The Poincare Conjecture
O'Shea then looks at Euclidean geometry, and explains how non-euclidean alternatives were eventually discovered. He describes the work of Riemann on differential geometry, and then gets on to the work of Poincaré including his rivaly with Klein. This is followed by a chapter on the attempts to prove the conjecture in the 20th century, culminating in the success of Grigory Perelman at the start of the 21st
The use of equationsis avoided in this book, but I'm not sure that it's particularly suitable for those without some previous experience of the subject. O'Shea is keen to get across the nature of the work that has been done on the problem, and I would recommend this book to those who know a bit about topology and want to get a glimpse of the more advanced results in the field.