Beauty of Mathematics (Third Edition)

Beauty of Mathematics grew out of a series of articles Wu Jun began serializing on the Google China blog in 2006. The articles received millions of hits online and were widely reprinted. Wu later rewrote almost every piece, making abstruse mathematical principles more accessible so that non-specialist readers could appreciate the beauty of mathematics and of information processing. The book’s main thread is natural language processing and information retrieval. It begins with the relationship between writing, language, and numbers and information, tracing humanity’s understanding of how machines comprehend natural language through the methodological shift “from rules to statistics.” It then discusses statistical language models, Chinese word segmentation, hidden Markov models, information entropy and mutual information, Boolean algebra and indexing, graph theory and web crawlers, PageRank, measures of relevance, finite-state machines and dynamic programming, the law of cosines and text classification, matrix operations, information fingerprints, cryptography, the maximum entropy model, pinyin input methods, Bloom filters, Bayesian networks, conditional random fields, the Viterbi algorithm, expectation maximization, logistic regression and search advertising, MapReduce, and other major topics, interspersed with stories of figures such as Jelinek, Singhal, Marcus, and Viterbi. The third edition adds three chapters to the original content: the mathematical foundations of blockchain (elliptic curve encryption), the mathematical principles of quantum key distribution, and Hilbert’s tenth problem and the mathematical limits of machine intelligence; it also includes an appendix on computational complexity. The book uses examples to connect applications, algorithms, models, and the mathematics behind them, emphasizing simplification, solving engineering problems with mathematics, and thinking innovatively beyond fixed patterns.