Plectis

I built Plectis to pursue research I found interesting with AI, and to make a back-and-forth with human experts possible. I choose a direction, work at it and prepare the results for someone who can interpret them. Their feedback changes the next direction; I work on that and return, recording their contribution and where later work builds on it¹. An expert should be able to shape the research without having to operate the AI.

I have time and prompting experience, but limited mathematical knowledge. I chose mathematics because formal proofs can be checked, while interpretation and significance still require judgement. That lets me explore how far I can get, where I need help, and how those boundaries change as models improve. The name draws on plectere², to weave or twist: bringing different capabilities into the same work.

The Navier–Stokes announcement³ makes the question more immediate. If comparable capabilities reach inexpensive open models, output could exceed what experts can examine. Tao and his co-signatories⁴ distinguish solving problems from developing understanding. I think mathematics needs a floor for AI-assisted submissions: intelligible arguments, appropriate checks, clear limitations and attribution. Meeting it should make engagement easier, not create an entitlement to review. Experts can favour well-prepared work, giving producers an incentive to reduce the burden they impose.

The mathematics repository⁵ prototypes that floor around eight deliberately difficult Erdős problems. All remain open. Its problem pages join partial results, computations, Lean proofs and Comparator checks of selected statements. Short papers introduce the mathematics; longer records retain the reasoning for researchers and agents. For #251, constructed sequences imitate features of prime gaps but give rational sums, exposing what a proof would need beyond those features. Preparing Palomar submissions also produced a merged renderer fix⁶. I have concentrated on exposition and interesting intermediate results rather than formalising everything.

Nineteenth-century mariners contributed observations and received improved sailing charts⁷. Each voyage benefited from what other crews had learnt. Plectis is designed around that cumulative approach. Failed routes remain alongside successful lemmas, with their conditions and limitations. Someone else, or a future model, may connect those observations differently, find another route or formulate a better question.

The website is the human wrapper. Its mathematics map connects questions, claims, papers and formal source; the glossary explains terminology. A downloadable source brief lets readers explore with their own assistant. Agents help prepare these views from the underlying work. I want increasing intelligence applied to making complexity manageable, not just producing more of it. A reader should encounter the depth they need, without losing the route to what an explanation leaves out.

The software repository⁸ applies this beyond mathematics. Its component pages expose code, examples and checks; one audit example checks completion reports against actual commits and test runs in a sample repository. The front-end recordings show navigation from system maps into files and agent activity. This is the direction I want for auditing agent-run organisations, not evidence that the whole private system is reliable. Uncertainty about releasing it led me to publish testable parts instead.

The safety doctrine sets out axioms, principles and anti-principles; checks and permissions enforce particular rules. My June questions ask how model capability, operating environments and independent scrutiny interact. The systems and open-source papers explain how people can contribute direction, review, exposition, software or compute. The back-and-forth still needs testing with independent collaborators. My aim is for improving AI to multiply what an expert can direct and understand, rather than multiply the output waiting on their desk.