Human languages, mathematical language, and programming languages

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Human languages are notoriously messy and historical. Although logic is not absent from human languages, they were not designed per a logical schema.

Programming languages are often the product of one or two minds, proceeding according to a single conception of how a "language" should work. They typically exhibit a high degree of consistency.

The "language" of mathematics is an in-between venture. Although it is typically more consistent and logical than a natural language, it does have lots of historical cruft built up.

We programmers sometimes get frustrated with mathematical notation for this reason. (E.g, "Why doesn't that have parentheses also?" or "Why should the power be there in one equation, but in a different place in another one?")


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