What kind of humongous tasks do supercomputers do? What type of mathematical models can be so complex that it requires a computer close to $1B?
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Mostly stuff like simulating things like nuclear explosions, climate/weather, earthquakes and other things of that nature where it would be worth a whole lot to know more about them, but simulating them in details involves a lot of computation to get close due to its chaotic nature.
You can learn more by looking at the Top 500 List of supercomputers and look at the sublist by application area.
https://www.top500.org/statistics/list/
Keep in mind though that much of what governments do with them is classified. (hint the US Department of Energy is in charge of Nukes)
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