Grok 4.5 Reportedly Discovers Research-Level Math Counterexample

Recently, Grok 4.5's performance in mathematical testing has attracted widespread attention. According to multiple reposted messages, the model successfully constructed an explicit counterexample to the hypercontractivity of the Poisson semigroup on the 4-sphere. This discovery is highly notable because it not only addresses a serious research-level mathematical problem but also suggests that large language models may possess the potential to drive original scientific discoveries.

Key Details and Background

The mathematical problem involves harmonic analysis and probability theory. According to a repost by @soumitrashukla9, a 2021 study proved that this property holds in 3 dimensions and below, but fails in higher dimensions like 13. The counterexample provided by Grok 4.5 demonstrates that the property fails starting in 4 dimensions, confirming that the earlier research findings were "sharp." Furthermore, @LiorOnAI noted that if this counterexample holds up to independent verification, it would indicate that the model is not simply regurgitating existing literature, but making a genuinely original contribution. Related reposts also mentioned that the model runs on xAI's V9 architecture.

Reactions

During testing, the author also tried other frontier AI models, some of which also managed to find the counterexample. However, the poster specifically praised Grok 4.5's solution, considering its proof to be particularly clear.

2026-07-10 ~ 2026-07-11 · 5 related posts

• Grok 4.5 Solves High-Dimensional Math Counterexample — prof_g · 2026-07-10
• [source] Grok 4.5 Potentially Provides Original Math Counterexample — LiorOnAI · 2026-07-11
• Grok 4.5 Rumored to Find Math Counterexample — elonmusk · 2026-07-11
• Grok 4.5 Finds Counterexample to Math Conjecture — rohanpaul_ai · 2026-07-11

1 near-duplicate retellings: soumitrashukla9