> The main characteristic of the language of mathematics is perhaps that different members of the community can completely agree about the meaning of each word

> The main characteristic of the language of mathematics is perhaps that different members of the community can completely agree about the meaning of each word and sentence. Haha, this got a laugh out of me :). While this is true in principle, the reality can be quite messy! For instance, there seems to be little consensus about what the words "vector", "contravariant", "covariant", and "coordinate" should mean on the Wikipedia page [1] claiming to explain just that! [1] https://en.wikipedia.org/wiki/Talk:Covariance_and_contravariance_of_vectors https://en.wikipedia.org/wiki/Talk:Covariance_and_contravari...