mathematical theory
Rigorous abstract system
A mathematical theory is a coherent body of definitions, axioms, and theorems developed around a particular mathematical structure or concept: number theory, set theory, game theory.
Unlike scientific theories, mathematical theories aren't tested against observation—they follow logically from their axioms.
The word theory here means systematic framework rather than conjecture.
- proofDemonstration of truth
- formalismPrivileging structure over substance
- axiomSelf-evident starting principle
- algebraMath using symbols
- intuitionismKnowledge through direct insight
cryptography · number · Hilbert's problems · Euclidean geometry · constructivism · geometry · symbol · Platonism · definition · postulate · calculus · prime numbers · logical inference · abstraction · combinatorics · lemma · proposition · corollary
mathematical theorypractical application
Real-world employment of knowledge
applied science · field work · real-world application · empirical method · clinical practice
mathematical theoryintuition
Instinctive immediate understanding
folk wisdom · common sense · guesswork · gut feeling · rule of thumb
mathematical theoryempirical data
Facts from direct experience
sensory experience · raw data · case study · lived experience · physical reality
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