Posted in A must read, Books to read, philosophy by: admin

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07 May

TweetLast week I got ahold of the new book by Daniel Dennett - Intuition Pumps And Other Tools for Thinking. I knew of Dennett - a prolific author and a noted philosopher at Tufts University - from his earlier books, Brainstorms, The Mind's I, Consciousness Explained. I've been recently spending time in physical therapy […]

Posted in A must read, About math, Algorithms, Applications, Books to read, Graph theory, philosophy by: admin

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20 Mar

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.

Posted in A must read, About math, Books to read, philosophy by: admin

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15 Jan

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.

Posted in Homeschooling, math education, Math in literature, philosophy by: admin

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08 Jun

Although the role of serendipity is familiar, what's not so well appreciated is how different serendipity is from luck. Serendipity is not just an apparent aptitude for making fortunate discoveries accidentally, as my dictionary defines it. Serendipitous discoveries are always made by people in a particular frame of mind, people who are focused and alert because they're searching for something. They just happen to find something else.

Posted in Curiosity, Homeschooling, philosophy, Simple math, Uncategorized by: admin

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16 Mar

TweetThis is a short note for the record. I've been preparing a page on the indivisibles (not ready yet), when my eighth grader boy came up to share his solutions to a couple of olympiad problems. We talked a few minutes about the olympiad and then, sensing his mood, I decided to catch the moment […]

Posted in Calculus, philosophy, physics by: admin

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11 Sep

Tweet Author Paul H. Nahin tells in Introduction to his new book how on several occasions the Nobel Prize winner Richard Feynman spoke condescendingly of mathematics. Nahin suggests that "Mathematics is trivial, but I can't do my work without it" may have been a joke and should not be taken too seriously. He may be […]

Posted in Curiosity, philosophy by: admin

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10 Jan

TweetA recent book Loving + Hating Mathematics by Reuben Hersh and Vera John-Steiner is a collection of stories and anecdotes about mathematcis and mathematicians. The stories have a purpose - to demonstrate that mathematics is a human endeavor and that mathematicians are as human as the next man. Some stories show the emergence of the […]

Posted in philosophy, vanity by: admin

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02 Dec

TweetThis is a hard question to answer because there are many views on what mathematics is and whether it is a science at all, let alone an exact one. And, of course, there is a question of what constitutes an exact science. To compound it all, not only it is possible to question the meaning […]