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This isn't a good analogy, because if you have a human brain then you already understand all the concepts that Japanese is used to represent (except maybe some

by injb 5y ago

This isn't a good analogy, because if you have a human brain then you already understand all the concepts that Japanese is used to represent (except maybe some cultural things that are hard to translate). In contrast, the language of mathematical notation is used for expressing concepts that are utterly unfamiliar and unintuitive. As a language, mathematical notation is nowhere near the complexity of a full human language, or even a programming language. It's much simpler than that. But the concepts behind it don't come naturally and have to be studied carefully.

samatman 5y ago
While this is true, it doesn't help that postwar mathematics seems to have run out of useful names for things. Understanding what an algebraic group "really is" (with variations and extensions e.g. Lie groups) is more than one lifetime's work, but if you know what "group" means in English, well, you won't be disappointed. "Ring", even "field" kind of work this way. If I ever really develop an intuition for what a magma is, and I doubt it, this will not resemble the molten core of the earth. Or will it?
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