AGI-complete in general? Obviously. But still, a lot can be done. See e.g.:
- The Busy Beaver Challenge deciders
deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/
AI achieves silver-medal standard solving International Mathematical Olympiad problems
"Autoformalization" refers to automatically converting a traditional human readable mathematical proof to a formal proof.
This section is about benchmarks designed to test mathematical reasoning.
How they "ensure" that models are not contaminated:
Most of their problems come from high school knowledge olympiads and they are therefore completely irrelevant for 2025 LLMs.
This project initiated by Terence Tao aims to find the relations between various statements in abstract algebra by using a combination of automated theorem proving and human effort. As mentioned by Terence himself, this is a bit similar to the idea of the Busy Beaver Challenge:
Paper: arxiv.org/abs/2411.04872
arstechnica.com/ai/2024/11/new-secret-math-benchmark-stumps-ai-models-and-phds-alike/ mentions what the official website is unable to clearly state out:So yeah, fuck off.
The design of FrontierMath differs from many existing AI benchmarks because the problem set remains private and unpublished to prevent data contamination
The expected answer output for all problems is just one single, possibly ridiculously large, integer, which is kind of a cool approach. Similar to Project Euler in that aspect.
The most interesting aspect of this benchmark is the difficulty. Mathematical olympiad coach Evan Chen comments:[ref]
Problems in [the International Mathematical Olympiad] typically require creative insight while avoiding complex implementation and specialized knowledge [but for FrontierMath] they keep the first requirement, but outright invert the second and third requirement
We introduce Putnam-AXIOM, a benchmark of 522 university-level competition problems drawn from the prestigious William Lowell Putnam Mathematical Competition, and Putnam-AXIOM Variation, an unseen companion set of 100 functional variants generated by programmatically perturbing variables and constants.
Articles by others on the same topic
Automated theorem proving (ATP) is a branch of artificial intelligence and mathematical logic concerned with the development of algorithms and software that can automatically prove mathematical theorems. The goal of ATP systems is to determine the validity of logical statements and derive conclusions based entirely on formal logical reasoning, without human intervention.