As with many articles in science and math, the discovery isn't that "this weird thing happens", but that "hey, we can model this weird thing using this equation/model (that sometimes comes from a totally unrelated field)." Maybe in 10, 20, 50 years this discovery will become the key to understanding yet another weird thing, and so on.

"Everyone understands" that if you drop an object it falls to the ground. Yet we still don't fully understand how gravitation works.

I mean socially, do you want to go to a party and be the only person who doesn't know anyone? If you had to pick, I'd imagine you'd either want to catch up with a couple people you do know OR meet new people. The trouble gets when the crowd is a mix of old and new and people feel alienated.

These types of abstract problems often get applied to physics or various optimization problems where efficient solutions can save a ton of work or enable new techniques

there's a lot of things that feel like they should be obvious, but are almost impossible to prove mathematically. it's the difference between seeing something happens, and understanding why it happens and proving that it will always happen (or not, and why)

Probably these two paragraphs sum up the background for the problem nicely

A common analogy for Ramsey theory requires us to consider how many people to invite to a party so that at least three people will either already be acquainted with each other or at least three people will be total strangers to each other.

Here, the Ramsey number, r, is the minimum number of people needed at the party so that either s people know each other or t people don't know each other. This can be written as r(s,t), and we know the answer to r(3,3) = 6.

I was more interested in finding out about Ramsey theorem, though, rather than this new result.