Mathematics is Much More than Proof: Toby Ord on What AI Hasn't Yet Automated

On August 23, Oxford scholar Toby Ord published a new essay on the nature of mathematics in the AI era. His central argument: AI systems are rapidly automating mathematical proof, yet proof is not all there is to mathematics—the ability to "ask the right questions" in mathematical research remains a key link that AI has not yet demonstrated it can replace.

Confirmed

• Toby Ord notes that symbolic computation has been automated over the past forty years, and we may now be witnessing AI automating mathematical proof (or most of it)—akin to how mathematicians once spent large amounts of time on computation before 20th-century computers automated it.
• He stresses that mathematical work goes far beyond proving; like science, a large part of mathematics lies in figuring out what questions to ask. From an information-theoretic standpoint, he even points out that a question contains almost as much information as the proposition it explores (a yes/no question has one bit less than the proposition).
• He gives an example: even if a machine could prove any true mathematical statement in microseconds, it would be of little help if it could not come up with questions like the "unit distance problem" before all the stars burn out.

Not Yet Confirmed

• Toby Ord explicitly states that there is currently little evidence either way on whether AI can replicate human mathematicians' distinctive ability to find important questions among an exponential space of possibilities.
• He identifies a key bottleneck: we lack good training data or verifiable rewards for "asking good questions"; unless this ability comes for free during pretraining on mathematical texts or learning to prove statements, it is hard to see why models would possess it.

Why It Matters

• This argument offers a finer-grained take on whether AI can replace mathematicians: the trend toward automating proof is clear, but higher-level mathematical work such as research taste and question selection may remain a long-term human preserve—or become a key target for the next generation of AI research.

2026-08-23 ~ 2026-08-24 · 9 related posts

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