- 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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