Comments on: General discussion

By: Mgccl

Mgccl — Tue, 03 Aug 2010 16:11:11 +0000

I’m interested in the platform for polymath. Clearly wordpress + wiki is not the desired model.

Are there any discussions of list of features one want from the platform?

Is it also possible to get financial support from any institution to develop such platform?

By: porton

porton — Mon, 18 Jan 2010 23:09:37 +0000

I solved a problem which earlier proposed for one of polymath projects.

The problem was at
http://portonmath.wordpress.com/2009/11/29/co-separability/

How to exclude the problem from the list of polymath proposals?

By: porton

porton — Sat, 07 Nov 2009 21:17:23 +0000

Dear Gowers,

I updated http://portonmath.wordpress.com/2009/11/02/exposition-complementive-filters/
adding there two new formulas as conjectures in the “Intersection with a set” subsection.

It is all I know about the “complementive filters are complete lattice” conjecture. I think this may be a starting point for other mathematicians who may be interested (personally I deem this an interesting problem).

I think that is does not extensively tells about “coinciding quasidifference and second quasidifference” is not a big defect, as it is an other problem and it may be not discussed here. Wiki reference where they may look for greater details on the full current state of that problem is available in this my exposition.

I ask you to publicize this my conjecture to be known for wider cycles of mathematicians. My blog visits are pretty low but this conjecture deserves wider attention.

By: porton

porton — Sun, 01 Nov 2009 22:45:26 +0000

Dear Gowers,

I wrote a longer exposition about “complementive filters are a complete lattice” problem:

http://portonmath.wordpress.com/2009/11/02/exposition-complementive-filters/

I’m not sure whether it is in the state ready to be publicized. You may read it in order to test whether this my writing is understandable.

Also it contains a very short reference to the problem about coinciding quasidifference and second quasidifference. Should I write a longer explanation about that problem to attract more people? Or it is OK to just mention this problem because it is not the problem we are solving now?

Please say how well I wrote this and publicize if it is OK.

By: porton

porton — Sat, 31 Oct 2009 19:50:02 +0000

Oh, well. I already solved this “little problem”. Sorry for my comment in haste that it was unsolved.

The solution:
http://portonmath.wordpress.com/2009/10/31/principal-filters-are-center-solved/

To write a longer explanation of the “complementive filters are a complete lattice” conjecture remains my priority:

http://portonmath.wordpress.com/2009/08/30/proposal-conjecture-complementive-filters/

By: porton

porton — Sat, 31 Oct 2009 16:44:36 +0000

Trying to write an exposition on the “complementive filters are a complete lattice” problem, I was going to write a proof of its certain special case. Trying to write this I noticed that I stumble over an open problem even in this special seemingly simple case.

This is the problem over which I stumbled:

http://portonmath.wordpress.com/2009/10/31/are-principal-filters-the-center-of-the-lattice-of-filters/

So I will attempt to settle this littler problem before going to the exposition of the original problem:

http://portonmath.wordpress.com/2009/08/30/proposal-conjecture-complementive-filters/

If the little problem over which I stumbled appears to be difficult also, I may offer it for a separate polymath project.

By: Scott Morrison

Scott Morrison — Thu, 29 Oct 2009 23:37:45 +0000

Hehe… from http://math.ucr.edu/home/baez/crackpot.html:
21. 20 points for suggesting that you deserve a Nobel prize.
I suppose the Abel prize will do, too.

By: porton

porton — Thu, 29 Oct 2009 19:37:08 +0000

Dear Gowers, I’m now busy. (I work as a programmer.) When I will have free time I will write a longer explanation about “complementive filters are a complete lattice” problem

http://portonmath.wordpress.com/2009/08/30/proposal-conjecture-complementive-filters/

I’ve chosen it from the three problems because:
1) I feel it more important than two other problems, and there are other important problems to prove which it may be used (if true).
2) I can think more about possible ways to attack this problem than the two other.

By: gowers

gowers — Thu, 29 Oct 2009 14:21:36 +0000

I might add that it’s not really up to Terry and me to select a project. If you want to start a project then you can. As the other replies above make clear, the main necessary condition for it to be successful is that you should attract the interest of other mathematicians. I think the best way of doing that is to give a more detailed post in which you say exactly what the project would be and what you don’t know how to do at the moment. If you have thought hard about the problems already, then you should be able to write an account that takes the reader to the point where you don’t know how to continue. Often a precisely posed problem that “ought to be doable” is exactly the hook that is needed for another mathematician to be interested. Have you got some of those?

If you do produce a detailed post, I will be happy to publicize it on my blog, and also on this blog.

By: porton

porton — Thu, 29 Oct 2009 12:26:34 +0000

I never suggested to write an expository book on lattices.

Among my suggestions there are a half expository half research book on filters on posets and generalizations thereof:
http://portonmath.wordpress.com/2009/08/29/polymath-filters-on-posets/

(Certainly it is related with lattices but isn’t an “expository book on lattices”.)

I’m not sure whether my theory of filters in interesting for general mathematical audience. (The theory of filters is mainly a technical not beautiful theory, however there I introduce some concepts which count to be beautiful, e.g. my theory of filtrators and related “core parts” and “dual core parts” is a beautiful part of the theory.) However the theory of filters is important for my further research “Algebraic General Topology”:
http://www.mathematics21.org/algebraic-general-topology.html

“Algebraic General Topology” is certainly a beautiful and interesting theory and I even hope to receive Abel Prize for that:
http://www.mathematics21.org/abel-prize.html