.org/classification/
• Mathematical Association of America. https://www.maa.org/press/periodicals/loci/joma/subject-taxonomy
• Lockhart, P. 2009. A Mathematician's Lament.
• Hammack, R. 2018. Book of Proof. 3.3 ed. Richmond, Virginia.

Legend:

Q: Question for later research

MYINC: My Insight/Conjecture [Could Be Unoriginal/False and Likely Is]

Disclaimer: This is an ongoing and incomplete project to unpack these concepts and serve as my distributed memory.