AI intelligence shouldn't be measured with a single metric like IQ. AIs exhibit "jagged intelligence," being superhuman in specific domains (e.g., mastering 200 languages) while simultaneously lacking basic capabilities like long-term planning, making them fundamentally unlike human minds.

Andrej Karpathy's 'Software 2.0' framework posits that AI automates tasks that are easily *verifiable*. This explains the 'jagged frontier' of AI progress: fields like math and code, where correctness is verifiable, advance rapidly. In contrast, creative and strategic tasks, where success is subjective and hard to verify, lag significantly behind.

Progress towards AGI is not a smooth climb. Models exhibit "spikiness"—they can perform at a world-class level on one narrow domain but degrade to a "bad high school student" with slight perturbations. This non-intuitive generalization makes their capabilities uneven and unpredictable.

The advancement of AI is not linear. While the industry anticipated a "year of agents" for practical assistance, the most significant recent progress has been in specialized, academic fields like competitive mathematics. This highlights the unpredictable nature of AI development.

An internal, general-purpose OpenAI model solved a famous combinatorial geometry problem without specialized training or scaffolding. Unlike task-specific AIs, this achievement demonstrates a significant advance in abstract reasoning, suggesting models are progressing towards more general intelligence faster than anticipated.

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."

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.

We have formal languages like Lean for deductive proofs, which AI can be trained on. The next frontier is developing a language to capture mathematical *strategy*—how to assess a conjecture's plausibility or choose a promising path. This would help automate the intuitive, creative part of mathematical discovery.

Frontier AI models exhibit 'jagged' capabilities, excelling at highly complex tasks like theoretical physics while failing at basic ones like counting objects. This inconsistent, non-human-like performance profile is a primary reason for polarized public and expert opinions on AI's actual utility.