A lot of my work is based on quantum mechanics, which can be described either using operator algebra (you can think of them as infinitely large matrices) or functional integrals (basically infinite-dimensional integrals), and we often need to use both because they both have some advantages. However, we cannot really do many concrete calculations with these, so the trick is to turn the problem into something that we can handle, which usually means (partial) differential equations. If you are really lucky you may be able to solve the differential equation with pen and paper, but usually you have to do it with a computer, and because these are big calculations, I use a supercomputer for that.
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