Computational Theology

Mathematics at the Boundary Between Model and God: What Would a Mathematics of Non-Exhaustive Knowledge Prove

~ YIN Renlong

Methodological note: This appendix records a personal, AI-assisted research exploration at the intersection of theology, computer science and mathematical logic. The formulas below therefore have different statuses: some state established mathematical results; others propose notation or conjectural research structures; and the theological interpretations require arguments beyond mathematics. AI helped translate my questions into candidate formal language and locate relevant fields, but its fluency is not evidence.

The question that interrupted the formalization

The main essay ended with a possible research…
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The Formal Limits of Speaking About God: From Cantor’s Absolute Infinity to Inexhaustible Representation

~ YIN Renlong

*This exploratory essay grew from personal theological reflection and sustained dialogue with AI. It investigates mathematical possibilities and limitations without claiming to present a new proof or completed formal theory.

I began with a question that seemed much simpler than the one I am now trying to formulate. Mathematics has studied infinity rigorously for more than a century and has shown that infinite collections can have different cardinalities. Theology, meanwhile, has spoken about the infinity and incomprehensibility of God for…
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Toward a Boundary-Relative Computational Theology: What Must Theology Become to Be Verifiable?

~ YIN Renlong

I did not begin by trying to design a methodology for computational theology. I began with a much smaller and more personal question. I had written three essays whose subjects seemed rather different: a generative artwork that gradually changed my understanding of creation, my later return to that artwork as its beholder, and Éric Rohmer’s A Tale of Winter, which moved me from romantic hope toward questions of certainty, relational responsibility and the people left outside a miraculous ending.…
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Can Theology Be Computed Without Being Reduced?: From Proof Checking to Machine-Scale Hermeneutics

~ YIN Renlong

A prediction about mathematics led me somewhere I did not initially expect. Jacob Tsimerman had suggested that artificial intelligence could become better than mathematicians at doing mathematics within two years. I began by asking how such an abrupt transition could be possible. The obvious question concerned capability: had AI suddenly acquired mathematical intuition comparable to that of the strongest human researchers? But another explanation seemed increasingly important. Mathematics may be among the earliest disciplines to experience this transformation because it…
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