I have been working for four years on modeling systems by transforming system logic dependency using stereographic projection. My goal was to simulate the creation/annihilation process.

I found consistently some patterns similar to Lie groups. From system’s perspective, these groups controls and balances the system evolution process. For example representing Fibonacci sequence as a system uses primes to create the sequence; the groups balancing the process are: Cyclic, Solvable and another group X.

I am not sure of its type, but this action resembles Euler Totient function.

My background is engineering and I am looking for help to further investigate these patterns. I would appreciate any guidance.

]]>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.

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