Thanks for your comment. Different people have different reading preferences, and your reading preference is probably shared by many. However, from what I’ve read of most blogs, TV documentaries and online magazines, intra-article linking is a fairly common practice and is generally considered a good idea, particularly when the links are used to corroborate facts stated in the article/blog post and when they are too numerous to be put in a bibliography. Also, when attacking other people’s opinions, it makes sense to link up to them.

This is really a style issue. The difference of opinion stems partly because of our different perceptions of the utility of blog posts: I think of it as both a vehicle for expressing opinion and as a place to make readers aware of the various other sources and viewpoints on the matter, and for you, it is more of the former and less of the latter.

In blog posts where I am more interested in waxing eloquent about my personal opinion (as in some of the TBC blog posts), I try to provide fewer external links.

It is getting too non-user-friendly. I mean the excessive web-linking that you do from your blog post is highly detrimental to smooth reading by the reader. The huge number of web-links make reading it a highly bumpy journey.

And many of the weblinks like the one that link to amazon price-lists are completely unnecessary. These are are sources that a reasonable reader can locate easily if he/she cares and most probably the reader reads with a certain amount of belief in the author.

Too much of hyper-linking make the author look very defensive and as if trying to clutch on to every possible straw floating on the web to support his/her point. You look weak when you put so much of hyperlinks.

Further this makes it hard for me to decipher in the articles as to what is your opinion and which one is other’s opinion you are quoting.

Kindly try to make this distinction very clear in your article. In general when I am reading someone’s blog I am more interested to know what is the author’s opinion rather than what every other guy on the street seems to say.

You can probably try adopting the format of research papers of putting all references (here the web-links) at the end of the article as a list and use reference numbers inside if possible.

thank you

@Ernie: You’re right — I know that in these kind of problems, even a slight improvement over the best bound is usually considered worthwhile, so I agree with you that if such a breakthrough is achieved, that would constitute success. Even if it takes several more months to achieve the breakthrough, that would still be pretty impressive and provide strong indications that the polymath strategy may be a replicable strategy for producing original research. Unfortunately, this isn’t my area of mathematical expertise, so looking at the comments, I cannot judge for myself how likely it is that the goals you state will be achieved.

1. With DHJ (Polymath 1), there was already one proof known, and then the problem was whether one could produce a combinatorial proof as well. Knowing that a problem already has a solution helps to guide the development of other approaches (e.g. combinatorial); and it also has the psychological effect of making one think it is doable, and therefore one is not as willing to give up so easily.

2. With Polymath 4 we have had *much* fewer contributors. Perhaps this is a matter of taste — people who regularly contribute to polymath projects tend to be more focused on combinatorics and computational complexity; yet Polymath 4 is more a problem in computational number theory, which tends to use ideas of a different flavor.

3. There doesn’t seem to be as many avenues from which to attack Polymath 4 as there are other problems. Many analytic approaches to the problem, for example, can be boiled down to certain problems about bounds on something called “Dirichlet polynomials”, and it is known to be a hard general problem to beat something called the “square-root barrier” for such approaches. Though, I do think that we have a viable approach for doing this by computing certain generating functions in (which is not what one would call an `analytic method’ — it is more algebraic… it has been the subject of the last tens of posts to Polymath 4).

Also note that Polymath 4 is not over yet! I think there is a very good chance of producing an algorithm to find primes of size (i.e. bits) in time better than (bit operations), perhaps assuming some “reasonable” conjectures in linear algebra. While this may not seem like much, if it could be achieved, it would beat “Odlyzko’s algorithm”, the current record-holder. I would consider that a “success” for Polymath 4, and a good place for the project to stop.

It should be interesting to see how this all plays out, for the mathematician community versus the programmer community and the parenting community.