- An attempt at unpacking Mathematics and its creation/discovery in layman's terms.
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def mathematics¹(Lockhart, 2009: 3): is an art like music and painting.
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def mathematics²(Lockhart, 2009: 4): is about pure reason to get at the truth about something.
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def mathematics³: is a formal language. this means it has precise definitions for its words(+,-,*, π,e, etc) and grammar.
- the symbols such as
∧,Σ,∀,+,×are merely a shorthand.∧means: ANDΣmeans: sum∀means: for all+means: add[which you know from Grade 1 Mathematics]-means: subtract[which you know from Grade 1 Mathematics]
- the symbols such as
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def mathematics⁴(Devlin, 2012:15): the science of patterns.
- examples:
- Logic = patterns of reasoning.
- Arithmetic and Number Theory = patterns of number and counting.
- Geometry = patterns of shape.
- Calculus = patterns of motion.
- Topology = patterns of closeness and position.
- Probability Theory = patterns of chance.
- examples:
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def mathematics⁵(Devlin, 2012): the science of abstract structure.
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def side | perspectives of Mathematics:(Hammack, 2018:viii):
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computation focused: use the below-mentioned computations to answer practical questions about the world.
- primary goals:
- solve equations.
- compute derivatives.
- compute integrals.
- multiply matrices.
- find determinants.
- ... NB: Mathematical techniques and procedures used in this side, are founded in the theoretical side.
- primary goals:
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theoretical focused:
- primary goals:
- understand Mathematical structures.
- prove Mathematical statements.
- invent or discover new Mathematical theorems and theories.
- use Mathematics to study itself.
- ...
- primary goals:
-
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def creation | discovery:
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Formal Classification Scheme:
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Theory
- Theoretical Basis: 03Exx_set_theory
- Formal Science:
- Philosophy: Philosophy of Mathematics
- 00_numbers
- 03_mathematical_logic_and_foundations
- 20_group_theory_and_generalizations
- 12_field_theory_and_polynomials
- 16_associative_rings_and_algebras
- 17_nonassociative_rings_and_algebras
- 15_linear_and_multilinear_algebra;matrix_theory
- 26_real_functions
- 34_ordinary_differential_equations
- 35_partial_differential_equations
- 11_number_theory
- 51_geometry
- 54_general_topology
- 60_probability_theory_and_stochastic_processes
- 18_category_theory;homological_algebra
- The repository is configured to use devcontainers for development.
It requires no setup except an editor that supports devcontainers, which will prompt you on first open to start it in a container.
- Mathematical Symbols
- Glossary of Mathematical Symbols
- The On-Line Encyclopedia of Integer Sequences (OEIS)
- Proof Wiki
- LEAN
- mathlib4
- Mathematica
- MathIsFun
- Lean
- 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
- Mathematics Genealogy Project
- The Academic Genealogy of Mathematics
- Asaf Karagila
- Emmy Noether
- David Blackwell
- Ada Lovelace
- Abdon Atangana
- Grete Hermann
- Katherine Johnson
- Loyiso Nongxa
- Norman J Wildberger
- Richard Hammack
- Terry Tao
- Index
- MΣΣT a Mathematician
- Math-life balance - Interviews
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pytest
pyspelling -c spellcheck.yaml- Mathematics Subject Classification. 2020
- Mathematical Association of America
- Lockhart, P. 2009. A Mathematician's Lament.
- Hammack, R. 2018. Book of Proof. 3.3rd Edition. Richmond, Virginia.
- Devlin, K. 2012. Introduction to Mathematical Thinking.
- Devlin, K. 2012. Mathematics: Making the Invisible Visible. Stanford University.
Q: Question for later research
MYINC: My Insight/Conjecture [Could Be Unoriginal/False and Likely Is]
see: ...: Points to the definition of a concept used in another definition.
Disclaimer: This is an ongoing and incomplete project to unpack these concepts and serves as my exosomatic memory.