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> It's virtually impossible to predict which mathematical tools will be "practical" or "useful" in the future

On a long enough timeline, you're right! But if we limit ourselves to, say, the next 5,000 years, it gets a lot easier to accomplish. ;)




How does limiting the timeline to 5,000 years enhance our ability to predict the future?


The more you limit your timeline, the easier is is to predict the future. That's why we only have 10-day weather forecasts.


Good point, maybe a better way of phrasing it would have been "It's virtually impossible to predict which tools will _not_ be useful" :)

Fast Fourier transforms, complex numbers, complexity classes, etc. are clearly useful. It's much harder to rigorously claim that a result will _never_ be practical or useful.

Just to be clear, I think it's fair to say that a result isn't _immediately_ useful. But who can say whether or not it will have a more practical application down the road? Only time will tell.




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