TheoremBench: Leveling Up AI's Math Game

AI's got a new playground, and it's not for the faint-hearted. Enter TheoremBench, a fresh tool for testing AI's prowess in formal math proving.

Beyond the Basics

TheoremBench isn't your average benchmark. It takes AI beyond the narrow confines of competition-style problems. Instead, it challenges them with nearly a hundred classical theorems. That's right. We're talking about the big leagues here. The benchmark splits into two versions: a straightforward main version and a more complex premised version. The latter breaks down theorems into related subtheorems, offering a deeper dive into the proving tasks.

This setup isn't just about whether AI can prove the final theorem. It's about how they navigate the entire proof structure. Can they handle the intricacies? Or are they just bluffing their way through?

Unpacking the Performance

So, what did the experiments reveal? Unsurprisingly, provers with explicit premises performed better. It's like giving a map to a traveler. But here's the kicker: current systems are still leaning too heavily on easy subtheorems. Instead of crafting sleek proof plans, they're often stuck in long, inefficient tactics. That's a problem.

If nobody would play it without the model, the model won't save it. You can't just brute force your way through math. TheoremBench exposes these weaknesses, offering a clearer picture of AI's formal reasoning skills.

Why It Matters

Why should we care about this? Simple. The AI proving game isn't just about winning contests. It's about developing tools that can tackle real-world problems. From cryptography to complex scientific computations, the applications are endless. But if current models can't handle anything beyond basic premises, we've a long way to go.

TheoremBench is a wake-up call. It's a reminder that the game comes first. The economy comes second. We need AI systems that aren't just chasing low-hanging fruit but are ready to climb the entire tree. Are today's models up to the challenge? Only time, and TheoremBench, will tell.