Discourse of Mathematics

  • Mathematical subfields come and go over the centuries
  • What is “mathematical maturity
    • Pre-rigorous
    • Rigorous
    • Post-rigorous
  • Model of the discipline of mathematics, (knowing what is known, knowing where lies opportunities for discovery)
  • Definition-theorem structure (c.f. ProofWiki)
  • Formalizing intuition gives insights; opportunities in model of discipline of mathematics result in new intuitions to formalize
  • We can shoehorn this conversation of discipline and formalization into Hegelian synthesis
  • Relationship between mathematics and other fields
  • Explored mathematical subfields occasionally map to generalizable patterns in life (c.f. electrodynamic waves, epidemic propagation)
  • Explored theorems in mathematics converse with observations
  • Models are contextualized instances of the definiton-theorem structure
  • Definition-theorem structure as a language to express objectives in the discipline and in real-world motivations; consider the definition-theorem structure and models a more expressive form of logical structure and syllogistic arguments.
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