On the 1st local time, OpenAI said its next-generation artificial intelligence (AI) model Astra produced new results on 10 hard math problems. The AI solved in a short time problems that could keep human researchers busy for years. But within days of the announcement, some mathematicians said "the ideas and achievements of prior researchers were not sufficiently recognized, while the AI's results were overly highlighted."
"They are deliberately trampling on the achievements of earlier researchers."
Steven Miller of Yeshiva University in the United States said this on the 6th local time to Scientific American, claiming that some of OpenAI's results essentially plagiarized his research.
Miller criticized the repeated omission of prior work, saying it "appears to be an organized pattern and suggests research misconduct." However, there has been no official inquiry or plagiarism ruling by an academic institution.
◇ Did the answers AI found already exist in earlier papers?
The paper OpenAI released runs 250 pages. It tackles hard problems including group theory, quantum complexity, lattice cryptography, and Ramsey theory. The AI constructed arguments, human researchers organized them into a paper, and then formalized it with the proof verification program Lean. Lean is a tool that checks by computer whether each step of a proof follows prescribed logical rules.
The controversy centers on the "high-dimensional sphere packing" problem. It extends the question of how tightly spheres of the same size can be packed into a box into spaces of hundreds or thousands of dimensions. OpenAI presented a proof that narrows the upper bound on the density at which spheres can be packed compared with previous results.
Miller said the core logic of this proof already appears in a paper he and a coauthor released in 2016. He said OpenAI used this idea to generate new results but did not properly credit the source.
Some mathematicians took issue less with the citations in the paper than with how OpenAI presented the work. Francesco Fournier-Facio, a researcher at the University of Cambridge in the United Kingdom, said "there was an effort in the paper to disclose prior work as much as possible," but noted that "even though human mathematicians had been making progress on the problem until recently, OpenAI's initial announcement made it sound as if AI had broken through a problem that had long been stuck."
That does not mean the scholarly value of the results themselves has been dismissed. Andreas Thom of Technische Universität Dresden, a coauthor of the prior research Astra drew on, called the outcome "creative yet fundamental."
Kim Jong-rak, a professor of mathematics at Sogang University who read the paper, also said AI's problem-solving process cannot be seen as a simple pastiche of existing papers. Kim said, "There are cases where AI does not merely cite other papers or paste together what is in them, but instead solves problems on its own logically," adding, "as a result, the logic AI discovers can overlap with research humans have already done."
He added, "OpenAI chose to take on famous and extremely difficult problems in each field, not fringe open problems, and produced results," and said, "it is meaningful in that AI actually found true results and even provided proofs."
◇ The era of AI solving hard problems: the math community seeks new roles amid concern
The controversy reflects an issue the math community has wrestled with since before AI began to be used in earnest in mathematical research. The Leiden AI and Mathematics Declaration, published in June, warned that AI models may synthesize existing mathematical literature to produce results but fail to properly cite the human research on which they are based. The International Mathematical Union (IMU) officially endorsed the declaration.
The declaration particularly noted that if research results are publicized through press releases or blogs before sufficient scholarly review, AI's role can be overstated and the contributions of human researchers diminished. It also stressed that even if AI is used, human researchers are responsible for the accuracy of the results and for citing prior work.
OpenAI also told Scientific American that it "takes responsibility for the correctness of the mathematical results and will adhere to the same standards required of human mathematicians," and said it "will revise the paper according to standard academic practice."
Separate from this controversy, as AI begins to show real capability in solving hard problems, some expect the role of human mathematicians to change.
Kim likened it to how AlphaGo revealed new Go strategies by choosing moves that human players might not readily pick. "If AI solves problems in ways humans have not used," Kim said, "we should look into why AI thought that way," adding, "mathematicians' roles could expand by adopting that mode of thinking, applying it to other problems, and adding human ideas to it."