陶哲轩点出了AI领域最核心的认知盲区——我们能用简单数学造出强大模型，却无法解释其行为，做AI研究或应用的开发者看完会重新思考“理解”的含义。
著名数学家陶哲轩指出，当前大语言模型（LLM）的训练和运行主要依赖线性代数、矩阵乘法和微积分，这些是本科生就能掌握的数学工具。然而，真正令人困惑的是为什么这些模型在某些任务上表现出色，而在其他任务上却失败，且无法提前预测。他认为，自然文本介于完全随机和完全结构化之间，而数学对中间状态的理解非常薄弱，类似于物理学在原子和连续介质之间的介观尺度面临的挑战。因此，尽管我们能描述LLM的机制，但无法解释能力跃迁或给出可靠的任务级预测。
Terence Tao says the math behind today’s LLMs is a…
Terence Tao says the math behind today’s LLMs is actually simple. Training and running them mostly uses linear algebra, matrix multiplication, and a bit of calculus, material an undergraduate can handle. We understand how to build and operate these models.
The real mystery is why they work so well on some tasks and fail on others, and why we cannot predict that in advance. We lack good rules for forecasting performance across tasks, so progress is largely empirical.
A key reason is the nature of real-world data. Pure noise is well understood, perfectly structured data is well understood, but natural text sits in between, partly structured and partly random. Mathematics for that middle regime is thin, similar to how physics struggles at meso-scales between atoms and continua.
Because of this gap, we can describe the mechanisms but cannot yet explain capability jumps or give reliable task-level predictions. That mismatch, simple machinery versus hard-to-predict behavior, is the core puzzle.
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Video from 'Dr Brian Keating' YT Channel (Link in comment)