Looking at this lovely blog which collects books published by the venerable Mir publishers, I cannot help but recall the happy happy days spent browsing books at Moore market in the Chennai Central Railway station. My train from Mangalore would come sometime in the evening and I would spend a couple of hours happily browsing these books. Any teenager madly in love with math and physics would instantly fall in love with the beautiful Mir books published in the Soviet Union. They were like a cross between Schaums outlines and the magnum opus written by the fields’ experts in that they were extremely practical, teaching you how to solve problems while at the same time they somehow managed to convey the beauty and feeling associated with the subject, not to mention that they sometimes had the dry, spare style reminiscent of Rudin’s analysis books, they never contained the colorful terminology of the standard American textbook like the sandwich theorem etc. No glossy paper, no distracting color photographs. Science at its pure best. Of course they were all extremely affordable, one could actually, in those days, get a Mir book for a prize of a good meal in a restaurant and spend many pleasurable hours poring and wondering. Happy memories.
David Mumford has a beautiful blog post about the ideals and integrity of the mathematical publishers, the husband and wife team of Alice and Klaus Peters.
Vladimir Arnold once famously said that every mathematics advisor gives his or her student a gift, which the student appreciates at the right time. Maybe life itself is like this. Every moment, happy or difficult, comes encoded with a gift, which is somehow our duty to decode.
An interesting new book. Looking forward to reading some of these essays. I have really admired the essays of people like Freeman Dyson and Yuri Manin, not only displaying enormous erudition in math and science, but also a tremendous breadth of knowledge and a range of feeling and understanding in subjects like art, literature, culture and the like, and how all of these things fit together in a humanist sort of way.
From the blurb:
Why are mathematicians drawn to art? How do they perceive it? What motivates them to pursue excellence in music or painting? Do they view their art as a conveyance for their mathematics or an escape from it? What are the similarities between mathematical talent and creativity and their artistic equivalents? What are the differences? Can a theatrical play or a visual image capture the beauty and excitement of mathematics? Some of the world’s top mathematicians are also accomplished artists: musicians, photographers, painters, dancers, writers, filmmakers. In this volume, they share some of their work and reflect on the roles that mathematics and art have played in their lives. They write about creativity, communication, making connections, negotiating successes and failures, and navigating the vastly different professional worlds of art and mathematics.
Gian-Carlo Rota is a writer of such crystal clear and beautiful prose, conveying the essence in an unconvoluted and direct manner. If your interests lie in the intersection of mathematics, science and technology and well written prose, I warmly recommend the book.
Israel Gelfand famously chided his students to declare that they didn’t study differential geometry or representation theory etc but that they studied mathematics. I was witness to the unity of mathematics in a rather stunning way. Working with the linearized Euler equations of hydrodynamics on the two dimensional torus, if one studies the spectrum of the linearization about a steady state, one is naturally led into counting problems associated with the integer lattice, stuff that shows up in number theory. To see this connection, between problems in the stability theory of fluid dynamics on the one hand and counting problems and number theory on the other hand, is startling to say the least, at least to the mathematically naive person such as me. At a deeper level, one is led then to wonder at such things as the Platonic nature of mathematical reality.
A few years ago, I saw this quote on somebody’s website:
When I grow up I will do hard mathematics ruthlessly
I was wowed. I somehow wanted to be like this guy. I suppose some people never grow up 😦
When one is struggling with mathematics, it is sometimes nice to know that even winners of the Chern medal, sometimes have difficulty following mathematics. From this beautiful interview of Nirenberg,
comes this gem from Peter Lax:
When Peter Lax and I were students, he always knew more mathematics than I did and that continued thru-ought our lives. And very often he would explain something to me and sometimes I would forget and ask him to repeat and once he said, ” You know, I am happy to explain things to you several times, not more than 10 times. “
From the Wikipedia page on Isaak Yaglom:
the breadth of his interests was truly extraordinary: he was seriously interested in history and philosophy, passionately loved and had a good knowledge of literature and art, often came forward with reports and lectures on the most diverse topics (for example, on Blok, Akhmatova, and the Dutch painter Escher), actively took part in the work of the cinema club in Yaroslavl and the music club at the House of Composers in Moscow, and was a continual participant of conferences on mathematical linguistics and on semiotics
From this interview of John Baez:
Learn a lot. Try to understand how the whole universe works, from the philosophical, logical, mathematical and physical aspects to chemistry, biology, and the sciences based on those, to the historical sciences such as cosmology, paleontology, archaeology and history, to the social sciences such as psychology, sociology, anthropology, politics and economics, to the aspects that are captured best in literature, art and music.
It’s a never-ending quest, and obviously it pays to specialize and become more of an expert on a few things – but the more angles you can take on any subject, the more likely you are to stumble on good questions or good answers to existing questions. Also, when you get stuck on a problem, or get tired, it can be really re-energizing to learn new things.
Problems in nature and technology, as we know well, do not come neatly packaged into “quantum, statistical, classical and continuum,…” any more than they come packaged into “biological, chemical, physical, mechanical, electrical, … ” categories. It is us humans who incapable as we are of comprehending the larger whole who break up the questions into bite sized pieces … but rarely are able to put back the pieces into a whole.
I was inspired by the Indian science magazine, Resonance, to further deepen my interest in math and physics. It is such a beautiful science journal for under graduate students. This month’s issue,
contains a beautiful tribute to one of the best loved mathematicians of the 20th century, George Polya