This book has been an enthralling and fascinating read for me. Mark Ronan outlines the mathematics of symmetry and details its historical development from Evariste Galois’s letter of May 1832 to about 2005.
Group theory is the mathematics of symmetry and the book has greatly helped me to learn and understand the fundamentals of group theory and especially simple finite groups.
Perhaps the most important revelation in the book is that the sum of the squares of the first twenty four integers is a perfect square (= 70^2). This means that every permutation of the 24-tuple list (1, 2, 3, …, 24) defines a line of length 70. There are 620 448 401 733 239 439 360 000 permutations. This number is very close to Avogadro’s number, an interesting coincidence of magnitudes. The size of the Monster, the largest simple finite group, is much larger than this.