Introduction

Artificial intelligence is the study of building systems that perform tasks we associate with human intelligence—perceiving, reasoning, learning, and acting. The field draws on mathematics, computer science, cognitive science, and engineering, and its modern successes rest on a small set of durable ideas: representing the world as data, defining an objective to improve, and searching for parameters or actions that improve it.

This section establishes the groundwork the rest of the library builds on. Rather than focusing on any single model, it covers the concepts that recur everywhere: how information is represented, how uncertainty is quantified, and how systems are made to improve from experience.

History

AI has moved through several waves. Early symbolic approaches encoded knowledge as explicit rules and searched over logical states, achieving notable results in games and theorem proving while struggling with ambiguity and scale. Statistical and connectionist methods—neural networks among them—shifted the emphasis toward learning patterns directly from data. The convergence of large datasets, parallel hardware, and better optimization eventually made deep learning practical, reshaping vision, language, and beyond.

Understanding this history matters because each wave left lasting tools and cautionary lessons. Periods of inflated expectation were followed by slower stretches, and many ideas dismissed early were later revived once data and compute caught up.

Mathematical Foundations

A working grasp of a few areas of mathematics makes modern AI legible. Linear algebra describes data and transformations as vectors and matrices. Probability and statistics provide the language of uncertainty, inference, and generalization. Calculus and optimization explain how models improve by following gradients toward lower error. Information theory quantifies surprise and the limits of compression and communication.

These tools are not prerequisites to be memorized in isolation; they are recurring instruments. The same gradient that trains a small classifier also trains a large language model, and the same probabilistic reasoning that underlies a spam filter informs how we evaluate a model's calibration and reliability.

Reasoning and Representation

Beyond learning from data, intelligence involves representing knowledge and reasoning over it. Search, planning, logic, and probabilistic graphical models offer structured ways to draw conclusions and make decisions under constraints. Contemporary systems increasingly blend these classical ideas with learned components, using structure where it helps and learning where rules are hard to specify. This interplay between learned and engineered knowledge is a theme that returns throughout the library.