Today’s episode maps a surprising split in AI power: superhuman mathematical reasoning on one hand and deeply personal, life‑management intelligence on the other. We unpack the intellectual bombshell of Vibe Proving, where Harmonic’s Aristotle solved a 30‑year Erdős problem in six hours and had the proof machine‑verified by Lean in one minute — a sign that discovery plus formal verification is now tractable at scale. We also critique how narrow exam‑style benchmarks miss the creative leaps these systems make and why a new generation of reasoning tests is urgently needed.

Then we switch to real‑world intimacy: how executives are feeding years of biometric, scheduling and dietary data to models to produce hyper‑personal training plans, and how consumer AI flagged a dangerously high homocysteine level, hypothesized an MTHFR variant, and helped a user correct it in weeks. We cover builders turning this into product — personal biodata stores, cross‑checking across models, and high‑ROI workflows like AI‑driven patent landscaping and automated invoice processing.

Underpinning all this is engineering: context plumbing — the continuous pipes that deliver live user context to agents — which explains why systems like the Warp development agent now lead benchmarks. Practical guidance for product teams: don’t port whole products into chat; expose a few high‑leverage capabilities the model can orchestrate; design around No (new private data), Do (real actions) and Show (rich, non‑text outputs).

Finally, we examine the shifting geopolitics and transparency crisis: Chinese labs now dominate open model downloads, true disclosure of training data has plunged from ~80% to ~39%, and massive valuations and ad pivots are reshaping incentives. For marketers and AI professionals the takeaway is clear: the opportunity to create transformative, personalized experiences has never been greater — but so is the responsibility to design for trust, verifiable provenance, and tightly scoped, context‑safe integrations.