Theory of Groups of Finite Order by William Burnside

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By Charlotte Girard Posted on Nov 15, 2025
In Category - Adventure
Burnside, William, 1852-1927 Burnside, William, 1852-1927
English
Okay, hear me out. I just finished a book that's basically the origin story for a secret code that runs our entire digital world. It’s not a sci-fi thriller—it’s a math book from 1897! William Burnside’s 'Theory of Groups of Finite Order' is the quiet, foundational text that helped mathematicians crack the hidden patterns of symmetry. The central mystery? How to classify and understand these perfect, abstract structures called 'finite groups.' Think of it as the rulebook for the universe's most elegant puzzles, written before we even knew we needed it. It's surprisingly dramatic for a book with so many equations.
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Copyright (C) 2004 by David Baumann, Jon Cooper, and Mike Dodd. THE RUNAWAY ASTEROID THE STARMAN SERIES by Michael D. Cooper MUTINY ON MARS THE RUNAWAY ASTEROID JOURNEY TO THE TENTH PLANET DESCENT INTO EUROPA THE LOST RACE OF MARS DOOMSDAY HORIZON (The seventh book, THE STARLIGHT MANEUVER, and other volumes are in preparation.) The short stories— The Flight of the Olympia, The City of Dust, SETI, A Matter of Time, and Return to Europa— are available in the first five issues of the Inter*Stellar, the fanzine for the Starman series. A novelette outside the main storyline, The Lost Tomorrow, is serialized in “The Starman Chronicles.” All items may be ordered through the Starman web site at www.StarmanSeries.com. David Foster Number Two THE RUNAWAY ASTEROID by Michael D. Cooper Artwork by Nick Baumann A David Foster Starman Adventure Copyright (c) 2004 David Baumann, Jon Cooper, and Mike Dodd all rights reserved ABCDE “A Baumann-Cooper-Dodd Enterprise” The Starman Team dedicates this book to Fred Woodworth a rare and gifted individual who practices generosity in a world of acquisitiveness, courage in a world of indifference, honesty in a world of opportunism, and personal responsibility in a world of buck-passing; an artist and craftsman few in this era know how to appreciate; who has done as much as any and more than most to advance the cause of series books; and whose genius has abundantly proven that the books deplored by librarians of a previous age are treasures that shaped several generations and made their readers better people. To Fred Woodworth of Tucson, Arizona, the series book world owes a debt that can never be repaid. Acknowledgments The Starman team wishes to thank STEPHEN AVERY for coining the term “greegles.” Though these remarkable beings will probably not reappear for several books, their place in the Starman series is an essential part of the saga. TOM NARWID, amateur astronomer, for supplying the photograph which we used for the endpapers. The scene was taken through his backyard telescope in Cottonwood, Arizona. KEVIN ANETSBERGER for preparing Tom’s spectacular, multi-colored original photograph for publication by reducing it to two colors. The number of fans of the Starman series is growing each day, and we appreciate the contributions many of them have made to the project. Their assistance, encouragement, and technical support have helped to improve the storyline and scientific accuracy of the Starman adventures. Introduction The Starman Team dedicated its first book, _Assault On Mars_, to Joseph Greene, the late author of the Dig Allen series which was the inspiration for the Starman series. A complimentary copy was sent to his son Paul, who was moved by the tribute. We then asked Paul to write an introduction to _The Runaway Asteroid_. The following is his response--surely one of the most unusual introductions in any book anywhere, and one we are privileged to share with our readers. Dear Dad, A most remarkable invention is weaving the world together in a way we never anticipated while you were on Earth, and it netted your writing. Fans of your books for juveniles, The Digby Allen series, were able to connect to each other, share their enthusiasm for your novels, and were inspired to continue the voyage. Led by Jonathan Cooper, the intrepid mastermind of the creative crew, they made a commitment to write their own vision of the future. Thoughtfully, they credit you as having shoulders broad enough for them to stand on and see the centuries beyond. The invention that has made this possible is called the internet. There seems no need to explain what it is here, but...

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Let's be clear from the start: this is not a beach read. William Burnside's Theory of Groups of Finite Order is a dense, technical masterpiece written for professional mathematicians. But its 'story' is fascinating. Published in 1897, it was one of the first major attempts to organize and build a complete theory for something called finite group theory. Groups are mathematical objects that capture the essence of symmetry—the ways you can rotate a square, shuffle a deck of cards, or even the underlying rules of particle physics. Burnside tried to bring order to this wild new landscape, proving foundational theorems and setting the stage for a century of discovery.

Why You Should Read It

You probably shouldn't, unless you have serious math training. But you should appreciate it. Reading bits of it (or even just holding the 1897 edition) feels like touching history. This book laid the groundwork for the mathematics that eventually made modern cryptography, quantum mechanics, and even the error-correcting codes in your phone possible. Burnside's work is the quiet, patient foundation upon which so much flashier science was later built. His clarity and depth set a standard.

Final Verdict

This book is strictly for historians of science, pure mathematicians, or the most dedicated and advanced students of abstract algebra. For the general reader, its true value is as a legendary artifact—the 'Source Code' of a fundamental branch of math. It's a reminder that the most world-changing ideas often begin as obscure symbols in a quiet study.



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