The Problem Is the Problem: Towards Scalable Mathematical Discovery

The Bottleneck Problem

Most AI-for-math systems today work the same way: a human picks a problem, an AI reasons about it, a human reviews the result. As AI gets better, this workflow breaks down. Frontier models are expensive to run, and expert mathematicians who can evaluate novel results are scarce. The real constraint isn't what the AI can do—it's human attention at the start (choosing which problems matter) and end (judging which outputs are worth publishing). These two stages have become the limiting factor for scaling AI-assisted mathematical discovery.

This paper reframes the problem. Instead of humans pre-selecting specific problems, they hand the system a research direction—say, combinatorics. The system then finds, attempts, and ranks candidate problems from the literature, using filtering stages to surface only the most promising work for expert review. This shifts human effort from individual curation into high-level guidance.

How FAR Works

The authors built a three-stage cascade called FAR (Find, Attempt, and Recommend):

Find scans a large literature corpus—in their pilot, 5,245 combinatorics papers—and extracts candidate conjectures and open problems. This yields 6,453 candidates.

Attempt filters for well-posed, apparently still-open problems (winnowing to 4,717) and applies AI reasoning to search for solutions or insights. This produces 598 potential resolutions.

Recommend uses automated triage—likely a combination of heuristic scoring and model-based ranking—to select which results are worth showing to human experts. The system surfaced 77 items for author-team review.

The key insight is that the system doesn't ask frontier models to solve arbitrary problems from scratch. Instead, it:

• Narrows the search space to known open questions in an area of human interest
• Uses cheaper filtering stages (literature extraction, well-posedness checks) before invoking expensive reasoning
• Focuses scarce expert time on artifacts that have already passed multiple sieves

This mirrors recommendation systems in industry: cast a wide net cheaply, then prune progressively.

What They Found

In the combinatorics pilot, the 77 items surfaced by the pipeline included discoveries related to notable open problems by Erdős–Straus, Davies–Jenssen–Perkins–Roberts, Ikenmeyer–Pak–Panova, and Lund–Saraf–Wolf. The abstract doesn't spell out what those discoveries were, but the fact that expert mathematicians found "interesting" results among the selected items suggests the filtering strategy successfully identified mathematically relevant work—not noise.

Why It Matters

Current AI-math workflows don't scale because they're bottlenecked by human curation, not model capability. By automating problem discovery and applying progressive filtering, FAR decouples human guidance from individual problem selection. A researcher can now steer the system at a higher level ("I want results in combinatorics") and trust the pipeline to surface work worth their time. This is a shift in how humans and AI collaborate: less back-and-forth on specific conjectures, more strategic direction-setting followed by filtering and review.

The numbers are encouraging: starting from thousands of papers, the pipeline reduces the decision space to dozens of candidates, each of which has passed multiple automated quality checks. For research-scale mathematics, where problems are hard to find and expert time is precious, this scaling mechanism could enable genuinely new workflows.