Current AI models are powerful at applying a vast library of known mathematical techniques to solve problems. However, they fall short in the more abstract, "fuzzy" areas of developing new theories, intuitions, and non-rigorous philosophies that often drive major breakthroughs in the field.

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 proofs often rely on brute-force mechanical searches across complex parameter spaces, yielding dense, unreadable constructions. This frictionless resolution separates verification from human understanding, discarding the intermediate intellectual detours that historically spurred new subfields of mathematical study.

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 generates ideas by referencing existing data, making it effective for research but poor for true innovation. Breakthroughs require synthesizing concepts from disparate fields and having a unique vision for the future—capabilities that AI lacks. It provides probable answers, not visionary ones.

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.

A major frontier for AI in science is developing 'taste'—the human ability to discern not just if a research question is solvable, but if it is genuinely interesting and impactful. Models currently struggle to differentiate an exciting result from a boring one.

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.