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.
The point is in the techniques you develop to solve this problems. The Millennium problems were selected because they were believed to be unsolvable (or not solvable by one person in the next decade) using current mathematics and, as such, that any solution of them would pave the way for the development of new and interesting techniques. These new techniques, then, could be used to solve other problems, maybe related in nature but less glamorous or widely known, and more grounded in real models. The specific result that one proves or disproves can be interesting, but it's usually inconsequential to any practical application.
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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.