AI isn’t outthinking mathematicians, it’s out-remembering them
TL;DR
Davide Piffer argues that much of AI's recent success in math comes from a huge written workspace, not deeper reasoning. A model's context window holds every assumption, equation and dead end, which is the bookkeeping math rewards. Human working memory holds only a handful of unfamiliar items.
The article
- Human working memory is tiny. That is why multiplying two three-digit numbers in your head is hard, even though each step is easy. Paper doesn't make you smarter. It extends your working memory. Expert chunking only compresses what fits under the same limit.
- Working memory predicts math performance beyond IQ. Piffer cites Alloway and Alloway (2010), where working memory at age five predicted later literacy and numeracy better than the IQ measure did. He also cites Blankenship (2015) and a 2013 meta-analysis. He warns that the two traits overlap heavily.
- A context window is a giant external notebook, not true working memory. Models are weak at holding a private, changing mental state. So their reasoning happens in the text they write. For math, where every assumption and eliminated case can be written down, this weakness turns into a strength.
- Math suits this setup because symbols stay fixed. Answers can also be checked by substitution, code or proof assistants. Social or historical questions depend on hidden facts and loose concepts. A bigger notebook can't supply facts nobody observed.
- The hypothesis makes predictions. AI should gain most on long calculations, case analysis and dense constraints. It should gain least on problems that hinge on one short conceptual leap. Cutting a model's usable context should hurt it most on long tasks. Giving humans better external memory should narrow the gap.
- Piffer closes with Eugene Wigner's comparison of von Neumann and Einstein. Today's AI resembles a machine-amplified von Neumann, fast and broad with an unlimited notebook. It does not yet have Einstein's ability to reframe a problem entirely.
Why it matters
Read the original for a concrete account of where AI math gains come from. It also has the full list of testable predictions near the end, which the summary only sketches. The cited working-memory studies are listed in full with DOIs.
The discussion
A large thread, mostly skeptical of the framing. Many readers traded stories about their own weak memory and strong reasoning, while others argued that memory, persistence and search are parts of intelligence. Long side fights broke out over string theory and over proofs no human can follow. A few commenters flagged Piffer's history and the article's AI-sounding prose.
Is intelligence mostly memory?
The top thread opened with a developer saying his best work came from recombining knowledge others lacked, which is what LLMs do too. Dozens of replies pushed back with their own experience. They have poor factual memory but good conceptual memory, and they derive formulas instead of memorizing them. Others split the difference by citing fluid versus crystallized intelligence, or by calling compression the real skill.
I don't think I've had a truly original idea in my life. Combine A + B, when it's rare for people to know A and B at the same time. So from that perspective, what LLMs are doing is basically the same thing.
I had a thought when I was fairly young that the only reason I was (maybe, sometimes) outperforming others intellectually is that I was habitually compensating for my poor memory by working things out on the fly, while others could rely more on rote memorization.
Tireless brute force, and moving goalposts
Many added that AI also out-works mathematicians, trying direction after direction without discouragement. Others noted that mathematicians already spend years on single problems. Some read the whole genre as goalpost-moving, peeling off memory, persistence and search until nothing called intelligence is left. Skeptics answered that computers always had speed and stamina, and that understanding and real novelty are still missing.
This thing just does not ever get tired or discouraged or care; it's just onto the next thing until something ends up working.
We're just going to slowly deconstruct every element that could be a factor of intelligence.
Proofs no human can follow
One commenter predicted AI will soon produce math too intricate for people to understand, ending the age of human comprehension. Opponents said a proof is a finite chain of rule applications that anyone can check given time. They cited Terence Tao's point that shared understanding, not the proof itself, is what math produces. The exchange became a long argument over what "incomprehensible" means, with the 5G spec and high-temperature superconductors offered as examples and rejected.
As to your second point, Terry Tao already has an answer [1]: the proof isn’t the contribution, shared understanding is.
A mathematician could understand any proof given enough time to study it; the only way for AI to make proofs that a human couldn't understand is by making really, really long proofs.
Why math and code, not law and medicine
Commenters agreed with the article that checkability explains why labs keep choosing math and code for demos. Compilers, solvers and Lean let a model fail thousands of times and keep only what passes, which medicine and law can't offer. A mathematician added that outside Lean, the standard of proof is still what other mathematicians accept. They sometimes disagree, as with Mochizuki's claimed abc proof.
With code and math you can have failures 1000 times for every success and still get rewarded.
That makes it possible and worth it for them to spend 1 week of compute on a problem until the validator passes, then publish marketing pieces.
Big context and bloated code
Programmers saw the article's thesis in their own codebases. Models can hold a lot at once, so they skip the abstractions humans need and duplicate logic, like eleven date-math helpers in one project. Some argued clean abstractions still pay off for models by saving tokens. Others reported that a huge context makes models worse at close, focused review of a single method.
It's also why LLMs don't need abstractions or parsimony as much as humans. They can work on something complicated without simplifying it first.
They're really bad at noticing when a helper function is needed, when some structure they repeated five times slightly differently can become a struct, when a whole section of code can be encapsulated in a simpler design.
Consensus
Memory and recombination matter a great deal. AI's ability to keep vast amounts of material in view gives it a real edge in math and code, which machines can check. Most also agreed that this edge falls short of the conceptual reframing the article attributes to Einstein.
Dissent
A sizable group rejected the framing outright. Some called it cope that redraws intelligence to exclude AI, and argued that bigger working memory simply is more intelligence. Others dismissed the article as AI-polished prose or pointed to Piffer's record of race-science writing and a claim of ESP.