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Comment by whatevertrevor

14 days ago

Textbooks aren't just communicating theorems and proofs (which are often just written in formal symbolic language), but also the language required to teach these concepts, why these are important, how these could be used and sometimes even the story behind the discovery of fields.

So this is far from an accurate comparison.

> Textbooks aren't just communicating theorems and proofs

Not even maths papers, which are vehicle for theorem's and proofs, are purely symbolic language and equations. Natural language prose is included when appropriate.

Theorems and proofs are almost never written in formal symbolic language.

  • My experience in reading computer science papers is almost exactly the opposite of yours: theorems are almost always written in formal symbolic language. Proofs vary more, from brief prose sketching a simple proof to critical components of proofs given symbolically with prose tying it together.

    (Uncommonly, some papers - mostly those related to type theory - go so far as to reference hundreds of lines of machine verified symbolic proofs.)

    • Common expressions such as f = O(n) are not formal at all -- the "=" symbol does not represent equality, and the "n" symbol does not represent a number.