I would like to know if knowing the history(elevation, temperature, etc) of montains has any application, different from killing curiosity of scientist.
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).