Neural Networks: Myths, Reality, and the Mathematics Behind AI

When we think of AI-especially neural networks-we often envision layers of tiny computer “neurons” acting in a way analogous to the cells in our brain. We imagine them passing signals among one another, recognizing shape and form in images, and meaning in sentences, learning much like humans do from real-world problems. It’s easy to assume these networks are logical, inquisitive machines which “think” in a manner similar to us.

The surprise comes when we delve a little deeper into how neural networks really work: most of what we imagine isn’t quite right. Yes, neural networks do learn from data created by humans, but they don’t understand the world and don’t reason like a human mind. What they actually do is recognize patterns.

Why Are They Called Neural Networks?

The name neural network wasn’t an accident. These systems are inspired by the structure of the human brain: just like biological neurons, artificial neurons receive inputs, process signals, and pass information forward. Neural networks can even “remember” in a mathematical sense patterns from previous data.

This, however, is only a superficial similarity. Human memory, emotion, creativity, and thought are biological and deeply complex; neural networks are precise mathematical systems. They don’t think or feel-but they work with such astonishing accuracy that we sometimes wonder whether they might eventually think like us.

So What Are Neural Networks Really?

Everything that happens inside them, from signal processing to pattern recognition in images or text, is done through mathematical operations. On the surface, neural networks depend mostly on linear algebra and calculus.

A single perceptron, which is the very basic unit of a neural network, is really just a combination of linear algebra and a function that converts that result into a probability. The base of these complex tasks is still purely mathematical.

Where the Math Comes In

Neural networks employ mathematics in every aspect of their operational cycle. They do math in order to:

• calculate the probability of the right answer
• Convert words to numerical tokens.
• calculate a notion of how bad the prediction is, called loss
• Improve the output step by step.
• learn from past mistakes

And this is just the beginning, really, as mathematics governs nearly every aspect of how a neural network works.

Linear Algebra: The Core Engine

A simple question arises: How do dense neural networks use linear algebra to compute?

The answer is surprisingly simple. We see an equation like this in school:

In machine learning, it becomes:

where w is the weight and b is the bias.

Each perceptron has a set of weights that define how important each input is to the model. A higher weight means a stronger influence.

For instance, the model predicts whether a person will buy insurance using two input variables: an individual’s age and financial status. If the data indicates that age has more influence on the decision, then the network gives a higher weight to age. The bias term allows the perceptron to fire even when the input signals are small. By modifying these values, neural networks train to recognize patterns and make predictions with high accuracy.

Why AI Still Makes Mistakes

The mathematics is both the strength and limitation of today’s AI. Neural networks may feel intelligent, but behind the scenes they are still just sophisticated combinations of formulas. That’s why current AI models can make mistakes. They predict patterns, not meanings.

A truly humanlike thinking machine is called Artificial General Intelligence, or AGI. AGI would require real reasoning, understanding and creativity-not just mathematical prediction.