Why do math journals' aim and scope provide so little information?

Question

When one encounters a journal one does not know, one way to obtain some information about it is via the journal's "aim and scope" in the journal web site.

However, I noticed that for many journals, this section provides virtually no information about the journal.

Here are two examples that I think demonstrate my question.

Inventiones mathematicae - this is clearly one of the best mathematical journals, generally considered one as the top 3 (or 5) journals. Yet, nothing about its level is mentioned in its aim and scope. Instead, it says:

This journal is published at frequent intervals to bring out new contributions to mathematics. It is a policy of the journal to publish papers within four months of acceptance. Once a paper is accepted it goes immediately into production and no changes can be made by the author(s).

Mathematische Zeitschrift - while clearly not a top level journal, it is still considered a good general journal. Its short aim and scope contains a bit of history about the previous editors, and then says

"Mathematische Zeitschrift" is devoted to pure and applied mathematics. Reviews, problems etc. will not be published.

In both cases, there is not even a hint about the level that the journal aims at.

My question is — why do journals make the choice of providing so little information about the type of papers they wish to publish?

Answer 1

No information is probably better than misleading information. Any journal can talk about accepting "outstanding contributions", or whatever, on their homepage, without actually having high standards in practice. If you want to know how good a journal is, their aims and scope is not a good place to look. Either go to some independent source (e.g. Scimago journal rankings) or (more work, but perhaps more reliable) have a look at what they've been publishing and try to get a feel for how strong it is.

Most mathematics journals, however, will be specific about which areas of mathematics can be published, or at least, as specific as they need to be. A journal that specialises in a particular field will usually say exactly what parts of that field they like (and don't like). Here's a random example:

The research areas covered by Discrete Mathematics include graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, discrete probability, and parts of cryptography.
Discrete Mathematics generally does not include research on dynamical systems, differential equations, or discrete Laplacian operators within its scope. It also does not publish articles that are principally focused on linear algebra, abstract algebraic structures, or fuzzy sets unless they are highly related to one of the main areas of interest. Also, papers focused primarily on applied problems or experimental results fall outside our scope.

The journals you mention simply don't need to say anything about areas, since no area of mathematics is off-topic for them. If the paper is of sufficiently high quality, they will publish it. However, it's worth bearing in mind that some journals which do in principle publish in all areas still have preferences making the bar higher in some areas than others. A good way to gauge this is to search for papers published in that journal on mathscinet in, say, the last ten years, and see what proportion of them have the relevant primary classification (this breakdown is available with the search results). For example the figures for Inventiones are:

Algebraic geometry (126)
Dynamical systems and ergodic theory (89)
Differential geometry (75)
Number theory (70)
Partial differential equations (45)
Group theory and generalizations (41)
Several complex variables and analytic spaces (38)
Manifolds and cell complexes (31)
Topological groups, Lie groups (22)
Probability theory and stochastic processes (20)
Global analysis, analysis on manifolds (19)
Functional analysis (14)
Commutative rings and algebras (11)
Functions of a complex variable (11)
Nonassociative rings and algebras (10)
Statistical mechanics, structure of matter (9)
Algebraic topology (8)
Quantum theory (8)
Associative rings and algebras (7)
K-theory (7)
Fourier analysis (7)
Combinatorics (6)
Convex and discrete geometry (6)
Mechanics of particles and systems (6)
Operator theory (5)
Relativity and gravitational theory (4)
Mathematical logic and foundations (3)
Measure and integration (3)
Fluid mechanics (3)
Field theory and polynomials (2)
Category theory; homological algebra (2)
Special functions (2)
Ordinary differential equations (2)
Systems theory; control (2)
History and biography (1)
Linear and multilinear algebra; matrix theory (1)
Real functions (1)
Potential theory (1)
Approximations and expansions (1)
Abstract harmonic analysis (1)
Calculus of variations and optimal control; optimization (1)
General topology (1)
Statistics (1)
Astronomy and astrophysics (1)
Information and communication, circuits (1)

Answer 2

It's not just mathematical journals: most journals do not specify a "level of significance" or degree of selectivity that they intend to operate at.

To understand why, consider the question from the editor's point of view. At every decent journal, every manuscript starts with editorial review to determine whether it is worth the time of reviewers. Journals, like everything else on the internet, are under constant siege by a wave of incoming junk. In the case of journals, this wave is made of people required to publish for their jobs but who don't care, people doing bad science who don't realize it, scammers who want to claim their work is science, people pushing personal or political agendas, cranks and crazies, etc.

All editors thus have to make decisions about whether a manuscript is likely to be "significant" enough for their journal or not, and even "lower level" respectable journals are much more selective than you may realize. But that decision is inherently subjective and not subject to quantification. Consider: how would you meaningfully declare in your scope that "this is a mid-ranked journal that is sort of selective, not as much as the top ones but more so than these other journals."?

In practice, the de facto selectivity is just a dynamically determined product of:

• How many papers they are willing to publish per month, versus
• How large is the community that wishes to publish in the journal (combination of scope and reputation)

and an editor makes decisions according to their best understanding of that relationship.

For a megajournal like PLOS ONE, both numbers are high. For a "prestige" journal, the papers per month is low and the community is large. For a niche community journal, both numbers are low. And for a scam journal, the first is higher than the second.