CTK Insights

Archive for the 'About math' Category

17 Oct

Elementary Problems that Beg for Generalization

TweetIn a well known puzzle, a father willed to his three sons camels, with the proviso that of the inheritance should go to the oldest among them, with being due to the middle one and to the youngest. Shortly after the father's death, a wise man riding on his camel through the village noticed the […]

30 Aug

Math Associations on a Field Trip

I am just back from a wonderful 10 day trip to the central Alaska. It was cloudy and rainy for the first two days; low clouds common to Alaska were covering mountain peaks and even tree tops. But then the skies have cleared, the visibility was perfect, and the imagery of mountain ridges and jagged portions of glaciers easily evoked the idea of fractals. On a flight from Anchorage to Coldfoot it was fascinating to observe that many clouds had perfectly smooth flat bottoms that at a distance projected into straight lines.

06 Jul

Weather Forecasting: A Story of Mathematical Triumph

But naturally, mathematics was not evolving all by itself. The authors excel in presenting establishment of the science of meteorology as a human endeavor. The history of meteorology is rich in perseverance, sacrifice, enthusiasm, ingenuity, useful missteps, multinational collaboration ... and plain hard work. Authors' fluent recount makes the story all the more fascinating, even if math applications are only at the back of your mind. The book is a superior read.

05 Jun

Naming Infinity - the book

This is an unusual book that eludes categorization. It's an outline of fundamental mathematical ideas cultivated by human beings, of mathematics as a human endeavor in the most candid sense of the word. It's a collection of biographical sketches - and not only of mathematicians - on a historic background, spread from the Dreyfus affair in France, and over the failed Russian revolution of 1905, the WWI, the October revolution, the Stalinists purges, the WWII, and post-Stalinist experimentations.

The book is a tangle of documented evidence and, likely, anecdotal testimony. It's warm, humane and makes an absorbing reading

20 Mar

The Golden Ticket: P, NP, and the Search for the Impossible

The only known serious approach to the N versus NP problem today is due to Ketan Mulmuley from t he University of Chicago. He has shown that solving some difficult problems in a mathematical field called algebraic geometry (considerably more complex than high school algebra and geometry) may lead to a proof that N ≠ NP. But resolving these algebraic geometry problems may require mathematical techniques far beyond what we have available today.

15 Jan

Henri Poincaré: A Scientific Biography

Other chapters are organized topically, not chronologically. Each illuminates in depth one or other of Poincaré's works but all are set in context both historical and temathic such that each can serve as an introduction into the many subjects to which Poincaré made a contribution. Much of the book is a descriptive narrative, but the author never shies from displaying equations (even PDE and integral ones) when this is essential for the subject. I do not know whether this style has caused a price reduction, but for a book of this size, depth, and breadth, $33.10 (the amazon.com price) is an exceptional bargain.

14 Jan

Inspiration, Perspiration and Satisfaction

Still, there is great satisfaction in having solved a problem - even a simple one, and extra satisfaction in being able to appreciate an elegant proof; this kind of satisfaction is multiplied manifold after you devised a solution on your own. Yes, it all may start with inspiration, but to keep the flame burning involves hard work. The upside is that eventually it all comes together when, with evolving habit of solving problems, one begins to realize how right is the paraphrase of the well known statement by Thomas A. Edison: Solving problems is one percent inspiration and ninety-nine percent perspiration. The more you sweat the greater is the satisfaction.

20 Dec

The Forgotten Art of Spherical Trigonomtery

Now, do you really care how much mathematics went into building bridges, refrigerators, airplanes, or gasoline refinery? Mathematics is being used in every conceivable piece of technology, every branch of science, while some of it even proves useful to practically everyone in everyday life. So, my question is, Is it truly necessary to burden the students with a study of the subject which most of them won't be using in their work on the pretext of its extremely universal usefulness? I believe that past and present educational reforms keep beating a dead horse.

23 Oct

The Best Writing on Mathematics

If we learn to say things simply and build up slowly from the concrete to the abstract, we may be able to build many bridges among our various specialties. For me, this style will always be The Best Writing on Mathematics, and this book is full of excellent examples of it.

22 Oct

A Property of the Power of 5

My late father was an inveterate human calculator. During the 1930s at the height of the New Economic Policy (NEP) that allowed a degree of post-revolution entrepreneurship in the Soviet Union, he made a living by giving on-stage mental math performances. He became an electrical engineer when the NEP was curtailed.

Browsing through his notes I have recently come across an observation concerning the fifth powers of integers and its relevance to the absence of integer solutions of x^5 + y^5 = z^5 - Fermat's equation for n=5.

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