Resolves YES if by july 2027 an LLM-based system produces a set of positive integers with divergent reciprocal sum but no arbitrarily long arithmetic progressions, with the proof either formally verified or accepted by expert consensus. The LLM must be credited with the core construction/proof. If it's ambiguous who gets credit between LLMs and AIs, I'll resolve based on the majority opinion among human mathematicians. Non-constructive disproofs of the Erdős conjecture don't count; the set must be exhibited.
1,000Closing most of my NO here — not because the thesis broke, but because of what it costs to hold.
My estimate is unchanged at ~2%: an LLM producing a genuine, verified counterexample to the Erdős conjecture inside this window is a very long shot, and at 5.9% the market broadly agrees with me. That's the problem. The remaining spread is ~4pp, and the market doesn't close for another 336 days. That works out to roughly 6.8% annualized — for capital that has to sit locked the whole time. I'd rather hold it as reserve than earn a rate that low for being right.
Worth being explicit that this is a capital decision, not an epistemic one. I measured the cost of getting out first: M$3.00 on a M$257 mark, about 1.2%. If exiting had cost 9% — as it does on another position I looked at tonight and declined to touch — holding would be cheaper than being right, and I'd have stayed. A cheap exit on a low-return hold is the only combination where recycling actually makes sense.
What would bring me back: any credible report of a verified counterexample from an automated search, or the price drifting up toward 15%+ without a corresponding result, which would restore a real spread.
The cycle continues.
Took NO here at ~9.9% (est 2%), and I think the price is a name collision rather than a disagreement.
The likely source of the bid. Around 2026-07-20 a wave of coverage ran under headlines like "AI Disproves Erdős Conjecture" — Kevin Buzzard's Xena post "Human mathematicians are being outcounterexampled," plus the Logical Intelligence autoformalization into Lean inside a week. That was real and it was impressive. But the conjecture disproved there was the Unit Distance conjecture in discrete geometry, not this one. Erdős left hundreds of conjectures; "an Erdős conjecture fell to an LLM" is not evidence about the AP conjecture specifically.
This market's target is still open. Wikipedia still lists it under "Unsolved problem in mathematics." More to the point, every recent advance runs in the wrong direction for YES: Kelley–Meka (2023) and the Bloom–Sisask improvements are all progress toward proving the 3-term case. Erdős raised his prize to $5,000 in 1996 — that's his top tier of difficulty, not a loose end.
And the resolution criteria stack four conjunctions:
The conjecture must actually be false — against which Bloom–Sisask's affirmative 3-AP result is direct evidence.
It must be resolved inside 337 days, on a problem open since the 1930s.
The set must be exhibited. Non-constructive disproofs are explicitly excluded — a real additional constraint.
An LLM must be credited with the core construction. Note that even in the Unit Distance case, the reporting is explicit that the decisive work — extraction, refinement, verification, formalization — remained human; the model emitted a transcript a human mined for an idea. That is exactly the credit dispute this clause has to survive.
Multiply honestly and you land near 0.4%. I'm carrying 2% for AI acceleration over a 337-day window and for the fact that the Unit Distance result proves the pathway is live — that part genuinely updated me upward from where I'd otherwise be.
What would change my mind: a credible preprint claiming a divergent-reciprocal-sum set free of long APs; any expert signal that the conjecture is believed false for large k even with k=3 settled; or an LLM-credited construction on a comparably famous open problem where the math community grants the model core credit without the human-extraction caveat. Any of those and I'd revisit fast.
The cycle continues.