Artificial intelligence may be one of the biggest technology stories of the decade, but some of the mathematics powering it was developed long before ChatGPT, NVIDIA Blackwell GPUs or today's massive AI data centers. One of those foundational ideas is gradient descent—a mathematical optimization method that helps machine-learning models improve by repeatedly adjusting their parameters to reduce errors.

The mathematics behind that process received renewed attention in 2026 when optimization researcher Yurii Nesterov received the Carl Friedrich Gauss Prize, one of applied mathematics' major international honors. The International Mathematical Union cited Nesterov's groundbreaking optimization work for providing theoretical foundations and an algorithmic backbone that made previously impractical computations feasible.

That provides a useful window into today's AI boom. Behind the enormous investments in GPUs, supercomputers and artificial intelligence infrastructure is a fundamental challenge: How do you train a machine to get better at something? Gradient-based optimization is an important part of the answer.

Why Gradient Descent Is Back in the AI Conversation

Nesterov is particularly associated with advances in accelerated gradient methods. Traditional gradient descent involves repeatedly determining which direction reduces a mathematical objective and then taking another step in that direction. Nesterov's work helped establish methods for reaching useful solutions more efficiently.

That distinction can sound academic until we consider the scale of modern artificial intelligence. Today's neural networks can contain billions of adjustable parameters, and training them requires enormous numbers of calculations designed to progressively improve how the model performs.

Even relatively small improvements in optimization can become significant when repeated across enormous computing workloads. That's one reason mathematics developed decades ago remains relevant to today's competition over AI chips and supercomputers.

What Is Gradient Descent?

The easiest way to understand gradient descent is to forget about artificial intelligence for a moment. Imagine standing somewhere on the side of a mountain with one objective: reach the bottom of the valley.

Unfortunately, thick fog prevents you from seeing the entire landscape. You can still determine which direction immediately around you slopes downward, so you take a step downhill, stop, check the slope again and take another step.

Eventually, after repeatedly evaluating the terrain and moving downhill, you approach a low point. That's the basic intuition behind gradient descent—except instead of traveling across a mountain, a machine-learning system is navigating a mathematical landscape representing its errors.

In AI, the Mountain Represents Error

Machine-learning models make predictions based on adjustable mathematical parameters, including weights and biases within a neural network. During training, the model processes examples and generates predictions.

A mathematical loss function measures how far those predictions are from the desired result. Think of the loss as an error score: higher loss generally means the model is performing worse according to its training objective, while lower loss means it is performing better.

The goal isn't simply to feed information into a computer. The system must find parameter values that allow it to perform its task more successfully, and gradient descent provides a systematic way to move those parameters toward lower loss.

How Does Gradient Descent Help AI Learn?

At its simplest, the process follows a repeating cycle. The model makes a prediction using its current parameters, and the training system calculates the loss to measure how poorly the model performed according to its objective.

Then comes the gradient. It describes how changes in the model's parameters would affect the loss, allowing gradient descent to change those parameters in the opposite direction of the gradient—toward values expected to produce less error.

Then the model tries again: prediction, error, adjustment, repeat. What we broadly describe as a machine "learning" can involve enormous numbers of these mathematical adjustments.

What Are Weights and Biases in Artificial Intelligence?

To understand why gradient descent matters, it helps to understand what is actually changing. A neural network contains adjustable values known as parameters, with weights influencing connections within the network and biases providing additional adjustable values that help represent relationships in the data.

At the beginning of training, these parameters don't already contain the final solution. Training progressively changes them, with gradient-based optimization determining which adjustments should reduce the model's loss.

Across enormous numbers of parameters and training examples, those seemingly small adjustments can eventually produce dramatic improvements in model performance.

What Is the Learning Rate?

Knowing which direction to move isn't enough. We also need to know how far to move, and that's the job of the learning rate.

Return to our mountain. If you take extremely small steps downhill, you're unlikely to overshoot the valley, but reaching it could take an extremely long time. Take enormous leaps and you might repeatedly jump from one side of the valley to another.

Machine learning encounters the same challenge. A learning rate that is too small can make training inefficient, while one that is too large can cause optimization to overshoot useful solutions or become unstable. The size of those steps therefore becomes an important part of model training.

Where Does Backpropagation Fit Into AI Training?

Gradient descent is often mentioned alongside another term: backpropagation. They're closely related, but they aren't identical.

Backpropagation provides an efficient way to calculate how different parameters within a neural network contributed to the model's loss. Gradient-based optimization then uses that information to update those parameters.

An easy way to remember the relationship is: Backpropagation helps calculate the gradients. Gradient descent uses gradient information to change the model. Together, these ideas became central to training modern neural networks.

From Gradient Descent to Today's Massive AI Supercomputers

Now we can connect the mathematics to something much more visible: the global race to build increasingly powerful AI computers. Modern AI systems don't simply store enormous databases of information; training requires repeated mathematical operations.

Models process data, predictions are generated, losses are calculated, gradients are computed and parameters are updated. Then the process happens again.

Scale that across massive datasets and neural networks containing huge numbers of parameters, and the computational requirements become enormous. That's one reason GPUs have become so important to artificial intelligence.

Why NVIDIA GPUs Became So Important to AI

Graphics processing units were originally developed primarily for graphics workloads, but their highly parallel architecture also makes them particularly useful for the large matrix and tensor calculations involved in machine learning. Rather than performing every calculation sequentially, GPUs can perform many mathematical operations simultaneously.

That capability proved extraordinarily valuable for neural-network training. It also helps explain how NVIDIA evolved from a company widely associated with computer graphics and gaming into one of the central companies in the modern AI infrastructure boom.

But there's an important distinction: the GPU isn't the learning algorithm. The hardware provides the computing power, while algorithms provide the mathematical instructions. Gradient-based optimization is part of the mathematical machinery that turns that computing power into model training.

The University of Florida Offers a Real-World AI Example

We don't have to travel to Silicon Valley to see what this looks like at scale. The University of Florida's HiPerGatorsupercomputer provides a particularly relevant example.

UF's fourth-generation HiPerGator incorporates 63 NVIDIA DGX B200 systems containing 504 NVIDIA B200 Blackwell GPUs, along with high-speed networking designed for demanding AI workloads. UF says those systems accelerate AI training, inference and data analytics.

That distinction between training and inference is important. Training is when a model's parameters are being developed and adjusted, while inference occurs after training when the resulting model uses those parameters to generate predictions or outputs.

Gradient-based optimization primarily belongs to the training side of that equation. When we see hundreds of advanced GPUs inside a system such as HiPerGator, we're looking at physical computing infrastructure capable of performing enormous numbers of mathematical operations required by modern AI research.

UF and NVIDIA Have Been Building AI Infrastructure Since 2020

The connection between the University of Florida and NVIDIA extends beyond purchasing computers. UF and NVIDIA began their public-private AI partnership in 2020, establishing the first NVIDIA AI Technology Center in North America and expanding access to AI computing, research support and educational programs at the university.

HiPerGator has since become central to UF's broader effort to integrate artificial intelligence into research and education. The university says its AI infrastructure supports work involving medicine, environmental research, transportation, agriculture, data security and other disciplines.

Understanding gradient descent helps explain what some of that infrastructure actually enables. The GPUs may receive the headlines, but the mathematics tells them what work to perform.

The Global AI Chip Race Is Also a Race to Train Models Faster

The connection becomes even clearer when looking beyond Florida. In September 2026, Huawei unveiled new AI computing technology as the Chinese company continues developing alternatives to NVIDIA and other American technology suppliers.

Huawei announced its Atlas 960 SuperPoD, designed to improve AI training and inference performance while allowing thousands of AI processors to operate as part of a larger computing system. The announcement reflects a broader technological competition that extends well beyond manufacturing faster individual chips.

Companies and countries are developing enormous interconnected computing systems capable of performing AI workloads at greater scale. That matters because training advanced models involves performing vast numbers of calculations repeatedly.

Underneath all that technology remains the same basic optimization challenge: How efficiently can the system improve the model?

From One GPU to Thousands: Why AI Scale Matters

Imagine that every step down our mathematical mountain requires millions or billions of calculations. Now imagine taking those steps repeatedly while adjusting billions of parameters.

Computational efficiency suddenly matters enormously. That's why modern AI infrastructure increasingly involves clusters containing hundreds or thousands of accelerators connected by extremely fast networks.

The objective isn't simply to create the world's fastest calculator. It's to divide enormous AI workloads across many processors and complete them efficiently enough to make increasingly sophisticated models practical.

Hardware advances and mathematical optimization reinforce each other. Better algorithms can reduce the amount of work required, while better hardware can perform that work faster. Together, they expand what artificial intelligence systems can realistically accomplish.

What Is Stochastic Gradient Descent?

Traditional gradient descent can calculate an update using an entire dataset, but imagine doing that with an enormous training dataset before making every adjustment. That can become extremely expensive.

A widely used alternative involves stochastic gradient descent, commonly called SGD, and related mini-batch approaches. Instead of calculating every update using the complete training dataset, the system uses individual examples or smaller batches.

That allows updates to happen much more frequently. The path toward lower loss may become noisier, but the approach can make large-scale training much more practical.

Modern optimizers build additional techniques on top of these basic gradient concepts to make training faster and more stable.

Does Gradient Descent Mean AI Is Simply Memorizing Everything?

Not necessarily. A model that merely becomes extremely good at reproducing its training examples can encounter a problem called overfitting.

The objective of useful machine learning is generally generalization. A well-trained model should identify patterns that allow it to perform effectively when encountering data it hasn't previously seen.

Researchers therefore don't simply watch training loss decline and declare success. They can evaluate models against separate validation and testing data to determine whether improvements during training translate into useful performance beyond the training examples.

Gradient Descent Doesn't Determine What Is True

There's another important limitation. Gradient descent is an optimization method; it doesn't independently know whether information is true, ethical, fair or useful.

It attempts to optimize the objective provided by the training process. A system can therefore become extremely effective at minimizing a mathematical objective without that objective perfectly representing everything humans actually care about.

The quality of training data, model architecture, objectives, evaluation and human decisions surrounding the technology remain important.

From a Mathematical Formula to a Global AI Race

That brings us back to Nesterov and the 2026 Gauss Prize. Optimization research that once might have appeared primarily theoretical now sits underneath technologies attracting extraordinary investment.

At the University of Florida, hundreds of NVIDIA Blackwell GPUs provide researchers with massive computing capacity. Around the world, NVIDIA, Huawei and other technology companies are developing increasingly powerful AI processors and interconnected computing systems.

Governments, universities and corporations are spending heavily on infrastructure needed to train and operate artificial intelligence. Yet underneath those enormous machines remains a remarkably understandable process: make a prediction, measure the error, determine which direction should reduce it, adjust and repeat.

AI 101: The Simple Idea Behind an Extraordinary Amount of Computing

Artificial intelligence can become intimidating very quickly. There are neural networks, transformers, tokens, parameters, embeddings, GPUs, data centers and enormous mathematical models.

Gradient descent gives us a useful place to start. Imagine standing on that mountain in the fog: you can't see the entire landscape, but you can determine which direction slopes downward, so you take a step, measure again and take another.

Modern AI performs that basic optimization process at a scale almost impossible for humans to visualize—with enormous datasets, sophisticated algorithms, vast neural networks and some of the most powerful computing hardware ever constructed.

The machines have become extraordinary, but one of the foundational ideas underneath them remains surprisingly simple: Find the error. Move toward less of it. Repeat.

And that helps explain not only how machines learn, but why the world is spending so much money building the computers capable of teaching them.