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Is massively collaborative mathematics possible in forums?

mathbalarka

Well-known member
MHB Math Helper
Mar 22, 2013
573
The title is essentially dual to the one in blogposts of Nielson and Gowers, from which Polymath wiki developed. The subject is the same here, although different in the sense that whether or not that is possible in forums.

A member of this forum have tried to start a polymath project here on MHB. I won't deny that I felt similar way for many problems I have, perhaps a few of mine are already getting collaborated efforts in MMF, but the issues must be taken account to before stepping out in something that much big.

The whole point of this project is to get collaborative efforts on a certain problem, so definitely two different kinds of problems occur.

The statement of the problem

Massive collaborative mathematics is applicable to problems that are superiorly tough and only several tactical attacks may be sufficient to do this. Such problems are not in lack, but many of them are beyond the forum effort (I'll come to this later). What is needed here is some reasonable problem that might be tackled by some forum members. For example, RH must not be a subject to F-Polymath (Forum Polymath, I will abbreviate it like this afterwards).

Also, a subject might be a subject of collaboration if and only if there is an angle of approach available, otherwise there is no point. For example, if one can find a way to attack the Collatz conjecture, and believes there is a possible way to attack it further, then it is worthwhile to be a subject of massive F-collaboration.

Different peoples, different subject

This almost definitely the most painful part of starting a collaborative project on forums. Not everyone works on a particular field on every mathematics forum -- so the it must be heavily researched whether or not the statement of the problem can be attacked by -most- members of a forum, otherwise the forum collaboration is bound to get unsuccessful.

It is interesting to note that how this point is shown to be a positive side in Gower's blogpost, whereas here it is a negative point.

Above all, I think the main question, quoted from Gower, is

"Why would anyone agree to share their ideas?"

Right. Why would anyone agree to share there ideas when they might think that he could use this idea later and might be able to prove the whole problem, without collaborative effort. This is what happens to usual forum problems. People just don't share ideas and think "what's the big deal? What would come out of this stupid collaborative effort?"

Again from Gowers, I'd like to suggest that the ideal outcome would be a solution of the problem with no single individual having to think all that hard. The hard thought would be done by a sort of super-mathematician whose brain is distributed amongst bits of the brains of lots of interlinked people. So try to resist the temptation to go away and think about something and come back with carefully polished thoughts: just give quick reactions to what you read and hope that the conversation will develop in good directions.

Nevertheless, I think we need to discuss a few things before jumping on to a F-Polymath project here or in any forum. I would like to start a active discussion on these and if possible, would try to post a few polymath projects (I think we should also denote the polymath projects as 1, 2, 1a, etc for future reference). If we are successful, who knows? Perhaps we may have a MHB Polymath forum, or a MHB Polymath wiki where massively collaborative mathematics on several topics might be possible?

Balarka
.
 

mathbalarka

Well-known member
MHB Math Helper
Mar 22, 2013
573
Let's see, I will give a few pointers here on caffeinmachine's project here.

Perhaps the author is getting too excited about it. As for me, I'd think of discussing this first. Remember that Polymath project began at the hand of Gower and Nielson's blog posts!

I am not sure what king of problem caffeinmachine posted there, being an analytic number theorist, I have no idea about any problem related to Euclidean geometry. I believe this is still unsolved?

I don't see caffeinmachine gave a good introduction to the posting rules there, except the link to Polymath rules. I'd think it would be convenient to treat the thread as a collection of results and post another thread that concerns about the discussion. This is a matter of collaborative effort, so I believe any idea from any member, even in a very obscure form would be taken to account, if stayed on-topic.

I don't like to discourage people on doing these, but maybe we have to discuss before stepping on anything. I, too, am very excited that some people here are interested but the question is "how many?". Nevertheless, I believe caffeinmachine won't definitely mind and would do his (her? Nah. I don't think so...) best here.

PS : Uh, I am not anyone to say, but it seems I have a little bit experience on these things. Nevermind.
 

caffeinemachine

Well-known member
MHB Math Scholar
Mar 10, 2012
834
The title is essentially dual to the one in blogposts of Nielson and Gowers, from which Polymath wiki developed. The subject is the same here, although different in the sense that whether or not that is possible in forums.

A member of this forum have tried to start a polymath project here on MHB. I won't deny that I felt similar way for many problems I have, perhaps a few of mine are already getting collaborated efforts in MMF, but the issues must be taken account to before stepping out in something that much big.

The whole point of this project is to get collaborative efforts on a certain problem, so definitely two different kinds of problems occur.

The statement of the problem

Massive collaborative mathematics is applicable to problems that are superiorly tough and only several tactical attacks may be sufficient to do this. Such problems are not in lack, but many of them are beyond the forum effort (I'll come to this later). What is needed here is some reasonable problem that might be tackled by some forum members. For example, RH must not be a subject to F-Polymath (Forum Polymath, I will abbreviate it like this afterwards).

Also, a subject might be a subject of collaboration if and only if there is an angle of approach available, otherwise there is no point. For example, if one can find a way to attack the Collatz conjecture, and believes there is a possible way to attack it further, then it is worthwhile to be a subject of massive F-collaboration.

Different peoples, different subject

This almost definitely the most painful part of starting a collaborative project on forums. Not everyone works on a particular field on every mathematics forum -- so the it must be heavily researched whether or not the statement of the problem can be attacked by -most- members of a forum, otherwise the forum collaboration is bound to get unsuccessful.

It is interesting to note that how this point is shown to be a positive side in Gower's blogpost, whereas here it is a negative point.

Above all, I think the main question, quoted from Gower, is

"Why would anyone agree to share their ideas?"

Right. Why would anyone agree to share there ideas when they might think that he could use this idea later and might be able to prove the whole problem, without collaborative effort. This is what happens to usual forum problems. People just don't share ideas and think "what's the big deal? What would come out of this stupid collaborative effort?"

Again from Gowers, I'd like to suggest that the ideal outcome would be a solution of the problem with no single individual having to think all that hard. The hard thought would be done by a sort of super-mathematician whose brain is distributed amongst bits of the brains of lots of interlinked people. So try to resist the temptation to go away and think about something and come back with carefully polished thoughts: just give quick reactions to what you read and hope that the conversation will develop in good directions.

Nevertheless, I think we need to discuss a few things before jumping on to a F-Polymath project here or in any forum. I would like to start a active discussion on these and if possible, would try to post a few polymath projects (I think we should also denote the polymath projects as 1, 2, 1a, etc for future reference). If we are successful, who knows? Perhaps we may have a MHB Polymath forum, or a MHB Polymath wiki where massively collaborative mathematics on several topics might be possible?

Balarka
.
Hello mathbalarka.

You have raised several important questions in your post.

I don't know myself if a F-Polymath can be a success.
But there is no harm in trying.

You might say 'wait.. what about the possibility of ideas getting plagiarized?'.
I agree. That may happen. But the problem I have posted is not something which earns anyone a prize of any kind for solving it. It is a problem which has been solved long ago. In fact, this way of putting it is giving an idea that it was an open problem at some point. I don't think it was. I was reading a paper on 'Tensegrity Structures' where the authors had used the result without giving the proof or reference to where a proof can be found. They just stated it and used it. And I was able to prove the result with some effort. I chose this problem for precisely this reason. I think it is a hard problem and at the same time not a problem which is going to earn anyone any fame in solving it.

My idea of MHB-Polymath (not necessarily F-Polymath) is members collaborating in solving a much-harder-than-usually-posted-on-the-challenge-subforum problem but not at all an open problem or an insanely hard problem.
 

Bacterius

Well-known member
MHB Math Helper
Jan 26, 2012
644
In my mind caffeinemachine's thread is more about pure collaboration and fun rather than actual producing something of value. It's not like it is an open problem, since caffeinemachine solved it on his own.

As for the kind of problem, well, you can't please everyone, really. Not everyone is going to be into Euclidean geometry, and not everyone is going to be into number theory. Perhaps this is an occasion to broaden one's horizons, or, failing that, maybe multiple polymath projects on different fields could coexist on the forum (though if there are too many it might overload some people or get difficult to follow in general).
 

mathbalarka

Well-known member
MHB Math Helper
Mar 22, 2013
573
Hmm, well, my idea of collaborative mathematics is different. I have ran a few massively collaborative projects with some number theorists on MMF and they have been a success (leading to a paper, etc). To my understanding, polymath projects needn't necessarily be labeled "collaborative mathematics", so except that, my topics really have been a Polymath project.

caffeinmachine said:
My idea of MHB-Polymath (not necessarily F-Polymath) is members collaborating in solving a much-harder-than-usually-posted-on-the-challenge-subforum problem but not at all an open problem or an insanely hard problem.
I don't see the difference with a challenge competition then. Perhaps a more broad and collaborative one, but essentially a challenge.

Maybe I am thinking differently because mine have never been a challenge, more of a tightening of a bunch of results together. Currently on-research, though, see this.