Source Map

This file maps article claims to sources. Use ../concepts/reference_inventory.md for the full inventory.

Citation Policy

  • Cite sources for specific claims, not for atmosphere.
  • Prefer one source at the point where it matters.
  • Do not cite sources whose bibliographic details remain unverified, except in private scaffold notes.
  • If a claim comes from the internal vault rather than a public source, either present it as the author’s synthesis or remove it from citation-dependent prose.
  • The final .qmd should use the citation style already used by the site, likely a local ref.bib plus pandoc citations.

Verified Sources

Avigad: Mathematicians In The Age Of AI

Reference:

  • Jeremy Avigad, “Mathematicians in the age of AI”, arXiv:2603.03684, https://arxiv.org/abs/2603.03684.
  • Citation key: Avigad2026.

Use for:

  • AI can prove research-level theorems.
  • Mathematicians should respond to changes in mathematical practice.
  • Understanding is broader than checking.
  • AI-assisted mathematics raises practical questions about proof, explanation, and use.

Do not use for:

  • A hard prediction about the date of AI replacement.
  • Claims that AI cannot do conceptual work.

Avigad: Is Mathematics Obsolete?

Reference:

  • Jeremy Avigad, “Is Mathematics Obsolete?”, arXiv:2502.14874, https://arxiv.org/abs/2502.14874.
  • Citation key: Avigad2025.

Use for:

  • Background on the value of symbolic and mathematical reasoning in the age of AI.

Do not use as a main pillar unless reread before drafting.

Klowden And Tao

Reference:

  • Tanya Klowden and Terence Tao, “Mathematical methods and human thought in the age of AI”, arXiv:2603.26524, https://arxiv.org/abs/2603.26524.
  • Citation key: Klowden2026.

Use for:

  • Human-centered framing of AI in mathematics.
  • Tool use and mathematical practice.
  • Caution around broad social and educational consequences.

Do not use for:

  • Specific claims about skill atrophy unless the exact passage is checked.

Commelin, Jamnik, Ochigame, Taelman, Venkatesh

Reference:

  • Johan Commelin, Mateja Jamnik, Rodrigo Ochigame, Lenny Taelman, and Akshay Venkatesh, “Shaping the Future of Mathematics in the Age of AI”, arXiv:2603.24914, https://arxiv.org/abs/2603.24914.
  • Citation key: Commelin2026.

Use for:

  • Mathematical community response to AI.
  • Values, practice, teaching, technology, and ethics.
  • Intellectual autonomy and educational concerns.
  • Tools reshaping mathematical practice.

Do not use for:

  • Strong claims about inevitable community collapse.

Alon, Bloom, Gowers, Litt, Sawin, Shankar, Tsimerman, Wang, Wood

Reference:

  • Noga Alon, Thomas F. Bloom, W. T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang, and Melanie Matchett Wood, “Remarks on the disproof of the unit distance conjecture”, arXiv:2605.20695, https://arxiv.org/abs/2605.20695.
  • Citation key: Alon2026.

Use for:

  • A concrete example of AI-generated mathematical work followed by human digestion.
  • The distinction between producing a proof and producing a short, human-verified, digested argument.
  • The role of breadth, search, and patience in AI-assisted proof discovery, if supported by the paper text.

Do not use for:

  • Generalizing all AI math progress to combinatorics.

Schwer

Reference:

  • Petra Schwer, “The meaning of doing mathematics”, arXiv:2509.15998, https://arxiv.org/abs/2509.15998.
  • Citation key: Schwer2026.

Use for:

  • The question of what doing mathematics means beyond solving problems.
  • Community standards, mathematical communication, and human mathematical practice.

Do not use for:

  • Detailed technical claims about AI systems.

Gwern

Reference:

  • Gwern Branwen, “Guardian Angels: LLM Personalization for Productivity and Security”, https://gwern.net/guardian-angel.
  • Citation key: Gwern2025.

Use for:

  • The Amdahl’s-law argument that a human bottleneck limits AI-assisted productivity.
  • The economic pressure from assistant workflows toward more autonomous workflows.
  • The principal-agent framing of personalized AI.

Do not use for:

  • Mathematics-specific claims.

Unverified Source-Note References

These sources are in ../concepts/reference_inventory.md, but should not be used in public prose until verified:

  • Scott Aaronson, “Dispatches (Possibly Last Days)”.
  • Leiden Declaration on Mathematics and AI, DOI listed as 10.5281/zenodo.20302944.
  • Terence Tao EMS webinar on AI and mathematics.
  • Anonymous 2026 AI-in-physics public lecture.
  • MathOverflow question 511562, “Incentivizing Mathematics”.
  • Max Welling Information Bottleneck interview.

Claim-To-Source Map

Claim Preferred source Backup/source note
AI progress depends on cheap feedback Alon et al.; Avigad internal synthesis; Max Welling unverified
Proof generation, verification, and digestion differ Avigad; Alon et al. internal card proof-has-three-stages-only-digestion-is-human
Importance is not verified by proof checkers Avigad; Schwer internal card closed-objective-prerequisite-for-self-play
AI can increase synthesis debt Alon et al.; Avigad internal card synthesis-debt-knowledge-overhang
Mathematical knowledge lives in communities Commelin et al.; Schwer internal card knowledge-lives-in-community
AI use can weaken training Commelin et al.; Klowden and Tao Tao EMS webinar unverified
Metrics and tractability reshape goals Commelin et al. Leiden Declaration unverified; internal card means-reshape-ends
Proof gets cheaper, questions get more valuable Avigad; Alon et al. MathOverflow unverified; internal card conjecture-economy-value-shifts-from-proving-to-asking
Plateau should be split by feedback regime Avigad; Alon et al.; Klowden and Tao internal card posttraining-specialization-has-limited-transfer
Assistant workflows may move toward replacement Gwern internal card ai-amplification-is-local-optimum-replacement-is-global