The Mathematics of the Unknown: with Applications to Machine Learning

This book is a comprehensive, self-contained, introduction to the Theory of Nescience, a new and powerful mathematical theory that has been developed with the aim of automatically discover new knowledge. The book also covers applications to artificial intelligence (data science, machine learning), the scientific method, and software engineering
The quest for knowledge always starts by identifying a set of research entities we would like to understand. The elements of this collection can be almost anything. If we are mathematicians, our set of interest will be composed by mathematical concepts; if we are biologists, the set will be living things; and if we are engineers, it will be practical problems. Our goal, as scientists, is to understand as much as possible about those entities. We want to understand how things work because that allows us to forecast both, future events in environments with high uncertainty, and the consequences of our own actions. Also, and more challenging, looking at events/consequences we can try to infer the causes; for example, if I have fever, maybe it is because I have been infected with a virus. Understanding is how humankind makes progress, and understanding means to find patterns or regularities that allows us to provide models of the original entities under study.
If we want to study a research entity, first we have to provide a representation of that entity. A representation is a string that captures as many details of the original entity as possible. In science, traditionally, these representations have had the form of texts (e.g. mathematics), collection of facts (e.g. sociology), or the result of experiments (e.g. physics). Recently, and due to the huge advances in the capacity of computers to collect and store data, a new and powerful way to encode entities has emerged: the use of large collections of data as representations.