I’ve run across what seems like a peculiar property of a particular subset of primes; namely, those generated by Euler’s polynomial n^2 – n + 41. For each 41-cycle (barring the 1st which is 100% primes), a simple quadratic sieve identifies all composite numbers with 100% accuracy, thereby leaving only primes. Sieve quadratics in adjacent 41-cycles are related by expressions which are easily derived. I am surprised that it only takes a set of simple quadratics to produce a perfect prime number generator which works forever. Do you have any insight here? Should I publish? ]]>

I’m a Chinese sophister majoring in finance.There being extensive applications of analysis in equlibrium theory and others, I started to learn it and choose the translation of your masterpiece. But there exists an problem:Lack of correspondent answers,I’m not sure whether my proof was acceptable or not after I finished some of the exercises in the book.So would you please tell me how to get complete answers of this book?Thanks a lot for your help.

Bill ]]>

Mathematics education in US middle and high-school, albeit generally acceptable, is literally in the 1900’s level in several key areas (even for AP courses). For example, Gibbs vector analysis (not even useful for Physics in three-dimensions), complex numbers, and linear algebra.

I wonder what your thoughts or plans might be on this topic. I can volunteer to help, and would love to also have your participation in some of our “experiments” in La Jolla / San Diego.

As a physicist, I see that not only the exponential increase in scientific knowledge but also the increasing jargon (err, language specialization) in physics and mathematics has driven this situation — i.e, keeping modern knowledge insulated — to an extreme lag of more than two centuries. Only the humanities might be further behind in US middle and high-schools (e.g., look at the essay level we see there).

Thank you for your blog and space for mathematical science as well as gifted-child education.

]]>I have written a book on problem solving using puzzles and games. Would you know or recommend anyone to proof the book?

Someone with basic math skills and an eye for detail would be desirable.

Please view the samples, and you are welcome to comment of forward the link.

http://ashley.mypressonline.com/puzzles-games.html

Have a nice day.

]]>You can also look at articles on popularisation on my web site. At Bangor we have run Masterclasses for selected 13 year olds and covered a variety of topics: spherical geometry, higher dimensions, knots. See also my presentation “Out of Line”.

Hope that helps.

]]>I am a high school mathematics teacher in Australia, but have been recently working with an 8 year-old boy who is having mathematical discussions with me that go well beyond the Australian National Senior Curriculum.

I am in the process of trying to provide him with opportunities to be challenged in his mathematics (Senior Level) while still provide social and emotional connection with his peers. Do you have any advice or programs or resources that would be useful in ascertaining what the capabilities of this young boy are? His interests are so far beyond his age that I am sure there gaps in his understanding of mathematics if it were to be taught in a linear, scaffolded manner. I want to provide a focus and purpose to his mathematical studies, including filling in the gaps, without tempering his natural curiosity and interest to push the boundaries of what he is capable of understanding.

Any advice would be much appreciated.

Regards, Luke

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