THE ESSENTIALS
- OpenAI has announced that it has solved a millennia-old mathematical problem, consisting of proving the existence of unique solutions to the Navier-Stokes equations, which are ubiquitous in fluid mechanics.
- The carbon footprint of this mathematical proof, even if it is difficult to estimate precisely, is of a considerable order of magnitude: 1,000 tonnes of CO₂ equivalent.
- This is equivalent to the resources of large space observation instruments, for operational durations of around ten years. This raises questions about the allocation of such resources.
OpenAI’s successive announcements about scientific discoveries leave a persistent impression: artificial intelligence (AI) is now indispensable for doing science.
The company first announced in early September 2026 that its generative AI technology had risen to the challenge of the major scientific issues of our time by solving one of the Millennium Challenges, proposed by the Clay Institute. This challenge consisted of demonstrating the existence of unique solutions to the Navier-Stokes equations , which are ubiquitous in fluid mechanics .
She then published , on October 6, 2026, several hundred automatically generated mathematical proofs, purported to solve numerous open problems in mathematics. More recently, on October 26, she announced three new major results in mathematics, physics, and computer science, specifying this time how she intends to collaborate with the scientific community.
These three announcements reinforce the idea of close collaboration between OpenAI and universities. It would even be within reach of every scientist to receive assistance in their research. In its announcement of October 6, the company stated that, on average, “each result required computing resources equivalent to approximately three hours of ChatGPT Pro processing,” which a significant portion of the target audience already consumes regularly.
However, major theoretical questions, such as those concerning the Navier-Stokes equations, require significantly more computation. While criticisms are emerging regarding the usefulness of algorithmic solutions to these questions, the environmental cost of OpenAI’s services to the scientific community can also be questioned.
As an example, let’s try to estimate the carbon footprint of the calculation that led to the discovery of a non-trivial solution to the Navier-Stokes equations.
AI, a “bulldozer” for modern mathematics?
One might think that mathematics is the intellectual discipline par excellence, that all it takes is a large whiteboard and a black marker to prove theorems, invent new formalisms and, ultimately, produce new knowledge.
This is no longer the case. The complexity of certain proofs now requires computer assistance . With the emergence of Large Language Models (LLMs) and autonomous “agents,” even the creative aspect of research can be automated using AI.
By publishing a deluge of results, OpenAI has inspired Robert Hart, a journalist for the American media outlet The Verge , and Gaël Varoquaux, a researcher at Inria and columnist for Le Point , to use the image of a bulldozer. These two authors draw slightly different conclusions, but the analogy is excellent from an energy perspective: from its inception ten years ago, OpenAI claimed to have 1,600 computers at its disposal , whose combined electrical power was on the same order of magnitude as that of a construction vehicle.
In its September statement , OpenAI said it used tens of thousands of agents to solve this problem, interacting with each other for 88 hours, generating
“2.7 million messages and using approximately 130 billion “tokens” (exit tokens).”
At the price offered by OpenAI, the bill for this volume of computing represents the equivalent of funding around forty PhD scholarships in France.
Such a concentration of “thinking,” accomplished in a few dozen hours where a thesis requires at least three years of work, implies considerable electricity consumption. This raises questions about the true environmental cost of the operation.
How to estimate the carbon footprint of an AI system?
Ideally, a multi-criteria environmental assessment should be conducted, but here we will limit ourselves to calculating the carbon footprint based on an estimate of electricity consumption. This is already complex enough to estimate due to the lack of transparency maintained by technology companies.
Indeed, it is necessary to estimate the electrical consumption of LLMs with partial information and many assumptions: if the order of magnitude obtained is not good, OpenAI will not hesitate to point it out, as Google has done here or there , in response to academic publications on the subject.
OpenAI, in its announcement, informs us that it took 130 billion operations to produce a proof. An operation consists of producing a token , which can represent a letter, a word, or a portion of a word.
Furthermore, the services company Neuralwatt, one of the few to provide its consumption data, indicates an average consumption of 33.6 kilojoules (kJ) per thousand tokens (or about 10 watt-hours) for the LLM Kimi K3 , which can be assumed to be close to that of OpenAI.
We can therefore estimate the energy consumed for this proof at 1.3 gigawatt-hours. Also, in 2026 in the United States, the production of one kilowatt-hour of electricity generates on average 388 grams of greenhouse gases in CO₂ equivalent, which gives, as an order of magnitude, a carbon footprint approaching 500 tonnes of CO₂ equivalent.
In just 88 hours, OpenAI’s AI system would therefore have emitted as much as 50 people residing in the European Union (EU) for a year (for food, housing, transportation, etc.).
A high failure rate that increases the carbon footprint
In its search for a solution to the Navier-Stokes equations, the company states that it attempted to solve other problems without specifying whether they were also solved. This is probably not the case. Therefore, this exploratory phase can be included in the calculation, just as failures must be taken into account in a research process.
Consequently, it wasn’t 130 billion operations that were required, but a total of 300 billion to find a worthwhile result among the problems posed. Using the same assumptions as before, we can therefore consider that it was necessary to emit more than 1,000 tonnes of CO₂ equivalent to achieve a publication.
We can hope that the order of magnitude of this estimate is correct, but it is based on fragile assumptions:
- The energy of a calculation depends less on the number of symbols generated than on the duration of the calculation;
- No one outside of OpenAI staff can know if Kimi K3 is actually comparable to OpenAI’s model.
However, the figures given by Neuralwatt on other smaller LLMs, such as DeepSeek v4 Flash, are comparable to those that Google and OpenAI are willing to give about their consumer services, i.e. about 0.3 watt-hours per request.
The carbon footprint of AI compared to that of astronomy
We can put it even more cautiously: if a mathematician or a theoretical physicist were to try to solve the singularity problem posed by the Navier-Stokes equations without access to OpenAI’s AI system, they would have to emit more than 1,000 tonnes of CO₂ equivalent, i.e., multiply their annual carbon footprint by 100 (for the EU).
What other research activity allows itself such a footprint? A study published in Nature estimated that the carbon footprint of astronomy research infrastructure, a major emitter of greenhouse gases, is between 22 and 50 tonnes of CO₂ equivalent per astronomer (in addition to the average of 10 tonnes of CO₂ equivalent per person for the EU). This is a far cry from 1,000 tonnes.
Let’s now consider the example of large-scale astronomy research projects involving dozens, or even hundreds, of scientists. The organization Labos 1point5 (referring to the goal of limiting global warming to 1.5°C) offers a methodology for assessing the carbon footprint of a laboratory on this type of project.
The Giant Radio Array for Neutrino Detector (GRAND) project , for example, which involves installing antennas across 200 square kilometers to observe space from Earth, has an estimated carbon footprint of 471 tonnes of CO₂ equivalent. For a telescope in the Cherenkov network, the figure is even higher: between 2,400 and 2,950 tonnes of CO₂ equivalent.
OpenAI’s carbon footprint over the 88 hours of computation may be lower than these figures, but when considered in relation to the duration of the projects, the difference is, quite literally, astronomical. These projects are, in fact, scheduled to last twenty and thirty years respectively. In the case of the telescope, 55% of the carbon footprint comes from operating the telescope over thirty years.
Trade-offs to be made for sustainable research
At a time when reducing our greenhouse gas emissions is supposed to be an objective of the European Union, this emerging practice of algorithmic problem-solving threatens the sustainability of theoretical research , which until now has been one of the least greenhouse gas emitting fields.
In the near future, we may have to choose between such “bulldozer-like” theoretical research, astronomical research, and any other research activity that consumes material resources and energy. In other words, in mathematics, we may have to abandon the generation of proofs by LLM.
Author Bio: Victor Charpenay is a Lecturer-Researcher at the Laboratory of Computer Science, Modeling and Optimization of Systems (LIMOS) at Mines Saint-Etienne – Institut Mines-Télécom
