[core-explorer]

We usually don't talk about "the dimensions", we talk about the general case: n-dimensional spaces (theorems covering all dimensions simultaneously) or infinite-dimensional spaces (individual spaces covering all finite-dimensional spaces).

Of course, when you try to generalize your theorems you are also interested in the cases where generalization fails. In this case, there is something that happens in a 2-dimensional space, in a 6-, 14- or 30-dimensional space. Mathematicians would say "it happens in 2, 6, 14 or 30 dimensions". I never noticed that this is jargon specific to mathematicians.

Problems in geometry tend to get (at least) exponentially harder to solve computationally as the dimensions grow, e.g. the number of vertices of the n-dimensional cube is literally the exponential of base 2. Which is why they discovered something about 126-dimensional space now, when the results for lower dimensions have been known for decades.

[Karliss]

But that's not how the article says it. It says "in dimensions 2, 6, 14, 30 and 62" instead of "in 2,6,14 or 30 dimensions". The later sounds fine, but "dimensions 8 and 24" to me sounds too much like something is happening in "8th and 24th dimension". It even uses singular "dimension 126" as if you took >=126 dimensional space, ordered the axis and something interesting happened along 126th and only that one.

[Sniffnoy]

Yeah, that's not what that means. In math "dimension" is used as a statistic. As in, "this manifold has a dimension of 4". So you can say things like "in dimension 4" to mean "when the dimension is equal to 4". We do also say "in 4 dimensions"; it just varies. The two phrases are equivalent. There is no ordering of dimensions or anything like that.