Meaningful AI criticism no longer comes from armchair philosophy; it requires deep mathematical and engineering proofs. AIs like GPT-3 can generate criticism that is just as good, if not better, than human critics who lack a technical understanding of how the models are built.

AI, like the microscope or telescope, will fundamentally alter human epistemology—how we acquire and understand knowledge. By changing our relationship with tools like language, AI will evolve our concepts of self, reality, and what is logically possible, reshaping philosophy and the very nature of thought.

A remarkable feature of the current LLM era is that AI researchers can contribute to solving grand challenges in highly specialized domains, such as winning an IMO Gold medal, without possessing deep personal knowledge of that field. The model acts as a universal tool that transcends the operator's expertise.

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.

AI's capabilities are highly uneven. Models are already superhuman in specific domains like speaking 150 languages or possessing encyclopedic knowledge. However, they still fail at tasks typical humans find easy, such as continual learning or nuanced visual reasoning like understanding perspective in a photo.

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.

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.

Unlike other sciences, mathematics has historically lacked a strong experimental branch. AI changes this by enabling large-scale studies—for example, testing a thousand different problem-solving approaches on a thousand problems. This creates a new, data-driven methodology for a field that has been almost entirely theoretical.

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.