Years ago I had the pleasure of witnessing Simon Thomas giving a wonderful talk about Martin's conjecture, which I just now fondly remembered reading this question. Even though I am not well-versed in all (or even many) fields of mathematics I find it quite curious that it was the only time I ever heard about two contradictory "official" conjectures. In chit-chat I definitely heard colleagues expressing different sentiments about which way a certain problem might finally be resolved but my guess is that they usually would not have been eager to put it in writing, possibly not even be happy to "go on the record". Also, the problem in question may have been a quite specific one relevant only to a small number of people...

So...my question is: What are other example pairs(triples?) of that kind you are aware of? They ideally shout have appeared in writing but I guess that I would be satisfied with conjectures which are ascribed to people by a nontrivial part of the (respective) mathematical (sub)community.

Years ago I had the pleasure of witnessing Simon Thomas giving a wonderful talk about Martin's conjecture, which I just now fondly remembered reading this question. Even though I am not well-versed in all (or even many) fields of mathematics I find it quite curious that it was the only time I ever heard about two contradictory "official" conjectures. In chit-chat I definitely heard colleagues expressing different sentiments about which way a certain problem might finally be resolved but my guess is that they usually would not have been eager to put it in writing, possibly not even be happy to "go on the record". Also, the problem in question may have been a quite specific one relevant only to a small number of people...

So...my question is: What are other example pairs(triples?) of that kind you are aware of? They ideally should have appeared in writing but I guess that I would be satisfied with conjectures which are ascribed to people by a nontrivial part of the (respective) mathematical (sub)community.

Years ago I had the pleasure of witnessing Simon Thomas giving a wonderful talk about Martin's conjecture, which I just now fondly remembered reading this question. Even though I am not well-versed in all (or even many) fields of mathematics I find it quite curious that it was the only time I ever heard about two contradictory "official" conjectures. In chit-chat I definitely heard colleagues expressing different sentiments about which way a certain problem might finally be resolved but my guess is that they usually would not have been eager to put it in writing, possibly not even be happy to "go on the record". Also, the problem in question may have been a quite specific one relevant only to a small number of people...

So...my question is: What are other examples pairs(triples?) of that kind you are aware of? They ideally shout have appeared in writing but I guess that I would be satisfied with conjectures which are ascribed to people by a nontrivial part of the (respective) mathematical (sub)community.

Years ago I had the pleasure of witnessing Simon Thomas giving a wonderful talk about Martin's conjecture, which I just now fondly remembered reading this question. Even though I am not well-versed in all (or even many) fields of mathematics I find it quite curious that it was the only time I ever heard about two contradictory "official" conjectures. In chit-chat I definitely heard colleagues expressing different sentiments about which way a certain problem might finally be resolved but my guess is that they usually would not have been eager to put it in writing, possibly not even be happy to "go on the record". Also, the problem in question may have been a quite specific one relevant only to a small number of people...

So...my question is: What are other example pairs(triples?) of that kind you are aware of? They ideally shout have appeared in writing but I guess that I would be satisfied with conjectures which are ascribed to people by a nontrivial part of the (respective) mathematical (sub)community.