[mauriciolange]

Still not a sufficient explanation but I pretty much like the headline:

Mathematicians are finding inevitable structures in sufficiently large sets of integers.

[_a_a_a_]

The word structure is commonly used but never seems to be defined.

[somrand0]

you need to study lots of higher algebra to get a sense of what they mean...

all I can tell you (because it's all I know) is that "the structure" is preserved by transformations.

and what the subject focuses on and studies is the transformations, more than 'the structures'.

so I suppose they don't precisely and explicitly know what 'the structure' is; but the incredible thing is how this does NOT matter.

as far as I've figured out so far, the point is that it gets preserved across transformations, and that they can inter-relate it across different mathematical objects.

[rightbyte]

Won't a sufficiently large set contain any pattern?

[_8j50]

Why? E.g. numbers that start with 1 are more commonly seen in random sets than other numbers. Things might repeat forever in a pattern

[brookst]

Assuming a random distribution in the set and any finite pattern, I think so?