New thief on the block

Academia has seen countless instances of researchers hurling accusations of intellectual theft. But this is a new plot twist

Let’s set the stage for an academic crime. Two mathematicians are trying to solve a difficult problem. Their approach involves conceptual breakthroughs, and complex calculations. They’re sharing notes. A third person has access to the notes. That third party hires many smart assistants, instructs them to do the calculations and voila, a solution!

 

Most people would consider this an act of intellectual theft. And, what if that third party seems to make a habit out of stealing other people’s notes, and thereby “solves” more problems? There would be outcry across academia.

 

This is happening right now. Mathematicians across the globe are up in arms with accusations of intellectual theft flying to and fro. But the alleged “thief” (and its assistants) is not human. It is artificial intelligence (AI).

 

The controversy started when OpenAI published a partial solution to the Navier-Stokes (NS) equations. That hyphenated name evokes groans in mathematics, physics and engineering circles. NS consists of a set of differential equations that examine the velocity, pressure, temperature, and density of moving fluids such as air, water, and oil.

 

Differential equations look at changes in derivatives (for example, acceleration is a derivative of velocity) and the rules or functions governing such changes. Viscosity — the internal friction of a fluid — slows down movement and reduces turbulence, for example.

 

The NS equations were derived independently, by Frenchman Claude-Louis Navier and Englishman Sir George Stokes, in the early 19th century. If you stir a cup of tea, or shake a martini, NS comes into play. It also works with typhoons, whirlpools, water currents, and is of massive importance across climate science. Anybody designing a car, plane, boat, rocket or drone must take them into account.  

 

Scientists plug in numbers to the NS equations to derive accurate answers for the behaviour of moving fluids. But the NS equations can sometimes return apparent nonsense, predicting things like infinite velocity and zero volume (called a “singularity”). While this doesn’t happen in the real world, it is a puzzle that indicates we don’t understand exactly what is going on.

 

Can it be proved that the NS mathematics don’t allow infinite velocity? Or alternatively, can it be proved that this can happen in some theoretical cases, weird as that may seem? Mathematicians refer to this possibility as a “breakdown” in the “existence and smoothness” of NS.  

 

Some 200 years after the equations were written, they remain among the most important unsolved problems in mathematics with applications across many fields. NS is one of the seven famous Millennium Problems that were listed in 2000. The Clay Institute offers a prize of $1million for a proof that, one way or another, addresses four specific conditions for NS.

 

On Tuesday, September 8, OpenAI announced that it had found a solution to the NS problem by using a new AI model after 88 hours of intense computation involving 10,000 AI agents and 17 hours of verification. The agents exchanged 3 million messages and used 130 billion output tokens, which amounts to costs of well over $10 million. OpenAI claims its AI resolved two out of the four statements in the proof demanded by the Millennium Prize and that, indeed, infinite velocity is theoretically possible under certain conditions. The solution hasn’t yet been peer reviewed, and OpenAI has said that it has no intention of claiming the prize.

 

However, a mathematics professor at New York University, Tristan Buckmaster, said that he and Levent Alpöge, a mathematician who works for OpenAI’s rival Anthropic, had been working on NS. They had used OpenAI's tool, Codex, for sharing notes. Buckmaster-Alpöge claim that on September 3, “information about our progress had been passed to OpenAI”. They also claim OpenAI used the same logical approach to the problem as Buckmaster-Alpöge and, of course, OpenAI had the resources to do the computations.

 

OpenAI seems defensive. While denying this happened deliberately, Open AI says, “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models??.”  

 

According to OpenAI, at the end of August, it started to train a new model that was particularly adept at maths. On September 1, OpenAI admitted it had “heard rumours that two Millennium Prize problems had been resolved”, and so decided to put its thousands of AI agents to work to solve some of the remaining problems.

 

Another mathematician, Andreas Thom of Dresden University of Technology, says he suspects OpenAI stole his results in August when it announced that it had solved 10 open maths problems using its Astra model. OpenAI had then published machine-checkable proofs.

 

Thom claims that he and his collaborator, Gabor Kun, had used ChatGPT to discuss their work. He also says he asked OpenAI if ChatGPT could have accessed their notes and used it for training. OpenAI says, “That did not happen.” Thom and Kun claim they were using an unusual approach, which was also deployed by Astra. Of course, there’s no proof such a “theft” happened.  

 

Down the ages, academia has seen countless instances of researchers hurling accusations and counter-accusations of intellectual theft at each other. Newton-Leibniz and the discovery of Calculus would be among most famous controversies in this regard. But this is a new plot twist. AI is obviously a huge force multiplier in many ways where research is concerned. But if AI is also a thief, using it presents a conundrum for academia.

 

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The writer is a Delhi-based independent journalist

 

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