An AI model disproved a mathematical conjecture not through a flash of creative genius, but by methodically applying a known technique from a different math subfield. This highlights AI's current strength: synthesizing vast, disparate human knowledge rather than generating truly novel, alien ideas. It's an exhaustive librarian, not an intuitive genius.

AI's current strength lies in niche, formalized domains with a large training corpus and underexploited mathematical structure, like population ethics. This creates a "capability overhang" where AI can apply its mathematical prowess to problems previously tackled mainly by philosophers, yielding novel insights.

While AI models are highly effective at accelerating research by implementing existing papers or ideas, they currently lack the 'taste' for true innovation. They tend to explore incremental improvements rather than rethinking concepts from first principles, meaning human creativity remains critical for paradigm shifts.

AI shows uneven progress in mathematics. While it can solve complex geometry problems from the International Math Olympiad (IMO) almost instantly, it struggles with combinatorics, which requires more playful, puzzle-like creativity. This highlights the 'spiky frontier' of AI capabilities, where proficiency in one domain doesn't guarantee it in another, closely related one.

Future AI-driven mathematical discoveries will likely follow two paths. One is finding 'lightning bolt' connections between existing, disparate fields (e.g., number theory and physics). The other, more profound path, is 'mountain building'—constructing entirely new theoretical frameworks, a skill signifying a much higher level of general intelligence.

The core fear isn't just automation, but that AI will mechanistically solve existing problems without the creative leap that opens up entirely new fields of research. This could leave the discipline sterile, with a list of solved questions but no new avenues for human-led discovery.

Norman Foster argues AI is inherently backward-looking, as it relies on the accumulation of past data. It can optimize existing models but cannot produce paradigm-shifting ideas that have no precedent. Genuine breakthroughs still require a human creative leap beyond history.

Even if AI could instantly prove any mathematical claim, it wouldn't end the field. The truly creative and valuable work in mathematics lies in higher-level tasks AI can't do: asking interesting questions, identifying fruitful problems, and inventing entirely new branches of mathematics like calculus or information theory.

Moving beyond solving existing problems like the Millennium Prize problems, the true test of advanced AI in mathematics will be its ability to generate novel, interesting conjectures and create new, unifying definitions. This represents a higher tier of mathematical creativity, akin to the work of the greatest mathematicians who frame the questions for others to solve.