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Notes from the intersection

Essays on applied math, AI, and the shape of trustworthy systems.

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Synthetic Universes: How AI Creates Knowledge That Never Existed

When AI can generate its own problem universes and verify the results formally, it's no longer limited by human data or human imagination. This is the most credible path to superintelligence we have — and the foundations are being laid now.

2/25/2026

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Lost in Translation: What LLMs Actually Understand About Mathematics

The 'LLMs hallucinate math' narrative is a coarse oversimplification. Recent research reveals that models encode deep mathematical structure internally — the real bottleneck is the lossy translation from latent space to human-readable output.

2/20/2026

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Beyond Next-Token Prediction: The Case for Immutable Verification

If the bottleneck between AI and mathematical reasoning is the output channel, the fix is a better channel. Formal verification — proof assistants like Lean — provides the lossless interface that transforms LLMs from pattern-matchers into trustworthy reasoning agents.

2/3/2026

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