Love and Math: The Heart of Hidden Reality

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.

Frenkel’s book deserves a much wider audience this side of the Atlantic than it currently has. I read Love and Maths alongside Hacking’s “Why is there a Philosophy of Maths at all”, and at least in the first few days, I persevered with the dual task until I eventually focused on Frenkel almost exclusively. I’ve now read the book twice and must admit to having been moved from being merely entertained to being seriously impressed. The title and the first few largely biographical chapters are, in truth, slightly misleading. Once Frenkel gets going, however, he impresses as a serious writer with no quarter given for the less than serious reader. But the “cost”, as can happen so often, is not clarity of accessibility. This last point is interesting. The way that Frenkel ensures no compromise is by providing, in the main body of the book, a fairly low lying terrain. Think of this as a strenuous but ultimately achievable trek up Kilamanjaro. Yes, you have to be able to breath the thin air, but there are no serious 5:5 stretches. You don’t need your climbing rope and crampons or ice pick. However, laced, literally page by page, are footnotes that are more like the diversion to K2. And what an amazing diversion. You can (if you want) be seriously addressed with credible mathematical discourses, and yet stay the course if you feel threatened. Its a smart way of delivering a superb read. Leaving aside this very clever mechanism, the heart of the book brings together a beautifully crafted exposition of the importance of the Langlands programme with a topical weft and weave of contemporary maths. A few months after I read the book a second time I had the chance to meet Frenkel very briefly. He is a disarming and charming man with a steely eyed determination to convey his feelings. The book is the same. Don’t be fooled by the title, and don’t give up in the foothills. The peaks are what count. You will be infected by the love of the subject that so many of us wish we could share with loads more people. I just hope the book gets more of an audience in Britain. Frenkel also wrote the obit for Grothendieck in the NY Times. Well worth the read for those who dont know a mathematician who may well deserve the title of the 20th century's greatest (and yes, I include Godel, Hilbert and Weyl et al in that comparison).

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.