Claims Ledger

This file records the claims the article may support, the claims it must qualify, and the claims it should avoid. The goal is to keep the final post sharp without overclaiming.

Claims To Support

  • AI progress is fastest where candidate outputs can be checked cheaply.
  • The useful split is often feedback cost, not discipline label.
  • Proof generation, proof verification, and proof digestion are different tasks.
  • Formal verification can certify correctness but not mathematical importance.
  • A machine-generated proof that nobody digests can close a problem while adding little reusable understanding.
  • AI can increase the production of mathematical results faster than communities can synthesize them.
  • Mathematical knowledge depends on living communities as well as documents.
  • The same AI tool can amplify experts and weaken the training path for novices.
  • Tools and benchmarks can reshape what institutions reward.
  • If proof becomes easier to obtain, the relative value of good questions, good definitions, and good synthesis rises.
  • The plateau question should be split by feedback regime.
  • “AGI” is less useful here than asking which tasks become cheap and which remain hard to score.
  • AI assistance can be economically unstable when the human is only the serial review bottleneck.

Claims To Qualify

  • “AI is good at math.” Qualify by task. AI looks strongest where correctness or success can be checked cheaply.

  • “AI cannot do taste.” Do not state as an absolute. Say that there is no cheap training or evaluation signal for many taste judgments.

  • “AI proofs are bad.” The issue is not whether every proof is bad. The issue is the cost of checking, compressing, teaching, and reusing them.

  • “Students using AI will not learn.” Qualify by use. Expert-guided use can help; bypassing formative struggle can weaken judgment.

  • “Institutions will reward the wrong work.” Qualify by mechanism. Institutions tend to reward what is visible, measurable, and comparable.

  • “AGI is a malformed concept.” Use cautiously. The post can say that AGI is too coarse for this question, because capability is task- and feedback-dependent.

  • “AI will replace researchers.” Qualify by role. Labor inside verifiable pipelines is easier to automate than question selection, responsibility, taste, and interpretation.

Claims To Avoid

  • AI cannot make real mathematical discoveries.
  • AI will soon solve all mathematics.
  • AI is only pattern matching.
  • Human mathematicians are safe because taste is magical.
  • Formalized mathematics is shallow.
  • Combinatorics is easy.
  • Pure mathematics is more vulnerable than applied mathematics as a blanket claim.
  • All generative or AI-assisted methods ignore the forecast, context, or human intent.
  • The current prize system is simply wrong.
  • Students who use AI are cheating.
  • AGI definitely will or will not arrive.
  • Full replacement is inevitable on a fixed timeline.

Red Lines

These sentences, or close variants, should not appear in the draft:

  • “AI changes everything.”
  • “The central insight is…”
  • “This is not merely a technological shift but an epistemic rupture.”
  • “The future belongs to…”
  • “Human creativity will remain uniquely…”
  • “The real question is not X but Y” unless X has been established as a live misconception.
  • “This framework shows…”

Safe Core Claim

If the draft feels too broad, return to this:

AI changes the cost of producing candidate answers. It changes the cost of checking some answers much less. Where checking is cheap, progress can compound quickly. Where the check depends on taste, experiments, institutions, or long-term understanding, the bottleneck remains.