La Jornada: Work by Spanish academics allowed OpenAI to solve mathematical puzzle

Madrid. The mathematician Luis Martínez Zoroa, professor at the University College of Financial Studies (Cunef), has been, together with Diego Córdoba, from the Institute of Mathematical Sciences of the Higher Council for Scientific Research (Icmat-CSIC), one of the intellectual bases that allowed progress in the solution of the Navier-Stokes problem, one of the great mathematical challenges of the 21st century that the company OpenAI claims to have solved thanks to artificial intelligence.

“OpenAI, in the first version, cited very few articles, not only mine, but those of the entire scientific community. There were few texts cited and it is not something that surprises me,” the researcher told Europa Press, in reference to the controversy generated by the company’s lack of recognition of the previous work of other mathematicians that has made it possible for AI to solve the problem.

Martínez Zoroa acknowledged that it is not a practice that surprises him, since “there are also other researchers who cite less than they should. OpenAI is a company and tries to get all the publicity it can. Then they have made more versions of the article where they included more citations, although I think there are still very relevant works that have not been cited. In the first version I think we did not appear,” he commented.

However, he avoids talking about plagiarism on the part of OpenAI and recognizes that the article published by the company “is really impressive. They use our tools, as well as those of many other researchers, and they must be properly accredited,” he pointed out.

In this context, the professor assured that “it is very normal” to use tools from others when doing research, although he warned that with AI “it is less clear to know where it came from”, which, in his words, “makes it difficult to give adequate credit. Plagiarism would surely be a strong word, but there would have to be a greater effort to give the necessary recognition to all the research,” he claimed.

However, mathematician Tristan Buckmaster has denounced a lack of transparency and pressure on the part of OpenAI after the company announced that its models had solved one of the Millennium Prize Problems, shortly after the New York researcher shared with them the achievements of his work, for which he used the company’s artificial intelligence models.

In addition to using powerful AI models, the starting idea for Buckmaster and Alpoge’s research was based on the previous research of Spanish mathematicians Diego Córdoba and Luis Martínez Zoroa, who had been exploring this avenue for years.

However, this finding goes hand in hand with controversy, because OpenAI also announced that it had found a solution with its AI models for this same mathematics problem, going beyond the achievements achieved by Buckmaster and his partner Alpoge, and without consensus on whose merit it is.

OpenAI’s response, in the announcement made days ago about Navier-Stokes, maintains that it will not claim the Millennium Prize, and recognizes the priority of Buckmaster and Alpoge’s work, although it states that it did not access specific user data to achieve its result. Of course, it points out that it cannot rule out that “anonymized data derived” from this use helped train its models. Furthermore, in his advertisement he does not mention the Spanish mathematicians and denies Buckmaster’s version of the pressures.

Regarding the prize of one million dollars for solving the problem, the Spanish mathematician assured that he does not “lose sleep” and points out that the Clay Institute “will do whatever it wants. They will see, what they should do is not give the prize to anyone, then they will see if they can offer it to OpenAI and have them reject it, but I have no expectation of seeing a euro of this money,” he noted.

“Deserves a Fields Medal”

Professor de Cunef stressed, however, that he was “very happy” that his work has contributed to solving the Navier-Stokes problem.

“It was a problem we were working on, we would have liked to continue doing it and have solved it, it was a project for the next few years. So we are very happy, we have been given very clear recognition from the scientific community. Our strategies have been a key piece in solving the problem,” he said.

Although he does not believe that AI will solve all the Millennium Problems, Martínez Zoroa acknowledged that it has “made mistakes many times,” so he believes that “it would not be surprising, given how good they are today, if the problems are being solved,” although, if so, he hopes it will be a “collaboration between AI and mathematicians.”

For his research, TristanBuckmaster argued that the Spanish “deserves a Fields Medal.” This is something that I personally have not spent much time thinking about, there are many very brilliant researchers around the world to consider it being a possibility. “I will continue doing my research as best I can and, if in a few years they give it to me, I will be happy, but it won’t stop me from sleeping,” he stated.

For the Cunef academic, AI “will accelerate the research process greatly and will transform it in a brutal way,” while human beings go “much slower.”

“Could we have used AI to speed up the process? Surely yes, but we cannot compete with the resources of OpenAI,” declared Martínez Zoroa, who considers that “it is too early” to say whether the use of AI is positive, since “it is not clear how its use will impact doctoral training.”

At this point, he explained that many of these tasks “can now be done with AI” and warned that if they run out of doctoral students “it is a death sentence. AI also accelerates the research process, so lights and shadows,” he concluded.

For its part, the Royal Spanish Mathematical Society (RSME) demanded “fair recognition” for the contribution of the Spaniards Luis Martínez Zoroa and Diego Córdoba in solving the Navier-Stokes problem, one of the great mathematical challenges of the 21st century that the company OpenAI claims to have solved thanks to artificial intelligence.

“In this case, it is evident that AI relied on previous contributions made by human mathematicians, an aspect that surely has not been sufficiently clear when presenting this finding,” the president of the RSME, María Victoria Otero, told Europa Press.

“Human dependence on AI will always be present, and in this case it is very obvious.

“Beyond the impact of the solution, what is still missing in this process, and is something of vital importance, is a complete, rigorous validation with scientific criteria of the discovery, and when this arrives there is no doubt that there must be fair recognition of the essential contributions of Spanish mathematicians and members of the RSME,” he claimed.

Otero assured that the OpenAI demonstration “is strongly based” on the ideas and previous work of Spanish researchers on the Navier-Stokes problem. “It is as simple as, if it had not been for Córdoba and Martínez, there would be no demonstration,” he said.