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.

While AI excels at writing software—a domain with clear, verifiable outcomes (it compiles or it doesn't)—its application in fields like drug discovery is limited. Progress stalls where outcomes aren't easily and quickly verifiable, requiring complex, expensive, real-world testing.

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.

While powerful for analyzing existing medical data, AI struggles with true scientific discovery where the underlying biological principles are still unknown. Since AI learns from existing data, it cannot easily generate hypotheses that violate the very rules it was trained on, limiting its role in frontier science.

The Stanford AI Index reveals a "jagged frontier" where advanced models achieve superhuman performance on complex tasks like the International Mathematical Olympiad, yet fail at simple, common-sense activities like reading an analog clock. This highlights their lack of real-world grounding and the need for more holistic "world models."

Unlike medicine or biology, which require messy, expensive real-world experiments, pure mathematics offers a cost-effective and prestigious arena for AI labs to demonstrate their models' abstract reasoning power. A proof is a proof, requiring no lab work or physical trials to validate.

AI excels at solving problems with clear, verifiable answers, like advanced math, allowing for effective training. It struggles with complex societal issues like unemployment because there is no single, universally agreed-upon "correct" solution to train against, making it difficult to evaluate the AI's path.

AI models can solve complex, benchmarkable problems like advanced math or chess, yet their overall real-world impact remains limited. This suggests a persistent gap between specialized capabilities and true, world-altering generalization, a modern version of Moravec's paradox where hard problems are easy and easy problems are hard.

Traditional science failed to create equations for complex biological systems because biology is too "bespoke." AI succeeds by discerning patterns from vast datasets, effectively serving as the "language" for modeling biology, much like mathematics is the language of physics.