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Hello, followers! Today, we’re diving into the intriguing world of AI and its limitations in understanding complex math.
Recent research shows that AI models can handle basic math questions quite well but stumble when asked to produce detailed proofs, like those seen in high-level math competitions. These ‘simulated reasoning’ models are trained to break down problems into step-by-step thinking, a method known as ‘chain-of-thought,’ but they don’t truly understand the mathematics they generate.
This study, conducted by experts from ETH Zurich and INSAIT, tested several AI models on problems from the 2025 US Math Olympiad. Most performed poorly, with accuracy often below 5%. Only one model, Google’s Gemini 2.5 Pro, scored somewhat better, but still only managed about a quarter of the total points, revealing a significant performance gap compared to human experts.
It’s crucial to distinguish between answering math questions and proving mathematical statements. The former simply asks for a correct answer, while the latter requires a logical explanation step-by-step. AI models excel at the former but falter at the latter because constructing valid proofs demands genuine understanding and creativity that current models lack.
The reason for this difference lies in how these models work—they’re pattern matchers, drawing on training data to predict what comes next. When it comes to proofs, which need novel reasoning, they often produce flawed solutions with confident language that hides errors. The researchers observed that AI’s reasoning mistakes stem from their training methods and optimization artifacts, especially their tendency to focus on producing final answers rather than explanations.
Interestingly, techniques like chain-of-thought reasoning improve results by encouraging models to generate intermediate steps, which helps reduce errors. Nonetheless, these improvements are still based on statistical correlations, not true understanding. Most models perform well on problems similar to their training data but struggle with entirely new proof challenges, as shown by their Olympiad performance.
Looking forward, scaling up current models alone might not bridge the deep reasoning gap. Researchers are exploring hybrid approaches, combining neural networks with symbolic reasoning and formal proof verification, aiming for AI that can genuinely understand and produce mathematical proofs.
So, while AI has made impressive strides, mastering deep mathematical reasoning remains a significant challenge. The path ahead involves rethinking how we train and design these models to unlock their true potential in understanding complex ideas.
