Edward Frenkel writes “This book is an invitation to a rich and dazzling world. I wrote it for readers without any background in mathematics. If you think 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.” Love and Math contains a nice mixture of storytelling and expository description of mathematics. This makes the book very enjoyable.
One goal of this book is to describe, in a nontechnical way, how the Langlands program is the “Rosetta Stone” connecting the fields of number theory, finite fields, Riemann surfaces and Quantum Physics. This is indeed a lofty goal. Frenkel must introduce and discuss concepts that are typically covered in advanced undergraduate and graduate math classes. Frenkel incorporates much of his life story, including details about the Russian anti-Semitism that prevented him from being accepted into the prestigious Department of Mechanics and Mathematics at Moscow State University. He tells about his “opportunity of a lifetime,” which brought him to Harvard University, where he earned his PhD and became the mathematician he is today.
Frenkel gives the reader unusual insight into the life of a mathematician. Many non-mathematicians might not understand how one discovers a new theorem in mathematics nor the type of work that leads to this accomplishment. In the account of the moment when Frenkel told his advisor that he had proved his first theorem he writes “I solved the problem! I couldn’t contain my excitement…” The feeling of success that a mathematician gets when they finally figure out the solution to the puzzle might help to explain why mathematicians dedicate their lives to their field. Frenkel brings this feeling to life in his story. Including these personal details helps to motivate the future results he discusses.
Frenkel seems to be highly skilled at explaining deep mathematical concepts without the need of a broad mathematical background. Perhaps this is a skill developed from his years working on the Langlands program in collaboration with physicists. It is wonderful to read a truly expository book about mathematics that actually says something meaningful and allows a non-specialist to gain an appreciation for the beauty and power of the field.
One question that comes to mind is “how can I use this book?” Who should read this book? This is a good book for anyone who is curious about mathematics, but in particular I am sure that mathematicians and mathematics students would enjoy the book. Having a deeper understanding of these concepts really brings the story to life. As an algebraist, I found that the book gave me several examples of applications of my field that I was not previously aware of.
Students majoring in mathematics with plans of working in industry after graduation will eventually need to explain to a potential employer why their mathematics background makes them qualified for a job. This book includes several examples where innovative thinking in mathematics has led to applications which were never intended. Mathematicians solve problems, think logically and have skills that are transferable to many fields. This theme is artfully illustrated throughout the book.
Ellen Ziliak is an Assistant Professor of mathematics at Benedictine University in Lisle IL. Her training is in computational group theory. More recently she has become interested in ways to introduce undergraduate students to research in abstract algebra through applications.