The Impossible Test: A 2024 Unsolvable Dataset and A Chance for an AGI
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Authors: name: David Noever, name: Forrest McKee

This research introduces a novel evaluation framework designed to assess
large language models' (LLMs) ability to acknowledge uncertainty on 675
fundamentally unsolvable problems. Using a curated dataset of graduate-level
grand challenge questions with intentionally unknowable answers, we evaluated
twelve state-of-the-art LLMs, including both open and closed-source models, on
their propensity to admit ignorance rather than generate plausible but
incorrect responses. The best models scored in 62-68% accuracy ranges for
admitting the problem solution was unknown in fields ranging from biology to
philosophy and mathematics. We observed an inverse relationship between problem
difficulty and model accuracy, with GPT-4 demonstrating higher rates of
uncertainty acknowledgment on more challenging problems (35.8%) compared to
simpler ones (20.0%). This pattern indicates that models may be more prone to
generate speculative answers when problems appear more tractable. The study
also revealed significant variations across problem categories, with models
showing difficulty in acknowledging uncertainty in invention and NP-hard
problems while performing relatively better on philosophical and psychological
challenges. These results contribute to the growing body of research on
artificial general intelligence (AGI) assessment by highlighting the importance
of uncertainty recognition as a critical component of future machine
intelligence evaluation. This impossibility test thus extends previous
theoretical frameworks for universal intelligence testing by providing
empirical evidence of current limitations in LLMs' ability to recognize their
own knowledge boundaries, suggesting new directions for improving model
training architectures and evaluation approaches.