AI has access to a vastly larger working memory than the human brain

人工智能拥有比人脑大得多的工作记忆

AI Isn’t Outthinking Mathematicians. It’s Out-Remembering Them. 人工智能并非在智力上超越数学家，而是在记忆力上超越他们。

The key advantage may not be superior reasoning, but a virtually unlimited symbolic working memory. 关键优势可能不是更优越的推理能力，而是几乎无限的符号工作记忆。

At the 1952 dedication of the Institute for Advanced Study computer. AI may be less like an electronic Einstein than a machine-amplified von Neumann: immense speed, breadth and symbolic memory. 在 1952 年高等研究院计算机的落成典礼上。人工智能可能不像电子版的爱因斯坦，而更像是一台被机器放大的冯·诺依曼：拥有巨大的速度、广度和符号记忆。

When an AI system solves a difficult mathematical problem, the usual explanation is that it has become more intelligent. 当一个人工智能系统解决一个困难的数学问题时，通常的解释是它变得更聪明了。

Perhaps it has absorbed millions of mathematical examples. Perhaps reinforcement learning has taught it better reasoning strategies. Perhaps it is beginning to develop something resembling genuine mathematical intuition. 也许它吸收了数百万个数学示例。也许强化学习教会了它更好的推理策略。也许它开始发展出某种类似于真正数学直觉的东西。

All of these explanations may contain some truth. But they overlook a simpler possibility:AI has access to a vastly larger working memory than the human brain. 所有这些解释可能都包含一些真理。但它们忽略了一个更简单的可能性：人工智能拥有比人脑大得多的工作记忆。

Or, more precisely, it has access to an enormous external symbolic workspace that performs many of the functions that working memory performs in humans. 或者更准确地说，它拥有一个巨大的外部符号工作空间，该空间执行了许多人类工作记忆所执行的功能。

This difference may be especially important in mathematics. 这种差异在数学中可能尤为重要。

A human mathematician can hold only a small number of unfamiliar elements in mind simultaneously. An AI model can keep the entire problem statement, hundreds of intermediate equations, several abandoned approaches, definitions, constraints and earlier conclusions inside its context window. 人类数学家只能同时在脑海中保持少量不熟悉元素。人工智能模型可以在其上下文窗口中保留整个问题陈述、数百个中间方程、几种被放弃的方法、定义、约束和早期结论。

We normally interpret the resulting performance as evidence of superior reasoning. But some of it may instead reflect the removal of one of the most important biological limits on human reasoning: our extremely restricted working-memory capacity. 我们通常将由此产生的表现解释为优越推理能力的证据。但其中一部分可能反而反映了对人类推理最重要的生物限制之一的消除：我们极其有限的工作记忆容量。

Mathematics is constrained by memory 数学受限于记忆

Working memory is the mental system that allows us to hold and manipulate information over short periods. 工作记忆是允许我们在短时间内保持和处理信息的心理系统。

When solving an equation, you must remember what each variable represents, which operations have already been performed and what the current goal is. During a proof, you may need to keep track of assumptions, intermediate lemmas, exceptions and multiple possible cases. 在解方程时，你必须记住每个变量代表什么，已经执行了哪些操作，以及当前的目标是什么。在证明过程中，你可能需要跟踪假设、中间引理、例外情况和多种可能的情况。

Human working memory is remarkably limited. 人类的工作记忆非常有限。

Its exact capacity depends on the task and on how information is organized, but the general limitation is obvious from everyday experience. Try multiplying two three-digit numbers in your head. The underlying operations are simple. The difficulty comes largely from having to preserve partial results while performing additional calculations. 其确切容量取决于任务以及信息的组织方式，但一般的限制从日常经验中就很明显。试着在脑海中乘以两个三位数。底层的操作很简单。困难主要来自于在执行额外计算时必须保留部分结果。

Writing the numbers down transforms the problem. 把数字写下来改变了问题。

Paper does not make you more intelligent. It expands your effective working memory. 纸张不会让你变得更聪明。它扩展了你的有效工作记忆。

The same principle applies at higher levels of mathematics. A mathematician uses notation, scratch paper, diagrams and previously written lemmas not merely to communicate the solution, but to make the reasoning cognitively possible. 同样的原则适用于更高层次的数学。数学家使用符号、草稿纸、图表和之前写下的引理，不仅仅是为了交流解决方案，而是为了使推理在认知上成为可能。

Experts compensate through “chunking.” A novice sees a long sequence of symbols. An expert recognizes a familiar structure and treats it as a single conceptual object. This allows far more information to fit inside the same biological working-memory limit. 专家通过“组块化”来补偿。新手看到一长串符号。专家识别出熟悉的结构并将其视为单一的概念对象。这使得相同生物工作记忆限制内能容纳多得多的信息。

But chunking does not eliminate the limit. It merely compresses the information. 但组块化并不能消除限制。它只是压缩了信息。

An AI model faces a very different constraint. 人工智能模型面临着非常不同的约束。

Working memory predicts mathematical performance beyond IQ 工作记忆在智商之外预测数学表现

The importance of working memory for mathematics is not merely theoretical. It is visible in the differences between human beings. 工作记忆对数学的重要性不仅仅是理论上的。它在人类之间的差异中可见。

Working memory is strongly related to general intelligence, which raises an obvious question: does it independently predict mathematical performance, or is it merely another imperfect measure of IQ? 工作记忆与一般智力密切相关，这提出了一个明显的问题：它是否独立预测数学表现，还是仅仅是智商的另一种不完美衡量标准？

Several studies suggest that it contributes something beyond conventional intelligence measures. Alloway and Passolunghi (2011), for example, examined working memory, verbal ability and mathematical skills in children. They found that working-memory measures made a distinct contribution to mathematical performance rather than simply reproducing the association between mathematics and general verbal ability. 几项研究表明，它贡献了超越传统智力衡量标准的东西。例如，Alloway 和 Passolunghi (2011) 检查了儿童的工作记忆、语言能力和数学技能。他们发现，工作记忆衡量标准对数学表现做出了独特的贡献，而不是简单地重现数学与一般语言能力之间的关联。

In a separate six-year longitudinal study, Alloway and Alloway (2010) measured children at age five and then examined their academic achievement six years later. Early working-memory performance predicted later literacy and numeracy even after IQ was included in the analysis. Indeed, working memory was a stronger predictor of the later academic outcomes than the IQ measure used in the study. 在另一项为期六年的纵向研究中，Alloway 和 Alloway (2010) 在五岁时测量儿童，然后在六年后检查他们的学业成就。即使分析中包含了智商，早期工作记忆表现也能预测后来的读写能力和计算能力。事实上，工作记忆是后来学业结果比研究中使用的智商衡量标准更强的预测因子。

Blankenship and colleagues (2015) similarly reported that working memory explained unique variation in mathematical fluency and calculation after statistically controlling for IQ and age. A large meta-analysis by Friso-van den Bos and colleagues (2013) also found a consistent relationship between working memory and mathematics across primary-school studies, although the strength of the relationship varied according to the type of working-memory and mathematical task being measured. Blankenship 及其同事（2015 年）同样报告称，在统计上控制智商和年龄后，工作记忆解释了数学流畅性和计算中的独特变异。Friso-van den Bos 及其同事（2013 年）进行的一项大型荟萃分析也发现，在小学研究中，工作记忆与数学之间存在一致的关系，尽管关系的强度根据所测量的工作记忆和数学任务类型而异。

These findings should not be exaggerated. Working memory and intelligence overlap substantially, and statistical control cannot perfectly isolate them as independent psychological mechanisms. Nor does the evidence imply that commercially training working memory will necessarily produce large improvements in intelligence or mathematics. 这些发现不应被夸大。工作记忆和智力在很大程度上重叠，统计控制不能完美地将它们作为独立的心理机制隔离开来。证据也不意味着商业训练工作记忆必然会在智力或数学方面产生巨大的改善。

The narrower conclusion is nevertheless important: among children with similar measured intelligence, differences in the ability to hold, update and manipulate information still predict differences in mathematical performance. 然而，更窄的结论仍然很重要：在测量智力相似的儿童中，保持、更新和处理信息能力的差异仍然预测数学表现的差异。

This provides a crucial clue for understanding AI. If human mathematical performance is partly capped by a working-memory bottleneck, then giving a machine an enormous symbolic workspace changes the nature of the contest. The machine may appear more mathematically intelligent partly because it is much less constrained by a cognitive limitation that suppresses human performance. 这为理解人工智能提供了一个关键线索。如果人类的数学表现部分受到工作记忆瓶颈的限制，那么给机器一个巨大的符号工作空间就改变了竞争的性质。机器可能显得在数学上更聪明，部分原因是它受限于抑制人类表现的认知限制要少得多。

The context window is a gigantic notebook 上下文窗口是一个巨大的笔记本

A modern language model can process an enormous sequence of tokens at once. This sequence may include the original question, definitions, examples, intermediate cal 现代语言模型可以一次处理巨大的令牌序列。这个序列可能包括原始问题、定义、示例、中间计算