- Chapter 1 Introduction
- Chapter 2 Fundamental Elements
- Chapter 3 Miscoding
- Chapter 4 Inaccuracy
- Chapter 5 Surfeit
- Chapter 6 Nescience
- Chapter 7 Interesting Questions
- Chapter 8 Machine Learning
- Chapter 9 Analysis of Science
- Chapter 10 The Discovery of the Unknown
- Chapter 11 Discrete Mathematics
- Chapter 12 Discrete Probability
- Chapter 13 Computability
- Chapter 14 Coding
- Chapter 15 Complexity
- Chapter 16 Learning
- Chapter 17 Philosophy of Science
A Mathematical Theory of the Unknown
Journey Beyond the Frontiers of Human Understanding
This book is 100% completeLast updated on 2026-05-19
This book introduces a formal framework for measuring ignorance (or nescience) and for guiding scientific discovery. Grounded in computability theory, Kolmogorov complexity, and artificial intelligence, the book analyzes how representations and models encode knowledge, and how their limitations can be quantified. The result is a new perspective on unknown unknowns, perfect knowledge, and the limits of science.
For readers interested in artificial intelligence, scientific discovery, and the foundations of knowledge.
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About the Book
We celebrate knowledge, build systems of extraordinary complexity, and uncover the laws of nature. Yet the vastness of what we do not know still dwarfs our achievements. A Mathematical Theory of the Unknown turns attention to this neglected domain: ignorance itself.
At the center of the book is the concept of nescience, a quantitative measure of the lack of knowledge. Built on computability theory and Kolmogorov complexity, the theory analyzes how information is encoded in representations and models, and how their limitations can be decomposed into measurable components such as miscoding, inaccuracy, and surfeit.
A striking consequence emerges: perfect knowledge implies randomness. From this result, the book develops a rigorous framework for evaluating scientific progress, comparing competing models, and guiding research toward the discovery of unknown unknowns, questions we have not yet learned to ask.
Far from being purely theoretical, the framework provides operational tools for model evaluation, scientific inference, and data-driven discovery. It offers a new perspective on how knowledge is constructed, how it fails, and how it can be improved in practice.
Whether you are developing advanced AI systems or exploring the foundations of science, this book provides a precise and unified lens for understanding not only what we know, but what we do not, and how to systematically reduce it.
This work is both a theoretical foundation and a call for a new scientific program centered on the mathematics of the unknown.
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About the Author
R. A. García Leiva
Rafael García Leiva is an AI and data analytics professional with more than 20 years of experience as a research engineer in academia and industry. He holds a Bachelor’s degree in Computer Science and a Master’s degree in Computational Sciences, and currently works as an Innovation Manager at Vodafone.
His work focuses on the application of artificial intelligence and information-theoretic methods to understanding complex systems and guiding discovery. He is the author of the Theory of Nescience, a framework for quantifying ignorance and studying the limits of scientific knowledge.
In his spare time, he enjoys walking in nature with his family, reading, and exploring new ideas.
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