New Book: Finding Moonshine: A Mathematician’s Journey Through Symmetry, by Marcus du Sautoy

February 20, 2008

Called articulate, fluent, funny, and personable, Marcus du Sautoy is passionate about mathematics-and wants to make others as excited as he is about its problems, patterns, and beauty.

The well-known Oxford mathematician tries to do that through his latest work, Finding Moonshine: A Mathematician's Journey Through Symmetry, in which he strives to bring to life a mathematical world that's a long way from the idea that something is symmetrical simply because its left side and right side are mirror images of one another.

"The mathematical world of symmetry is a the world of transformations of objects," wrote reviewer Lisa Jardine for TimesOnline, "such that the transformation leaves the original state of affairs apparently unchanged--like making a sixth of a turn with a hexagonal shape on the page."

“If one turns away while the shape is being turned,” she said, "you would have no idea anything at all had altered." “These sequences of transformations can be captured in simple groups, which provide a collection of building blocks for symmetry, and are akin to prime numbers, which are the building blocks of number theory.”

In his newest book, du Sautoy introduces the general reader to the subject of symmetry via the patterning possibilities found in the tiles of the Alhambra in Granada, Spain. Initially, du Sautoy seeks to uncover the 17 types of symmetrical transformations possible in two dimensions, around the Alhambra's walls.

But the real goal for du Sautoy involves mathematical problems associated with complex “sporadic groups," which do not conform to the regularities of the other members. The biggest of the sporadic groups is known as the “Monster” -a symmetry group in 196,883 dimensions. “Moonshine” is the mathematical link between the Monster and a function in number theory called the j-function. Du Sautoy brings out the excitement of trying to understand the properties of the Monster--and of trying to prove its existence.

“In the end,” wrote Jardine, Finding Moonshine turns out to be the story of du Sautoy himself, "as he grapples with the most extreme problems of group theory and number theory. The story is structured as 12 months in his life--and the year he turned 40," in 2005.

“Readers,” said Jardine, "experience the thrill of steps made towards uncovering ultimate mathematical beauty and share his sense of wonder at the intricacies and patterns that the search reveals. We are drawn into the curious lives of virtuosi from the past, whose brilliant discoveries continue to underpin modern mathematics."

Finding Moonshine: A Mathematician’s Journey Through Symmetry, by Marcus du Sautoy, is published by Fourth Estate (Great Britain).

Source: TimesOnline