Terence Tao is doubling down on his criticism of OpenAI’s 300+ math proofs dropped on October 6, which some have called the most important day thus far in science.
In a sharply worded guest post on Fields Medal-winning mathematician Terence Tao’s blog, mathematician Sophie Huiberts argues that OpenAI’s papers fall short of the standards expected of mathematical research. Huiberts received her doctorate from Utrecht University.
Huiberts’s post, titled “This is normal bad work”, takes aim at the presentation of the results rather than treating the sheer volume of mathematical claims as an achievement in itself. She argues that proofs must be accompanied by clear explanations, appropriate attribution and enough context for other researchers to understand and build on them.
“When you prove a theorem, you are imparted a responsibility to the field of mathematics,” Huiberts writes. She says researchers are expected to explain which parts of a proof require new ideas and which rely on existing knowledge — and, where necessary, to improve the way earlier ideas have been presented.
‘Poor quality work’ and ‘easy rejects’
OpenAI published a large collection of mathematical results produced by an internal model on October 6. The release catalogued 722 manuscripts grouped into 372 result families across 16 areas of mathematics. The claims range across pure mathematics, including results connected to famous open problems, but the collection has not been peer reviewed as a whole.
Huiberts contrasts the release with the norms that govern mathematical publishing. In her view, researchers are responsible not just for producing a result, but for making it intelligible and useful to the rest of the field.
“These demands are broadly accepted and are neither new nor controversial,” she writes, referring to the expectations around explaining and contextualising a proof. Papers that fail to meet them can face requests for revision or outright rejection, she argues.
Her assessment of OpenAI’s collection is blunt: “This is poor quality work and these pdfs are all easy rejects.”
Huiberts alleges that the release does not consistently provide appropriate attribution, divides results across a large number of documents, includes errors she says could warrant retraction, and sometimes promises code that is not supplied. She also criticises the proofs as difficult to follow. These are Huiberts’s criticisms of the release, rather than a finding from a comprehensive independent review of every manuscript.
Huiberts seems to argue that a mathematical claim can be interesting without being ready for publication. A proof needs to show its reasoning, identify its relationship to previous work and give other mathematicians a practical way to check it. Even a correct result can be difficult to use if the supporting exposition is opaque or the relevant context is missing.
Why Tao is amplifying this
Tao has not been shy about his own discomfort with the release. He’s argued that dropping 372 result, and separately warned that AI-generated proofs could end up being a net negative for the discipline if the verification and write-up culture around them doesn’t keep pace. He has also previously said that a result shouldn’t be published if its authors can’t give a clear talk explaining it — a bar Huiberts is essentially applying here too.
Running a guest post this pointed, rather than just linking to it, is itself a signal. Tao has generally been careful to separate his enthusiasm for AI as a research tool — he’s said current models are capable of producing proofs that look flawless while still hiding subtle errors — from his skepticism about how labs are choosing to publish results. Giving Huiberts his audience without softening her framing suggests that skepticism is hardening, even as OpenAI keeps pushing the idea that AI is approaching genuine contributions to open problems in mathematics.