As I was working on the new design for my blog, I kept thinking that I never really got into posting about anything related to mathematics. One problem I never got quite around was that parts of mathematics I find fascinating involve only abstract constructs and require a lot of background knowledge.
Sure, a lot of interesting stuff happens in mathematics on regular basis. But one can hardly write about breakthroughs such as Perelman’s proof of the Thurston’s Geometrization Conjecture which settles the first (and only) of the Millenium Prize Problems – The Poincaré Conjecture, when only a handful of people in the world actually understand it.
Recently I found that there is actually quite a lot of plea for help in mathematics around the web. The “problem” with sites such as Wikipedia is that they contain “too” much information about a topic but present it in as general form as possible. It is understandable that many (student) struggle with applying this general knowledge to specific problems. Dr. Math was one of the first places where you could ask a particular question and in general there were pretty good chances that your question would be answered. Sites such as Yahoo Answers, although not powered by only by mathematicians, have a similar advantage that Wikipedia used to become the online encyclopedia, i.e. the power of the web.
At Yahoo Answers, anyone can ask any question (for purpose of this post, by any question I mean “any question in mathematics”). Contributors can answer questions and rate already existing answers in a process resembling Wikipedia user moderation/editing in achieving the goal of quality. Recently, I began contributing to several areas (yes – mathematics, astronomy and computers/programming are a good guess) and found quite a few math questions interesting. Therefore I’ve decided to pick a good math problem every once and then and post a well written, rigorous solution in the math section here.