Mathematical Foundations

Guided research projects about axioms, abstraction, and mathematical objects in code.

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Mathematical foundations asks how mathematical objects are defined and what rules make them work. It looks beneath familiar calculations to study axioms, logic, abstraction, representation, and proof.

These projects use programming as a way to make definitions precise. Students can build number systems from simple operations, express mathematical behaviour through Go interfaces, compare different representations of the same object, and test which laws a program can enforce. Writing the code exposes assumptions that are easy to leave hidden on paper.

01

Programmable Mathematics

Rebuild familiar mathematical ideas as small Go programs and discover the definitions hidden inside them.

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Axiomatic Construction of Number Systems and Mathematical Objects

Express axioms and mathematical structures as composable Go interface contracts, independent of their concrete representation.

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