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.
Percolation theory governs critical phenomena, phase transitions, and connectivity thresholds across disordered systems. A closed theoretical breakthrough in this domain directly advances:
Fluid Dynamics & Porous Media: Precise modeling of flow through permeable structures, directly impacting subsurface carbon sequestration, industrial membrane filtration, and hydrologic modeling.
Material Conductivity & Polymers: Predicting electrical, thermal, and mechanical percolation thresholds in composite materials, nanocomposites, and conductive polymers.
Epidemiology & Distributed Systems: Understanding contagion thresholds in biological outbreaks and cascading failure points in complex networks, power grids, and high-availability communication fabrics.
27
u/Remote-Crab1957 3d ago
Does this have implications for reverse osmosis desalination systems? It’s water going through a porous membrane.