Unsolved Problems in Number Theory

Unsolved Problems in Number Theory catalogs hundreds of open mathematical problems and conjectures in the field of number theory. The book serves as a comprehensive reference guide for researchers and mathematicians interested in tackling these unresolved questions. Each problem is presented with relevant background, known results, and partial progress made by various mathematicians over time. The problems range from relatively simple-to-state questions about prime numbers and perfect numbers to complex conjectures involving algebraic number theory and Diophantine equations. Richard Guy includes detailed references and citations for each problem, allowing readers to trace the historical development and access key papers. The organization follows clear categories like prime numbers, Diophantine equations, and combinatorial number theory. The book stands as a testament to mathematics as an active, evolving discipline with many fundamental questions still awaiting answers. Its systematic collection of open problems illuminates the boundaries between known and unknown territory in number theory.

Readers describe this as a comprehensive catalog of open problems that serves both experts and motivated amateurs. Multiple reviewers note it functions well as a reference guide rather than a textbook. Liked: - Clear organization by topic - Historical background for each problem - Extensive bibliography and references - Accessible explanations of complex concepts - Regular updates in newer editions Disliked: - Some solutions/progress not included in latest edition - Can feel overwhelming for beginners - Limited worked examples - Price point ($109+ for hardcover) One mathematics professor wrote: "An invaluable source of research problems for graduate students." Several readers mentioned using it to find thesis topics. Ratings: Goodreads: 4.24/5 (21 ratings) Amazon: 4.6/5 (13 reviews) Mathematical Association of America: Recommended in review Most common descriptor in reviews: "treasure trove" - appearing in 6 different reader reviews across platforms.

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📚 First published in 1981, this book has become a vital reference work cataloging hundreds of open problems in number theory, many of which remain unsolved today. 🔢 Richard Guy continued updating the book well into his 90s, with the third edition published when he was 89 years old. He lived to be 103 and remained mathematically active until his final years. 💭 The book includes the famous "3x + 1 problem" (Collatz conjecture), which Paul Erdős said "mathematics is not yet ready for such problems." 📖 Many problems in the book were originally compiled from Guy's correspondence with fellow mathematician John Horton Conway, creator of Conway's Game of Life. 🏆 The book has inspired numerous research papers and doctoral theses, as mathematicians work to solve the problems it presents, making it one of the most influential problem collections in modern number theory.