Our direction is engineering and topology, journeys in mathematics

This book aims to introduce the mathematician William Thurston, to whom the science of mathematics owes a great deal, especially in two fields: geometry and topology, which earned him the deserved and rightful Faidles Award for his overall work, particularly since he made these two fields of knowledge reveal all their secrets to him, according to the words of one researcher. And with the successive chapters of the book, we discover that for him, mathematics is not an abstract, exalted science practiced by people from above who hold the keys to complex equations and intractable calculations unrelated to reality, but rather Thurston's most important question is how to elevate humanity. This book was written by researchers who worked hard to avoid reducing Thurston to a mere mechanical mathematician. It is, therefore, a journey to discover the personality of William Thurston and to learn about his achievements and contributions, divided into ten stages, highlighting various aspects of his work, especially some of his favorite mathematical topics. Throughout these journeys, we discover that Thurston did not limit himself to discovering abstract worlds but also worked skillfully to shed light on some aspects of classical mathematics from an innovative perspective.