In the empirical sciences, there are a number of journals that publish 'negative' results. Negative or null results occur when researchers are unable to confirm the findings obtained from earlier published reports. In the applied sciences, they may also come about when a scientist aims to to show that a particular technology (e.g., CRISPR) could alleviate a problem (e.g., a particular virus that kills that kills a specific type of plant), only to find out that it does quite the opposite (e.g. the technology led to the evolution of viruses that were more resistant to CRISPR).
In the formal sciences, including mathematics and logic, experiments like these aren't conducted*. However, it does happen that mathematicians develop machinery to tackle a particular thorny problem, only to find out it doesn't work. A good example is John R. Stallings' false proof of the Poincaré Conjecture.
Publications like these are few and far between. It seems to me that one of the reasons this is the case, is that there aren't any journals that are specifically geared to these types of papers. They are predominantly focussed on publishing articles that obtain 'positive' results, i.e. actually prove theorems or refute conjectures.
Yet it also appears to me that papers like these can be very useful to researchers in mathematics, for the following reasons:
A. They may inspire someone to slightly tweak the failed approach, in order to make it work and actually prove the theorem(s);
B. They may allow someone to see what has already been tried, and what types of avenues of research are probably not worth pursuing;
C. They may provide a platform for approaches to tackling difficult problems in mathematics, even if the methods don't work so far. Thus, they provide a place to share ideas, rather than throwing away months of work.
My question is twofold:
- Are there already any journals that are devoted to papers containing negative results in the above sense?
- Would it be worthwhile to set up such a journal, from your perspective?
(*) I am aware that experimental mathematics is a thing. The focal point of this question isn't really the experimental nature of the mathematics research, but it's about offering a venue to the failed approaches to solving problems developed through research - formal, experimental or otherwise.