The Hahn-Banach Theorem. The Sylow Theorems. Many, many others. These are some of the most important results in their respective fields.
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Replying to @EmilyGorcenski
Hahn-Banach in particular lets us construct linear functionals on a vector subspace from practically nothing! This is huge!
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Replying to @EmilyGorcenski
But I digress. The point is, important results in math often come from taking a powerful idea and pulling it back onto specific constructs.
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Replying to @EmilyGorcenski
Math is not always about "abstract abstract abstract". What that leads to is Category Theory. And oh boy, does FP love it some Cat. Theory.
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Replying to @EmilyGorcenski
But Category Theory is like actually really hard to understand and is so general that it's hard to wrangle it into constructive results.
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Replying to @EmilyGorcenski
Often times, what you have to do is find patterns that work, then pull them back onto more specific spaces to establish results.
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Replying to @EmilyGorcenski
Programming needs to do that, too. But often times all that work really just leads us back to where we started anyways.
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Replying to @EmilyGorcenski
Or we find that we do a whole lot of abstraction work to get not a whole lot that's new. No new problems get solved that weren't solvable b4
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Replying to @EmilyGorcenski
This isn't an invective against FP. OO iss just as bad at this. Enterprise Java is notorious for abstraction upon abstraction.
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Replying to @EmilyGorcenski
This is more a call to like, think about abstraction and use it when it makes sense, but also to remember the problem you're addressing.
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Because that problem usually has to do with people. And people can't be abstracted away so easily.
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