Mathematics and the Sovereignty of God

Will Johnson

Video: https://www.youtube.com/watch?v=s3yAAA1nclg

Abstract:

For millennia, poets and scientists have glorified God by contemplating His creative work in the natural world. Can I do the same as a pure mathematician? As Christians, we believe that the beauty, complexity, and structure of the natural world point to the God who created the universe. The same beauty and complexity seem to be present within the mathematical world. I would like to attribute this to God, but the logical inevitability of mathematics seems to present an obstacle. We Christians sometimes picture God as a fantasy writer, able to do whatever He wishes with the world, within the limits of logic. This would seem to give God no authority over mathematics, though. How then could He be responsible for the structure and beauty seen in mathematics?

As a Christian mathematician, this philosophical issue matters to me. Is what I study created by God? Can I pray for conjectures to be true? Is God bound by logic, or is He above it? Somewhat surprisingly, certain results from mathematical logic yield ways in which the laws of logic can be more flexible and variable than one would otherwise expect. I would argue that these results suggest that God can, in fact, influence and create mathematics. I will describe a specific way in which this might happen.

Bio:

I am a fourth-year mathematics graduate student at UC Berkeley, specializing in model theory, one of the branches of mathematical logic. I am interested in the applications of model theory to other branches of mathematics, particularly algebraic geometry and number theory. I studied computer science and mathematics at the University of Washington as an undergraduate, before entering the PhD program at Berkeley.

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