Symmetry and the Monster The Story of One of the Greatest Quests of Mathematics Book

The hero of this book, the Monster of Symmetry, is a giant snowflake that requires 196,884 dimensions to describe it. Rather than being a mere mathematical curiosity, its structure points to deep connections between symmetry, number theory, and mathematical physics. Ultimately it may help us come to understand the fabric of our universe -- or even the infinite multiverse.

This is the story of the quest to discover the Monster. Beginning in revolutionary France in the 1830s, it takes the reader up to the present day -- and beyond. Mark Ronan describes the driving determination, odd coincidences, and extraordinary people that were drawn into what became the greatest collaboration in the history of mathematics. He describes how the study of simple, regular shapes led to the whole field of simple groups, and the search for the basic nuts and bolts of symmetry. The hunt for the Monster began to classify all these nuts and bolts, the "atoms", of symmetry, and this bold project began to accelerate after World War II as new methods were devised to fill in the gaps in the classification, in the same way that chemists and physicists worked to fill out the Periodic Table of the Chemical Elements. The quest involves shapes in numerous dimensions, weird multi-crystals, and different ways of packing spheres that now underlie a good deal of modern technology. But some mathematical entities just don't fit the scheme, and the biggest, most bad-assed member of these outlaws was the Monster. As mathematicians drew ever-nearer to it, this dazzling entity's sheer scale and complexity became clear.

But mathematicians are still struggling to grasp the nature of the Monster. Given the extraordinary links between it and the deep physical form of the universe, it will become far more important in the future than we realize even now, a piece of 22nd- or 23rd-century mathematics arriving by chance in the 20th century, hinting at answers to questions not yet asked, which may not be asked for decades or even centuries. When we finally understand the nature of the Monster, we will probably thereby open up a whole new, far more profound vista of the nature of physical reality.