Who gets credit when AI contributes to a mathematical proof

Analysis. The hard number from Anthropic’s Riemann episode is already on the record. The culture fight starts after: who authors an unreleased model’s improved bound, what must be disclosed, and how journals should label machine help without laundering a lab demo into a CV line.

Stays with the existing Anthropic and TechCrunch record. No new mathematical claims.

Recap of the Riemann-bound episode

Anthropic’s research write-up says an unreleased research Claude raised a longstanding lower bound on the share of Riemann zeta zeros on the critical line from 41.6% to 67.2%. The model did not prove the Riemann hypothesis. It found the bound while trying, over two Claude Code sessions totaling about 31 million output tokens, after non-mathematician staffer Jarred Sumner told it to take a real stab and mostly sent variants of “keep going.”

Anthropic mathematicians Levent Alpöge and Ralph Furman studied and validated the paper. Outside experts Brian Conrey and Dan Goldston examined it on short notice. Claude also produced a Lean formalization. The paper lists the model as author, with humans responsible for communication and verification.

TechCrunch’s August 11 coverage treats that milestone as fuel for a wider authorship fight. Right call. The bound is Research. Credit is Culture.

Credit models that fail for agents

Traditional math credit assumes a human who can be named, blamed, and invited to the seminar. A June declaration from prominent mathematicians, cited by TechCrunch, defended that standard: proofs should be attributable to specific authors who take credit and assume responsibility for correctness.

Claude’s setup breaks the template. Sixty subagents, two carrying the key ideas, validators checking validators, a non-number-theorist at the keyboard, and staff mathematicians who did not invent the argument but must stand behind its presentation. “Author = the model” is honest about generation and thin about responsibility. “Author = the prompting engineer” is worse. “Author = the verifying mathematicians” fits liability, but erases who found the combination of prior results that moved the bound.

Fields Medalist Timothy Gowers, answering the declaration, floated a colder future: if theorems stop attaching to mathematicians the way stars stop attaching to astronomers, maybe that is survivable. Survivable is not journal-ready. Hiring committees still need a name that can be wrong in public.

Disclosure norms journals still lack

Labs publish capability posts. Journals publish papers. Those are not the same genre. Readers need, at minimum: which model version (including “unreleased”), token or compute scale if claimed, human roles (prompt, verify, formalize, communicate), dependence on prior human theorems, and whether a machine-checkable artifact exists.

Lean helps on correctness. It does not settle authorship. A sorry-free formalization can still leave a CV fight: byline, acknowledgment, tools line, or a checkbox nobody reads?

Without shared labels, every lab invents theater. One paper lists Claude as author. Another buries the model in a footnote. A third puts the human first and the system in methods. That inconsistency is how priority disputes start.

A practical checklist for AI-assisted math claims

Until societies and journals standardize, treat AI-math announcements like this:

1. Separate discovery from responsibility. Say who generated the argument and who accepts errors.
2. Require model identity and release status. Version hashes beat vibes.
3. Disclose the human loop. Prompt cheerleading differs from co-deriving lemmas.
4. Demand adversarial checks beyond the lab blog: named outside readers, preferably a public formalization.
5. Ban silent polishing. If a human rewrote the proof for readability, say so.
6. Keep “AI discovered” for claims with a checkable delta, not autocomplete restating a known paper.

The Riemann bound will get chewed on by specialists. The culture question is live: credit without disclosure is marketing. Disclosure without a responsible human is theater.