The Mathematics of Artificial Intelligence Agents: A Readable Guide to Decisions, Planning, Memory, Tools, Learning, and Cooperation
English | September 7, 2026 | ASIN: B0HJ349HH4 | 977 pages | Epub | 15.10 MB
Updated October 2026: This edition adds a comprehensive subject index with more than 2,000 entries, with each entry linked directly to the relevant locations in the ebook. It also includes an online companion with 29 Jupyter notebooks, 108 interactive mathematical demonstrations, and 28 ready-to-use skills for AI assistants. Readers can use the companion materials to run the book's examples, change parameters, check results, and explore the mathematics directly.What changes when an AI model stops merely answering and starts acting?A language model predicts what comes next. An AI agent has to do something more. It must choose, plan, remember, use tools, respond to observations, cooperate with other agents, manage uncertainty, operate within permissions, and decide when to stop and return control to a person.Each of those problems has mathematics behind it.The Mathematics of Artificial Intelligence Agents is a readable guide to that mathematics. It moves beyond the model itself to examine the larger system built around it: the loops, states, tools, memories, decisions, constraints, and interactions that turn predictions into actions.The book develops the mathematics through research, historical examples, constructed problems, diagrams, and worked calculations. Equations are presented at full strength, but important formulas are accompanied by two explanations:What It Does explains why the equation exists and what problem it solves.Reading the Formula walks through how to interpret the notation.The goal is not to remove the mathematics. It is to make the real mathematics readable.Inside the bookThe chapters move from the foundations of agent behavior into decision theory, planning, learning, architecture, multi-agent systems, safety, evaluation, and delegation. Topics include emergence and capability measurement, graph reachability, Markov processes, expected utility, Bellman equations, Bayesian belief states, value of information, heuristic search, exploration and regret, reinforcement learning, world models, inference-time search, memory and tool use, game theory, consensus, mechanism design, constrained optimization, capability frontiers, and human delegation.The central question is simple:Once a model is placed inside a system that can remember, act, observe, and act again, what new mathematical object have we created?This book treats that question as something to be measured rather than described with vague language. It distinguishes what is proved, what is measured, what is fitted, and what is proposed. It also makes the limits of each result explicit.Readers can follow the narrative explanations and conclusions, work through the mathematics in detail, or move between the two.For readers who want to understand not just how AI models work, but how AI systems decide, plan, learn, act, cooperate, fail, and hand control back, this is the next step.
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