Love and Math: The Heart of Hidden Reality

A boy who grew up in a town closer to Moscow became interested in quantum physics. Plenty of popular science books were easy for him to find to read. His parents were engineers and were quick to recognize boy's talents. A mathematics professor of the only college in the town who is also a friend of the family took the boy under his wings. The professor asked him if he knew about the group SU(3). This conversation made the boy realize that he had to learn math to answer many questions he had by reading popular science books. Thus began the journey of this boy becoming one of the premier mathematicians of today. He was introduced to great mathemati- cians from the beginning. Mathematicians gave him problems to solve. He solved his first problem on Braid groups as a freshman. He attended Israel Gelfand’s legendary seminars at Moscow State University. He was offered a visiting professorship at Harvard even before he received his bachelor’s degree. To get a permanent job he needed a degree. He enrolled in the Harvard PhD program and received his PhD in one year. He first heard about the Langlands Program at Harvard. Since then until today he has been working on the Lang- lands Program. Langlands program is like a Rosetta stone revealing similarities in three apparently unrelated fields; namely, Number the- ory & curves/finite fields, Riemann surfaces and Quantum Physics. The book "Love and Math" is Edward Frenkel’s autobiography. He has done a masterful job of trying to bring hard mathematics that he has been working on to a level of an average reader by inter-vowing it with his fascinating life experiences. It is hard not to get excited about the math that you know practically nothing about. "Love and Math" makes you wanting to read more and get to know more about this fascinating mathematics. Frenkel has included many references for an interested reader to follow through as notes at the end of the book. "Love and Math" is a must read for young and old alike.

I love this book. But, then, I teach math. Frenkel perfectly describes the frustration/thrill cycle of solving difficult problems. In that sense, he does a great job of explaining the experience of doing mathematics and why some of love it. My reservation about the book is that he's writing for those who don't 'get' the love of math, but his experience of math is at an extremely high level. The explanations of math sometimes work and sometimes require work on the reader's part. His area and level of expertise is challenging for me to comprehend fully, so the person who feels like an outsider in the field probably will still feel that way. Nonetheless, the book is worth reading for the fascinating story of Frenkel's life and experiences, even if you skim over the math. Frenkel, because of his Jewish heritage, struggled to get the education he wanted in the Soviet Union. That struggle and the generosity of the mathematics community is inspiring and heart-warming. He also tells good, human tales about other mathematicians who are writing the book of 21st century math and science.

Even if you struggled with grade school fractions, perhaps even more so because you did, this book is just the square root of 2 shy of essential. There's a whole world of magic in mathematics that eludes most of us. Our teachers fling us directly into the material without an ounce of background, application or concept. This is their colossal failure. Fascinating transcendent ideas like symmetry, congruence, dimensions and modulo primes hover like gods above the minutia. It's some of these ideas that Mr. Frenkel will introduce and that will open up a Pandora's Box of awe that will have the intelligent reader wanting more. His words to describe higher mathematics are elegance and beauty, usually associated with the arts, and once the Langlands program is introduced, it's a difficult description to deny. I would add magical or mysterious or majestic or any number of M's...The previous silly alliteration illustrates in micro form the mind boggling array of patterns that are revealed through mathematical analysis. It's a world of wonderful repetitions and shapes that reminds me of the Spyrograph toy I was fond of as a child. Edward marvels that these patterns somehow seem to exist outside of mankind and perhaps even outside the Universe itself in a Platonian Netherland. Spectacular stuff. Weaved within the narrative is Mr. Frenkel's own tale of his love for math and his struggles while growing up in the Soviet Union as recently as the 80's as a Jew. This is a remarkable story in itself which should inspire any youngsters who want to pursue difficult dreams. I highly recommend this book, not just for people with mathematical aptitude or interest, but especially for the liberal arts types out there who consider Math nothing more than a Draconian torture method for youth..

Es interesante como narra los retos, dificultadas que impone la vida, el esfuerzo que debe imprimirse para sobreponerse a ellas, y en el viaje cuenta como su pasión y el amor por las matemáticas lo guían a desarrollarse como persona y profesionista. Excelente libro, muy inspirador !!!

O livro toca em temas extrenamente complexos, o que pode desmotivar os leitores mais para o final. Contudo parece-me que é isso mesmo que se quer ser transmitido que fazer matemática é complexo e apaixonante, mesmo que não se perceba os promenores essas ideias de mais alto nível é que devem passar ao leitor.

文章だけなら、とてもやさしく書いてあります。実際、内容を理解できたかというと、あまり理解できていないと思います。結構数学の知識が必要となってきます。前置きで難しいところは飛ばして読んでもよいとあったので、一応最後まで読むことができました。また、どのような場面でラングランズ・プログラムが関わっていくのかが、よくわかりました。まだ一度しか読んでいないため、他の本と読み比べながら、また読んでみたいと思います。数学の最先端に触れられるよい本だと思います。よい頭の体操になりそうです。せっかく読み初めたので、読破したいと思います。理論がまとまったら、さらに一冊書き上げていただきたいです。そのときは、ぜひ専門的な内容の本をお願いしたいところです。この本では、著者のフレンケル教授の人となりがよく表されています。数学専門書とは言いがたい内容でした。ですので、もっとラングランズ・プログラムの内容に迫る本がほしいです。フェルマーの最終定理もこの一部だと考えると、いかに壮大なプロジェクトなのか考えも及びません。いつの日か、完成させていただきたいと思います。

This is a great book, it stimulated me to brush up on my maths. It's addictive, but to understand it I had to read every chapter multiple times and I had a few sessions on chatgpt on group theory, modular forms. In the end I am begging to really understand what modern maths is about, the grand unification seems to be a possibility. There are some great YouTube videos by the author that help a lot with some of the difficult ideas.

I'm a theoretical physicist with little exposition to the Langlands program and I felt very inspired by these ideas presented in a very simple way.