The Overlooked Advantage: Working Memory§
When OpenAI's o3 model achieves a gold medal on the International Mathematical Olympiad, or DeepMind's AlphaGeometry solves geometry problems at a near-human level, the default narrative is that AI is getting smarter—perhaps even approaching genuine mathematical intuition. But a provocative essay by cognitive researcher Davide Piffer, published on his Substack, suggests a simpler, more mundane explanation: AI systems have access to a vastly larger working memory than the human brain, and this asymmetry, rather than superior reasoning, may account for their apparent mathematical prowess.
Working memory is the cognitive system that holds and manipulates information over short periods—the mental scratchpad you use to multiply two three-digit numbers in your head. Human working memory is notoriously limited, typically holding only a handful of chunks of information at once. This bottleneck constrains human mathematical reasoning, forcing us to offload intermediate steps onto paper or to compress information into abstract chunks. AI, by contrast, can keep thousands of tokens—the entire problem statement, intermediate equations, abandoned approaches, and definitions—simultaneously available in its context window. This external symbolic workspace effectively removes the biological limit that has shaped human cognition for millennia.
The implications are significant for how we interpret AI performance. If much of AI's advantage in math comes from expanded memory rather than enhanced logic, then we may be overestimating the intelligence of these systems. Piffer's analysis, grounded in cognitive psychology and AI research, challenges the field to reconsider what we mean by 'machine intelligence' and how we evaluate it.
Memory Over Reasoning: The Core Argument§
Piffer's central claim is that AI's success in mathematics is less about 'outthinking' humans and more about 'out-remembering' them. He draws on established findings that working memory is a major predictor of mathematical ability, even after controlling for general intelligence. For example, Alloway and Passolunghi (2011) showed that working memory contributes uniquely to children's math performance, while a six-year longitudinal study by Alloway and Alloway (2010) found that early working-memory capacity predicted later numeracy and literacy better than IQ. A meta-analysis by Friso-van den Bos et al. (2013) confirmed a consistent link between working memory and mathematics across studies.
If human math performance is partly capped by a limited working memory, then giving machines a gigantic symbolic workspace changes the game. The author illustrates this with a simple analogy: writing down intermediate steps in a multiplication problem expands your effective memory, making the task easier. An AI's context window is like having an infinite scratchpad that never forgets, always retaining every step and every failed attempt.
But Piffer is careful to clarify that an AI's context window is not identical to human working memory. It's more like an externalized notebook combined with a search and attention mechanism. Human working memory is active and private—we can hold and transform a number internally without writing it down. Standard language models, on the other hand, are weaker at maintaining such private, continuously updated mental states. Their reasoning is often externalized: the text they generate is not just a record of thought, but the very medium through which thought occurs.
This externalization has profound consequences. In mathematics, almost every element can be captured in explicit symbols: definitions, assumptions, intermediate lemmas, eliminated cases, and constraints. Once written, this information stays stable—an integer remains an integer, and a strict inequality does not drift into a non-strict one due to ambiguity. Mathematics is uniquely suited to an intelligence that thrives on a large, explicit textual workspace. This is why the context-window advantage matters so much in math, more so than in fuzzy, context-dependent domains like natural language or social reasoning.
The author does not claim that context windows are perfectly used; models can overlook relevant information or get distracted. But the potential capacity difference is enormous: an unaided human might juggle five unfamiliar conditions at once, while a model can retain hundreds. This capacity difference, Piffer argues, may explain why AI systems often appear to 'reason' better than humans in mathematical domains—they simply never forget.
Historical Parallels: From Scratchpads to Deep Blue§
The idea that memory—not just raw processing power—is a key driver of cognitive achievement has deep historical precedents. One striking parallel is the rise of Deep Blue, the chess computer that defeated Garry Kasparov in 1997. At the time, many pundits declared that Deep Blue had achieved 'artificial intelligence' and outthought the human champion. But analysts later noted that Deep Blue's advantage lay not in superior strategic reasoning, but in its ability to evaluate 200 million positions per second and access a vast opening book of grandmaster games. Kasparov himself commented that Deep Blue's play felt 'alien' and that it exploited his human limitations—specifically, his inability to match the machine's relentless memory and speed. Deep Blue didn't outthink Kasparov; it out-remembered and out-computed him.
Another historical parallel is the development of proof assistants like Coq and Lean, used for formal verification of mathematical theorems. These tools don't reason on their own; they provide a massive symbolic workspace where every step of a proof is stored and checked. Human mathematicians work with these tools not because they are smarter, but because the tool's external memory eliminates the need to hold lengthy proof chains in working memory. For instance, the formalization of the Odd Order Theorem by Georges Gonthier and his team took over a decade, but it relied on the computer's ability to retain and verify millions of inference steps. The human mathematicians provided the strategic insight, while the machine provided the memory and error-checking. This division of labor mirrors the current AI paradigm, where the model's context window serves as a virtual scratchpad for extended reasoning.
Yet there's a critical difference between these historical examples and modern LLMs. Deep Blue and proof assistants were explicitly designed to enhance memory and computation, but they lacked the flexibility to generate novel solutions. Modern AI models, like GPT-4 or AlphaGeometry, go further—they can generate the steps themselves, using their training to propose plausible intermediate statements and then verify them, effectively simulating a chalkboard rumination at scale. This blurring of memory and reasoning makes it harder to attribute success to one factor alone. However, Piffer's argument forces us to question whether the models' ability to 'remember' the entire problem context is what enables them to generate coherent chains of reasoning, rather than any deep understanding of mathematical structure.
The lesson from history is that we often over-attribute success to intelligence when memory and computational brute force play a dominant role. Just as Deep Blue's win reshaped how we thought about chess and AI, Piffer's analysis may reshape how we evaluate AI's mathematical capabilities.
Reinterpreting AI's Mathematical Performance§
The implications of Piffer's thesis are substantial for the AI research community. If a large portion of AI's mathematical ability stems from an enlarged working memory, then we may need to recalibrate benchmarks and expectations. For example, when evaluating a model on a math competition, we might ask: Is the model demonstrating reasoning capabilities, or is it simply leveraging its context window to track more state than a human could? This distinction matters for practical applications. If the advantage is memory, then we can expect AI to excel at problems that require extensive bookkeeping, such as long-form theorem proving or multi-step algebra, but it may still struggle with conceptual leaps that require a flash of insight—precisely the kind of 'aha' moments that working memory does not capture.
Moreover, this perspective has implications for prompt engineering and model design. If context length is a proxy for working memory, then extending context windows (as models like Gemini 1.5 and Claude 3 do with millions of tokens) could lead to disproportionate gains in mathematical performance. The author hints at this: 'The context-window advantage is not equally useful in every kind of reasoning. It matters especially for mathematics because mathematical reasoning can be translated unusually well into explicit symbols.' By recognizing that AI's strength lies in being a giant externalized memory, we can design better tools that leverage this strength—for instance, by explicitly prompting models to write out all intermediate steps, as is often done in chain-of-thought prompting, which effectively turns the context window into a more efficient scratchpad.
However, this also raises a caution: if AI's performance is memory-driven, it may be fragile. Human mathematicians often develop intuition that goes beyond rote symbol manipulation—a sense of what a theorem 'really means' statistically, or how to choose a fruitful approach. AI lacks this semantic grounding; its 'reasoning' is entirely syntactic. This means that for problems that do not easily translate into symbolic form, AI may flounder. Piffer notes that 'mathematical symbols are designed to reduce ambiguity,' which is why AI excels in this domain. But in fields like social reasoning or creative problem-solving, where ambiguity is inherent, the same memory advantage may not translate, and AI's limited 'working memory' in the active sense could be a bottleneck.
Ultimately, Piffer's essay is a call to humility. It suggests that AI's recent mathematical triumphs may be less like an electronic Einstein and more like a machine-amplified von Neumann: immense speed, breadth, and symbolic memory. Understanding this distinction is crucial for setting realistic expectations for AI's future and for developing evaluation methods that differentiate between memory and reasoning. As the AI community continues to push benchmarks to new heights, we would do well to remember that sometimes the most profound advances come not from better cognition, but from nearly limitless recall.