Has there ever been an algorithm invented that improved performance so much that existing hardware went from Unable to do the thing to Easily able to do the thing?

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@WomanCorn Gradient descent and backpropogation are good examples. Prior to them, we were just sampling vectors.

Similarly, lots of stuff in linear algebra liibraries. In particular, stuff which allows you to find things like eigendecompositions, singular values, and other features of linear maps without ever explicitly representing the matrix in its entirety. See the use-cases of Scipy's linear operator.

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