Researchers have built a math research agent that remembers its own past proof attempts - and used that memory to crack three open Erdos problems.
The system, called Ansatz, is built around what the authors call Continual Graph Memory. Instead of starting each problem from scratch, it stores every intermediate result - facts, plans, counterexamples - as nodes in a graph, with edges showing how they relate. A retrieval layer pulls only the locally relevant pieces of that graph for a given subproblem, a separate curator component updates the research frontier and distills lessons from prior attempts, and a recall step resurfaces earlier findings, including dead ends, so they get re-checked locally rather than reused blindly. Tested on all ten problems in the First Proof Second Batch set, Ansatz reports closing out every one, and separately produced unaided solutions to the Jamison caterpillar conjecture and Erdos Problems 289, 348, and 488.
The interesting part isn't the raw problem count - it's where the bottleneck sits. The paper's own framing is that running enough agents in parallel to search for a proof generates an avalanche of intermediate results, and without a way to organize and reuse them, every new problem starts from zero. Ansatz's bet is that persistent, structured memory turns that avalanche into a reusable asset, so solving one problem should make the next one easier, not just faster to repeat.
Three Erdos problems and one unrelated conjecture is a modest haul, not a breakthrough - the paper itself says progress on several other open problems is only partial. But if memory really does compound across problems the way the authors claim, the next batch is the number worth watching, not this one.