Love and Math by Edward Frenkel is an excellent book about the hidden beauty and elegance of mathematics. It is primarily about Frenkel’s work on the Langlands Program (a sort of grand unified theory of mathematics) and its recent connections to quantum physics. Yet the author's goal is not merely to inform but rather to convert the reader into a lover of math. While Frenkel acknowledges that many view mathematics as an “insufferable torment… pure torture, or a nightmare that turns them off,” he also feels that math is “too precious to be given away to the ‘initiated few.’” In the preface he writes,
Dear reader, with this book I want to do for you what my teachers and mentors did for me: unlock the power and beauty of mathematics, and enable you to enter this magical world the way I did, even if you are the sort of person who has never used the words "math" and "love" in the same sentence. Mathematics will get under your skin just like it did under mine, and your worldview will never be the same.
In the following chapters, to help the reader understand his research on the Langlands Program, Frenkel covers a wide range of advanced topics in a warm and approachable manner. He begins with an intuitive introduction to symmetry groups and moves on to give a survey of braid groups, modular forms, elliptic curves, Lie groups, Kac-Moody algebras, Galois theory, topology, sheaf theory, gauge theory, (even a little string theory!) and much more. But don't worry if you're not familiar with these topics! The book is also a memoir of Frenkel's life, recounting his days as a young boy in the former Soviet Union to his current years as a professor at UC Berkeley. Thus the reader can happily skip the sections that are too math-y and still enjoy the narrative. But, in fact, the book was written for readers without any background in math. As Frenkel urges,
If you think that math is hard, that you won't get it, if you are terrified by math, but at the same time curious whether there is something there worth knowing - then this book is for you.
But even if math doesn't terrify you, I strongly recommend Love and Math, especially if you're curious about the Langlands Program. Frenkel's survey contains such a wide spectrum of mathematics-explained-well, you're bound to be captivated. Check it out!