What are data centers doing? A mind-boggling amount of math

Today’s artificial intelligence systems are more capable than ever — thanks to the mind-boggling amount of math it takes to train them.

The training mainly amounts to doing surprisingly simple arithmetic to get better at predicting the next word in a sentence. But there’s a lot of this math to do.

In 2018, OpenAI released GPT 1, the first AI model in the company’s GPT series. It took 18 million trillion additions and multiplications to train it.

The next year, OpenAI released GPT 2. Its training involved nearly 300 times as many calculations.

In 2022, the company released GPT 3.5. Its training involved over 140,000 times as many calculations as GPT 1’s. A version of this model was later launched as ChatGPT.

In 2023, GPT 4 took over a million times as many calculations to train as GPT 1 did.

In 2026, GPT 6 Astra took nearly an octillion calculations to train — over 50 million times as many calculations as GPT 1 did. Even calling this figure astronomical understates its size: An octillion is a thousand times the number of stars in the known universe.

Developing future AI models will probably involve even more math.

These figures are estimates, because the leading AI labs do not disclose specific details on how their systems are trained.

What is clear, however, is that AI’s demand for calculation is growing exponentially, despite a recent public grappling with AI safety and rising opposition to data center construction.

And while computer chips are becoming faster and more energy efficient, these efficiency improvements are outstripped by AI’s growing appetite. As a result, the power needed to train the largest AI models has doubled every year.

Researchers predict that by 2030, training the largest AI models may use electricity at a rate similar to New York City today. Energy experts project that by then, data centers may use around 12% of America’s electricity.

The reason for this exponential growth: an observation known in the tech industry as a “scaling law.” Over the past decade, researchers have found that training AI with more calculations and more data has reliably produced more capable AI systems.

Growing capabilities

It’s hard to know exactly how much AI has gotten better as its training has scaled up, because these capabilities are highly varied and difficult to assess.

But the improvements extend beyond writing. Newer models have scored higher on the Epoch Capabilities Index, which combines results from multiple benchmarks testing subjects such as math, coding, general knowledge and conceptual reasoning.

AI companies have been racing to extend this trajectory further up. This race is fueled by the belief that more calculations and more data will continue to produce more powerful AI.

And that means more and more math.

Why training AI involves so much arithmetic

The number of calculations needed to train AI is known as its training “compute.”

To a rough approximation, this depends on two things: the size of the AI model and the amount of data it is trained on. And these are both enormous.

The largest language models contain trillions of numbers (known as parameters) that they use to guess the next word in a sentence. (More accurately, they guess the next token, which can be a part of a word.)

You can picture these parameters as trillions of adjustable knobs, whose settings capture patterns in the data. At the outset, the knobs are set to random values, and so the AI’s responses are no better than random guesses.

During its training, the AI is fed a portion of a sentence, and the knobs are adjusted using a series of math calculations to improve its guesses for the next word. This process is then repeated over trillions of words of training data.

It takes only a few additions and multiplications to adjust a single knob. But when trillions of knobs are adjusted trillions of times, the math quickly adds up.

And this is just the first step in training a language model, known as pretraining. It’s followed by additional steps of calculations that hone the AI’s behavior and improve its ability to code and solve math problems.

The estimated number of calculations used to train GPT 6 Astra — roughly an octillion (or a thousand trillion trillion) — is enormous. As a possibly unhelpful comparison, an average adult human body contains between 1 octillion and 2 octillion molecules.

“The way we train generative AI models nowadays is really like a brute force approach,” said Sasha Luccioni, the co-founder and chief scientific officer of Sustainable AI Group.

The process involves making AI models bigger and bigger, and using as much data as possible and as much computing power as possible, she said.

This “brute force” approach has achieved impressive results. But it’s also why training AI requires a continually rising number of calculations.

Rising costs

So how can AI companies possibly do this much math?

“No single computer can handle all of that data, so you end up having to split it up into pieces,” said Benjamin Lee, an engineering professor at the University of Pennsylvania who studies how to make data centers more energy efficient.

Companies first split their enormous training data into smaller batches. They then send these batches to tens of thousands of AI chips that work in parallel as a giant supercomputer inside massive data centers.

Running these chips day and night consumes a lot of electricity. The data centers use additional power to cool them down, link them together and coordinate their calculations.

“Data center is actually a misnomer; they will be better called compute centers,” said Jaime Sevilla, the CEO of Epoch AI, a nonprofit organization that assesses AI’s capabilities and energy use.

Epoch AI estimated that training xAI’s Grok 4 involved doing roughly 500 septillion (or half an octillion) calculations, and that this cost around $490 million in hardware and electricity and released the equivalent of 150,000 tons of carbon dioxide — roughly the annual carbon footprint of 10,000 Americans.

An OpenAI spokesperson said the company was measuring its carbon footprint and supported greater transparency: “Training more capable models takes more computing power, but each training investment benefits more people as adoption grows, and we’re making models more energy efficient to run.”

While training an AI model is a one-time cost, the costs of running it are ongoing. These “inference costs” depend on how large the AI model is and how heavily it is used.

Inference costs are rising fast as AI models have become larger and more verbose. Today’s AI “reasoning” models write lengthy notes to a scratchpad before answering a question, and AI agents can keep working in a loop producing reams of text to solve a problem.

To take one extreme example, as part of solving a Millennium Prize math problem, OpenAI’s AI agents sent 4.9 million messages over five days in September, producing the equivalent of hundreds of billions of words. Billed at the company’s public rates for its Astra model, this would amount to $15 million in inference costs.

(The New York Times has sued OpenAI and Microsoft, claiming copyright infringement of news content related to AI systems. The two companies have denied those claims.)

Shifting goals

Before ChatGPT, most AI tools performed narrowly defined tasks, such as detecting spam, analyzing product reviews or recommending your next movie.

But modern generative AI is designed to be general purpose, and to try to answer any question that you could throw at it.

“The generality of it has made the models much larger and also much more expensive to train,” Lee said.

As recently as 2020, major tech companies were planning to offset their data centers’ electricity use with investments in wind and solar power. Google aimed to balance out the carbon emissions for the company’s electricity use by 2030.

But the industrywide growth of generative AI, and the resulting building spree of giant data centers that use exponentially more electricity, is making such net-zero goals slip out of reach. Many AI data centers are powered by natural gas generators, and some even plan to use nuclear reactors to supply electricity.

Google now says its net-zero ambition “remains a continuous, uphill pursuit” because of the rapid growth of its infrastructure.

Even if future AI data centers become more energy efficient, Lee said, it is no longer feasible to supply all of their electricity from renewable sources such as solar and wind power.

“The numbers are just too big,” he said.

This article originally appeared in The New York Times.