History [of concept of mathematics]

[History of] models of mathematics

Implementation [of proof example]

Substitution strategies [in proofs]

One-way transformations [as axioms]

Reducing axiom [system] details

[Mathematical] proofs in practice

Properties [of example multiway systems]

Truth and falsity [in formal systems]

Properties [of example multiway systems]

Essential incompleteness [in axiom systems]

[Universality of] predicate logic

[Universality of] algebraic axioms

Universal Diophantine equation

Statements in Peano arithmetic

[Examples of] unprovable statements

Encodings of arithmetic [by different operations]

Properties [of Diophantine equations]

Large solutions [to Diophantine equations]

Nearby powers [and integer equations]

Unsolved problems [in number theory]

More powerful axioms [for mathematics]

[Theorems about] practical programs

Rules [for multiway systems examples]

Consistency [in axiom systems]

Properties [of example multiway systems]

[Unprovable statements in] reduced arithmetic

Generators and relations [and axiom systems]

Comparison to multiway systems

Implementation [of operators from axioms]

Properties [of operators from axioms]

Algebraic systems [and operator systems]

Symbolic systems [and operator systems]

Groups and semigroups [and operator systems]

Forcing of operators [by axiom systems]

Multiway systems [and operator systems]

Properties [of logical primitives]

Notations [for logical primitives]

Theorem distributions [in standard mathematics]

Invention versus discovery in mathematics