This book traces a remarkable path of mathematical connections through seemingly disparate topics. Frustrations with a 1940's electro-mechanical computer at a premier research laboratory begin this story. Subsequent mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels led to discoveries of extremely efficient lattice packings of equal-radius balls, especially in 24-dimensional space. In turn, this highly symmetric lattice, with each point neighbouring exactly 196,560 other points, suggested the possible presence of new simple groups as groups of symmetries. Indeed, new groups were found and are now part of the 'Enormous Theorem' - the classification of all simple groups whose entire proof runs to some 10,000+ pages. And these connections, along with the fascinating history and the proof of the simplicity of one of those 'sporadic' simple groups, are presented at an undergraduate mathematical level.
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'Thompson provides an excellent example of the constant interaction between applied and theoretical mathematics. Thompson's work is first-rate historical research and good clear writing. As a mathematics teacher, he has gone to great pains to make the material understandable to anyone with even a casual acquaintance with vector spaces and groups.' Annals of the History of Computing
Book Description
Mathematical methods of encoding messages to ensure correctness when transmitted over noisy channels led to discoveries of extremely efficient sphere lattice packings. In turn, this suggested the possible presence of new groups of symmetries. These connections, along with the fascinating history, are presented at an undergraduate mathematical level.
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Fascinating!
14 Jun 2003
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One of the best math books around. It has a good story, clear explanations, and great subject matter.
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