Section Claim Ladders
For each section, use the safe claim by default. Use the stronger claim only if the section has enough examples and citation support.
Opening: The Wrong Question
Safe claim:
AI-for-math commentary is often too coarse because mathematics contains many different tasks.
Stronger claim:
The feedback-cost split predicts AI progress better than the usual split between mathematical subfields.
Avoid:
- “Everyone is asking the wrong question.”
- “The discourse is shallow.”
- Broad dismissal of public commentary.
Sources:
../concepts/cheap_feedback.md../concepts/feedback_cost_map.md
Section 1: Cheap Feedback
Safe claim:
Tasks with cheap checks are easier to automate and improve.
Stronger claim:
Cheap feedback is the main reason AI progress looks rapid in some mathematical tasks and slower in others.
Avoid:
- Saying cheap feedback is the only variable.
- Saying hard human problems become easy for AI whenever a verifier exists.
Sources:
- Avigad.
- Alon et al.
- Klowden and Tao.
Section 2: Proof Is Three Tasks
Safe claim:
Finding a proof, checking a proof, and turning a proof into usable understanding are different tasks.
Stronger claim:
AI progress in the first two tasks can increase the burden on the third.
Avoid:
- Saying AI proofs are useless.
- Saying human-written proofs are automatically understandable.
Sources:
- Avigad.
- Alon et al.
Section 3: The Importance Oracle Is Missing
Safe claim:
A proof checker certifies correctness, not importance.
Stronger claim:
Self-play-like progress in mathematics remains limited by the absence of a cheap importance reward.
Avoid:
- Saying AI will never develop taste.
- Treating taste as mystical.
- Saying RLHF is useless in general.
Sources:
- Avigad.
- Schwer.
- Internal source note on
closed-objective-prerequisite-for-self-play.
Section 4: Synthesis Debt
Safe claim:
A field can produce results faster than it turns them into usable understanding.
Stronger claim:
AI can worsen this imbalance by increasing result production faster than digestion.
Avoid:
- Saying theorem count is meaningless.
- Claiming that all AI-generated proofs are opaque.
Sources:
- Alon et al.
- Avigad.
- Internal source note on
synthesis-debt-knowledge-overhang.
Section 5: The Community Layer
Safe claim:
Documents need communities that know how to use them.
Stronger claim:
If automation reduces the number of people trained deeply in an area, the literature can remain available while working knowledge weakens.
Avoid:
- Nostalgia for manual labor.
- Claims about inevitable collapse of mathematical communities.
Sources:
- Commelin et al.
- Schwer.
Section 6: Acquisition Asymmetry
Safe claim:
AI tools can help experts while changing the training path for novices.
Stronger claim:
The same tool that amplifies expert work can remove the struggle by which students form mathematical judgment.
Avoid:
- Making the issue about cheating.
- Treating all student AI use as harmful.
Sources:
- Commelin et al.
- Klowden and Tao.
- Tao EMS webinar only after verification.
Section 7: Measurability Distortion
Safe claim:
Institutions tend to reward work that is easy to measure and compare.
Stronger claim:
AI can shift research attention toward problems whose progress is easy to verify, even when deeper problems lie elsewhere.
Avoid:
- Saying benchmarks are bad.
- Saying institutions are irrational.
- Claiming the Leiden Declaration says more than has been verified.
Sources:
- Commelin et al.
- Leiden Declaration only after verification.
Section 8: The Conjecture Economy
Safe claim:
If proof becomes easier to obtain, good questions become relatively more valuable.
Stronger claim:
Academic prestige systems may be misaligned with this shift because they mainly reward solved problems.
Avoid:
- Saying proof no longer matters.
- Saying prizes should reward only conjectures.
Sources:
- Alon et al.
- Avigad.
- MathOverflow only after verification.
Section 9: Feedback Cost Map Of Science
Safe claim:
AI disruption should be predicted by feedback cost, not just by field.
Stronger claim:
The same field can contain both AI-vulnerable and AI-resistant subproblems depending on feedback cost.
Avoid:
- Precise timelines unless sourced.
- Claims that an entire discipline is safe or doomed.
Sources:
- Alon et al. for mathematical example.
- Max Welling only after verification.
- Internal synthesis.
Section 10: Plateau, AGI, And Labor
Safe claim:
The plateau and AGI questions are too coarse unless split by feedback regime.
Stronger claim:
Even without general automation of all intellectual work, automation of cheap-feedback work can have large labor effects.
Avoid:
- Declaring AGI meaningless in general.
- Fixed timelines for replacement.
- Saying all humans will become bottlenecks.
Sources:
- Avigad.
- Klowden and Tao.
- Gwern.