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Have a Tough Math Question?

In contrast to last week's recommended website, suppose you have a higher-level math question that you have been unable to find a reasonable response. Some options:

  • Ask a colleage (but beware....)
  • Ask a student (make sure your ego can handle reasonable responses)
  • Search the internet...but no answer may appear (yet it may lie hidden somewhere...)
New possibilities appear regularly. A good option is to submit your question to MathOverFlow.net. Advertized as "a place for mathematicians to ask and answer questions," its primary focus is at the graduate or research level. BUT...do not be intimidated...!

Its FAQ section is clear as to what the website is and isn't. It is not for homework help, though some homework-sounding questions do slip through. It is not a discussion forum, though many of the questions do lead to on-going discussions. It is not an encyclopedia, where one would be able to research for known answers to expected questions.

Again, be forewarned that many of the questions/topics are beyond the grades 9-14 levels, so you will have to have a strong interest, math knowledge base, and a willingness to invest some time reflecting about questions and answers.

Some example questions that were of interest to me:

  • It there any relation between the axiom of choice and Euclidean Geometry? I mean what are the known statements, theorems or results in euclidean geometry that are dependent on AC?
  • A proper rigid motion is a transformation of the plane that preserves distances between points and orientation. For example, any sequence of rotations and translations (of the plane) is a proper rigid motion. I am looking for a proof or a reference for the following simple claim: any proper rigid motion can be described as a single rotation or a single translation.
  • Goldbach's conjecture states that every even integer greater than 3 is the sum of two primes. I'm interested in a weaker assertion: has it been proven that every positive integer n such that 6\vert n is the sum of two primes?
  • I'm teaching a course over the summer...and I'm planning on organizing it as a math history course, hitting on major threads through about 1900, and focusing on the evolution of ideas and on people, rather than on the details of proofs. I've also been having a lot of trouble finding a good book covering this material...and so, here's my question: What would be a good textbook for a course of this nature? Specifically, for a math history course targeted at non-science majors.
  • What are some fiction books about mathematicians? It seems to me rather difficult for writers to create good books on this subject. Some years ago I thought there were no such books at all. There are many reasons: it is difficult to describe the process of discovery and describe it in the exciting way. The subject has narrow audience and not the way to make best-seller...
I admit to having never asked a question on MathOverFlow.net. Nonetheless, I occasionally visit the site to keep tabs on questions being asked. Again, most of the questions are too specific, not of personal interest, or over-my-professional-head.

Be aware that some questions are marked "closed," which may mean that they are "off topic" or too elementary. When this happens, they refer the question-asker to "lots of other math Q&A sites where [the] question might fit right in, like math.stackexchange.com, Ask Dr. Math, Art of Problem Solving, Physics Forums, or NRICH."