As the title suggests, its hundred chapters, ordered chronologically, each deal with a major mathematical development (e.g. Aristotle’s analysis of logical syllogisms circa 350BC, the discovery of transcendental numbers in 1844, and the creation of Weaire-Phelan foam in 1993). My hope is that it should be accessible, attractive, and entertaining to people with little or no background in the subject – jargon and technical notation are kept to a minimum, and each chapter is accompanied by a beautiful full-page colour illustration.
My major concern was to avoid wrenching these breakthroughs out of context and artificially presenting them as stand-alone events. After all, mathematicians typically make advances by contemplating the insights of previous generations and answering questions posed by earlier thinkers. Without Kelvin’s conjecture (and perhaps without the work of Pappus and Thomas Hales on related geometrical questions) the discovery of Weaire-Phelan foam would have been less exciting. Equally, it often takes time and further insight for the significance of a breakthrough to become apparent: it was some years after their initial discovery that the deep importance of transcendental numbers was recognised.
So I hope that the book not only presents some wonderful discoveries, but also tells the back-stories, gives some sense of what the characters involved thought they were up to, and discuss why their work matters to us today.