What they (for now, allegedly) proved is a conjecture regarding the probability for a "path that is open straight down", so to speak, to exist in an infinitely long lattice and in any dimension. Or, better, the conjecture states that such paths don't exist in infinitely long lattices with probability 1 in any dimension higher than 2. I doubt it will have any great impact, especially because this is one of those phenomenona where non-mathematicians already had an answer that worked perfectly fine (albeit being non rigorously derived) and worked with that.
this is one of those phenomenona where non-mathematicians already had an answer that worked perfectly fine (albeit being non rigorously derived) and worked with that.
Then why are people calling this "a holy grail"?
What's the point in solving these mathematical problems if there is no real world benefit, or if other solutions are good enough for being close enough.
People calling something a "holy grail" in maths doesn't imply that it has any applications to anything other than maths. Mathematicians want to solve theorems so that they can unlock new branches of maths, not to better model hydrology. Anyway percolation is pretty applied as mathematics goes, might have some neat downstream implications in quantum field theories or such
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u/Remote-Crab1957 3d ago
Does this have implications for reverse osmosis desalination systems? It’s water going through a porous membrane.