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They are different enough that it's frankly a bit difficult to make sense of that question. I think in general, when asking "what is the difference between X an
by tprice7 7y ago
They are different enough that it's frankly a bit difficult to make sense of that question. I think in general, when asking "what is the difference between X and Y" questions, it helps if you elaborate a bit on why you think X and Y are similar / difficult to distinguish. That gives the person who answers the question a bit of a starting point: they can talk how the similarities you perceive might not be the whole story, or might be illusory (and you might end up answering your own question while clarifying your thoughts on the matter). Otherwise it might not be clear how to even begin answering the question.
- tprice7 7y agoReflecting on this more, my best guess is that you think they are similar because they are both a "grand unified theory of mathematics". To explain the difference extremely briefly then, I'd say it's a massive exaggeration to call either category theory or the Langlands program a "grand unified theory of mathematics." They each demonstrate connections between some areas of mathematics, but they are different connections, and fall very short of unifying everything. If you want to know more, I think you'd be better off learning more about category theory and the Langlands program independently of each other rather than looking for a comparison between them.