meditationatae

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Nascent idea for a project

Stimulated by the work of Zeilberger and Sills on the Rademacher Conjecture, I’m now thinking of a name for a Project that would collect computations relevant to well-known problems in mathematics.

With respect to Zeilberger’s Opinion piece,  don’t fault Mathematics of Computation for rejecting the submission.  I believe Journals should set their own standards, and if some article on empirical results, it may be of interest to some in the mathematical community.  That does not mean, in my opinion, that already existing journals should change their editorial standards.

My vision is inspired by Gauss’ counting of primes, i.e. tabulations of values of the prime counting function.  I read that he would count primes in blocks of a thousand consecutive integers in (say) 15-30 minutes of spare time.

What use was this?  Upon belief (I would have to check the literature from 150 to 200 years ago), this may have provided impetus to further computations of pi(n), more attention to what was then the Prime Number Conjecture, leading to the work of Riemann on zeta and the proof of the Prime Number Theorem by Jacques Hadamard and Charles-Jean Étienne Gustave Nicolas de la Vallée Poussin in 1896.

With empirical things, taking a hint from engineering, software development and so on, what seems to matter is the process of documenting carefully what one wanted to do, how one did it, and the result or results.

Mistakes can be corrected in further releases.  For empirical computations, confidence can be gained by two people implementing the same algorithm with no collaboration.

Like other mathematical writing, one should explain where the problem originates, cite prior work, explain what methods, algorithms were used.  Ideally, also mention the software and computer used as well as the the version of the software, compiler, CAS, and operating system. Ideally, a reader could go out and buy or borrow all that’s needed and re-do the same computations on a system with the same configuration (reproducibility).

Some principles embodied in the Polymath Project might be reusable in empiral Project.

http://en.wikipedia.org/wiki/Polymath_Project

 

I don’t dare say “Empirical mathematics” because in some sense, computations about problems that only add marginally to what is known, or don’t justify rigorously all error bounds, shouldn’t be considered polished, rigorous work, which is what I most often think of as mathematics.

So, for now I’m sticking with Project … Compendium… , Potpourri …, with more reflection on a suitable name required.

I’m new to using WordPress.  For me, it serves as a logbook, aka “Captain’s Log” to jot down my thinking.  That’s how I intend to use my WordPress account for now.

If you wish to comment, please do so!

 

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Written by meditationatae

November 17, 2012 at 5:55 pm

Posted in History

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