Love and math. The heart of hidden reality (Q2842523)

The editor's note printed on the dust jacket of the book says that the book ``tells intertwined stories: of the wonders of mathematics and of young man's journey learning and living it''. If somebody asked about a description of this book formulated in one sentence, this would be perfect.NEWLINENEWLINEOn the one hand, the book is the autobiography of Edward Frenkel and is concentrated mainly in the early years of his life. The author writes about his growing interest in mathematics, his mathematical education, the studies in the Soviet Union (in the Institute of Oil and Gas known also under the nickname Kerosinka), his first encounters with advanced mathematics, the first research, the participation in Gelfand's seminar, obtaining the fellowship in the United States at the Harvard University, the decision of his staying in the USA for good, his work in the States, the special meeting in Princeton and the film ``Rites of love and math'' he was engaged in. He writes about his contacts and collaboration with many eminent mathematicians, including his teachers. The personalities of many of those mathematicians are also described. Among others, we read about Evgeny Evgenievich Petrov, Dmitry Borisovich Fuchs, Boris Feigin, Israel Moiseevich Gelfand, Yakov Isaevich Khurgin, Victor Kac, Vladimir Drinfeld, Edward Witten. The author writes a lot about living conditions in the former Soviet Union, the oppressive regime in this country and his serious problems caused by the discrimination against the Jews in Soviet universities. It is described why and how he was not allowed to study at MGU (Moscow State University) although he passed perfectly extremely difficult entrance exam. There are also described troubles which the scientists in the Soviet Union had with publishing mathematical results. As a kind of comparison, we read about his impressions after coming to the United States.NEWLINENEWLINEOn the other hand, the book is not only the autobiography of Frenkel. It presents much more than the description of his life and people he met and worked with. The book presents also a lot of mathematics in a popular way. Mathematics is developed it the book parallely with the description of the author's life. The author presents mathematical objects and ideas simultaneously when he writes about the events of his life. There is described his mathematical interest, the topics he worked on. The goal is to come to the famous and ambitious Langlands Program. Landlands Program is by many mathematicians regarded as ``the grand unified theory of mathematics'' and is the theory which connects in an amazing way many different areas of mathematics. Its background is symmetry, given by Galois theory. The author writes about symmetry, groups, representations of groups, braid groups, Galois groups, Fermat's Last Theorem, modular forms, Shimura-Taniyama conjecture, Riemann surfaces, complex numbers, Lie groups, Lie algebras, the group \(\mathrm{SO}(3)\), Kac-Moody algebras, sheaves, some Grothendieck's ideas, differential equations, quantum field theory, Hitchin moduli spaces, sigma models, branes (the listed terms appear in the book approximately in the order presented above). Of course, the author writes much more. Finally, he shows the analogies between some objects in three different areas: the first is number theory, curves and finite fields, the second is Riemann surfaces and the third is quantum physics. The author describes also some important results obtained by Anton Kapustin in collaboration with Edward Witten and the research he made himself together with Witten.NEWLINENEWLINEThe book consists of the introduction, a special guide for the reader, 18 chapters, epilogue, glossary of terms, index. It contains also 202 notes that give extra information concerning several details of the material presented in ``Love and math''.NEWLINENEWLINEIn the introduction the author writes: ``My dream is that all of us will be able to see, appreciate, and marvel at the magic beauty and exquisite harmony of these ideas, formulas and equations, for this will give so much more meaning to our love for this world and for each other.''