[quickthrower2]

What level of expertise is this proof accessible to? Could a final year undergraduate understand this perhaps with a bit of help or background reading?

I am talking about reading and understanding it, not necessary validating the correctness.

[jfoutz]

Be bold!

Any paper, any field, if you can get your hands on it, Take a half an hour and read the words. Look at the pictures, Look at the graphs. Take a break. Go for a walk, maybe get some coffee, and decide if you want to continue. This will give you a very rough survey of the terrain. Often, I'll quit right here if there's nothing for me to latch on to.

Take a couple of hours, take notes about the things you don't understand - maybe take a minute here or there to look up concepts, maybe take a minute there to graph equations.

Get a good night's sleep. Look at your notes and think about all the stuff you don't understand. There are plenty of things I don't get _at all_. There are also things I can latch onto. Put some serious effort into linking the equations with the words. Decide if you want to spend days or weeks really digging in and _understanding_.

I find each step rewarding. I often quit early, and move on to the next shiny new thing. There's some real value in each step. I learn about things I never new existed. I certainly can't explain them, but sometimes things pop up again and again and I do get the motivation to take a deeper dive - not necessarily mastery, but at least an understanding of my depth of ignorance. Maybe watch a lecture on that topic for perspective.

You never know what's going to be useful. Nurture that spark of interest. You might get nothing out of it today, but 10 years from now, you'll see some other problem and vaguely recall this is kinda like that other thing I never really got. There's definitely some opportunity cost. But if you're just farting around on reddit, an hour here and there can be really enjoyable, and possibly someday useful.

[chx]

I would say yes because I am very close to understanding it :) Although I have a math teacher degree, we didn't really learn that much higher level stuff and also it's been twenty years since I touched anything like this. Notation wise I am missing A△B and not much else. For the theorems mentioned, I am reasonably sure if I worked through https://www.ihes.fr/~duminil/publi/2017percolation.pdf I would understand this paper in question.

Edit: ah! I paged through the percolation introduction and it mentions A∆B ∶= (B ∖ A) ∪ (A ∖ B) so that's the symmetric difference between A and B. And it seems the first ten pages is enough, we only need to get to the Russo theorem.

[M1rco]

I think so. To be honest not 100% sure but it seems you would need a bit probability theory + understanding what graphs/hypergraphs are. So my first impression is, it is very accessible, which I would also expect from an elegant proof...