I would like to know if knowing the history(elevation, temperature, etc) of montains has any application, different from killing curiosity of scientist.
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Compared to some other fields in geology, this one actually has immediate practical implications.
By "knowing the history of mountains", you can learn a lot about processes that involve erosion, weathering, seismicity, etc. This is important for risk management and mitigation. Landslides and rockfalls are a significant risk in some countries. There are many ways of studying these processes, one of them being the interpretation of past events: their causes and effects. This is also true for earthquakes (which as you know, move mountains up and down).
