Disclaimer: This is an ongoing and incomplete project to unpack these concepts and serves as my exosomatic memory.
- An attempt at distilling to layman's terms:
- Mathematics.
- Mathematics' Foundations and Invention | Discovery.
- Mathematics' Relationship with Logic and Computation.
-
def mathematics¹ (Lockhart, 2009: 3): an art like music and painting.
-
def mathematics²(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:
-
def mathematics³(Kuber, 2024): a collection of subjects/branches/theories in which each subject/branch/theory is a formal system.
- see: 03_mathematical_logic_and_foundations/1_formal_system.txt
-
def mathematics⁴(Wildberger, 2011): mathematics is common sense, precise use of language, and logical reasoning, applied to the study of patterns and problem solving.
- The Mathematical method
- Initialize mathematics from natural numbers
- Initialize mathematics from axiomatic method
- 0_numbers
- 51_geometry
- 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
- 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.
- The Map of Mathematics
- Mathematical Symbols
- Glossary of Mathematical Symbols
- The On-Line Encyclopedia of Integer Sequences (OEIS)
- Proof Wiki
- LEAN
- 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
- MΣΣT a Mathematician!
- Math-life balance Interviews
- Alan Turing
- Alonzo Church
- Asaf Karagila
- Emmy Noether
- David Blackwell
- Ada Lovelace
- Christine Ladd-Franklin
- Ruth Barcan Marcus
- Abdon Atangana
- Grete Hermann
- Katherine Johnson
- Loyiso Nongxa
- Norman J Wildberger
- Richard Hammack
- Terry Tao
- Index
- MΣΣT a Mathematician
- Math-life balance - Interviews
-
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.
- Kuber, A. 2024. Set Theory and Mathematical Logic. Indian Institute of Technology Kanpur - National Programme on Technology Enhanced Learning
- Wildberger, N.J. 2011. Counting using the grid plane, Elementary Mathematics Explained. Insights into Mathematics Math Foundations. University of New South Wales
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.