Generative AI can produce the "miraculous" insights needed for formal proofs, like finding an inductive invariant, which traditionally required a PhD. It achieves this by training on vast libraries of existing mathematical proofs and generalizing their underlying patterns, effectively automating the creative leap needed for verification.

The AI industry is hitting data limits for training massive, general-purpose models. The next wave of progress will likely come from creating highly specialized models for specific domains, similar to DeepMind's AlphaFold, which can achieve superhuman performance on narrow tasks.

LLMs shine when acting as a 'knowledge extruder'—shaping well-documented, 'in-distribution' concepts into specific code. They fail when the core task is novel problem-solving where deep thinking, not code generation, is the bottleneck. In these cases, the code is the easy part.

An LLM shouldn't do math internally any more than a human would. The most intelligent AI systems will be those that know when to call specialized, reliable tools—like a Python interpreter or a search API—instead of attempting to internalize every capability from first principles.

Broad improvements in AI's general reasoning are plateauing due to data saturation. The next major phase is vertical specialization. We will see an "explosion" of different models becoming superhuman in highly specific domains like chemistry or physics, rather than one model getting slightly better at everything.

Language models work by identifying subtle, implicit patterns in human language that even linguists cannot fully articulate. Their success broadens our definition of "knowledge" to include systems that can embody and use information without the explicit, symbolic understanding that humans traditionally require.

Deep expertise in one AI sub-field, like model architectures, isn't a prerequisite for innovating in another, such as Reinforcement Learning. Fundamental research skills are universal and transferable, allowing experienced researchers to quickly contribute to new domains even with minimal background knowledge.

A key decision behind Google DeepMind's IMO Gold medal was abandoning their successful specialized system (AlphaGeometry) for an end-to-end LLM. This reflects a core AGI philosophy: a truly general model must solve complex problems without needing separate, specialized tools.

An LLM successfully solved a toddler's sleep problem, a task that previously required a human consultant charging hundreds of dollars per hour. This demonstrates AI's immediate power to democratize specialized expertise. It synthesizes vast knowledge to provide personalized, actionable advice for a fraction of the cost of a human professional.