Philosophy

Why this exists

Conjura started from one bet: that AI can be pushed as far as it will go in mathematical research, provided the output is held to a standard that does not care where it came from.

Cryptographic research collides more than it compounds. Work happens in private notebooks, so partial progress is rediscovered and dead ends are walked into twice. Fear of being scooped keeps the notebooks shut, and the secrecy causes the waste. Conjura answers with a public, timestamped record of what has been tried, resolved or abandoned; claiming a problem in the open is cheaper than winning a race for it.

The list is modelled on Erdős, who priced his conjectures to say what each was worth and that anyone could take it. Cryptography keeps no such board, so Conjura keeps one, and intends to let anyone attach a bounty payable once a resolution is verified rather than when a committee has met. Over the longer run the cost of attacking a problem comes down largely to tokens spent, which makes an open question something that can be priced, funded publicly as readily as by a private bounty, ordered by whoever wants it solved, and given a real estimate of its difficulty instead of a reputation for one. Compute should be spread as widely as the prizes: a funded lab can run several models for weeks and a graduate student cannot, and a field whose output tracks budgets has stopped being checkable by anyone. Pooled idle capacity, searched across models, is the intended answer.

None of it is worth anything unchecked. AI has made it cheap to produce mathematics that reads as rigorous and nobody has verified, and a fabricated citation is as easy to write as a real one. So every claim carries a badge grading what was verified, which can understate but never overstate. Two mechanisms close the gap between reading well and being true: named human reviewers, credited permanently for what they checked, and autoformalization, which turns a prose argument into a Lean artifact a machine accepts or rejects.

That is also the reply to the venues. IACR conferences follow the ACM policy, which, read at source on 16 August 2026, sets a limit of degree: a work must be “not primarily the result of the tool’s generative capabilities”. Several results here cross that line on purpose. The clause has no operational definition and no stated test for a breach. How much of the work a model did has no measurable answer; what has been checked does. The side effect is a benchmark the field otherwise lacks: how models perform against unsolved problems.

Next are bounties on live problems, the session logs that belong beside every result and are the one promise still unkept, and enough resolved conjectures to make the case by existing rather than by argument. None of it works as one person’s site: a record of attempts is useful only if more than one group writes to it, and a badge means little until someone other than the author checks it. This site has not been reviewed either: its prose, schema, scripts and this page were AI-generated, directed by a human but never independently reviewed, and the notice narrows only as review happens. Bring a problem, a proof, a refutation, or an hour of checking to the repository.