TL;DR
This paper proposes viewing mathematics as an experimental science grounded in computation, where axioms are provisional and inferred from experience, reshaping the understanding of Godel's theorem and AI's impact on math.
Contribution
It introduces a computational perspective of mathematics as an experimental discipline, offering a new interpretation of foundational theorems and implications for AI.
Findings
Axioms are seen as provisional, inferred from computational experience.
Godel's theorem impacts the understanding of incompleteness, not contradiction.
Mathematics is reframed as an experimental science grounded in computation.
Abstract
We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience with the experiental substrate of mathematics which we locate within computation rather than encoding intuitive and absolute truths. This offers a reframing of Godel's theorem, placing its impact sharply upon the incompleteness rather than the potentially contradictory nature of any computational set of axioms. The essay originated in an attempt to make precise the nature of mathematics in order to estimate how AI might impact it. This exploration is continued in the paired essay "The mechanical creation of mathematical concepts."
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