I stumbled upon this quote by W. H. Auden (from *A Certain World: A Commonplace Book*, 1970).

Of course, the natural sciences are just as “humane” as letters. There are, however, two languages, the spoken verbal language of literature, and the written sign language of mathematics, which is the language of science. This puts the scientist at a great advantage, for, since like all of us, he has learned to read and write, he can understand a poem or a novel, whereas there are very few men of letters who can understand a scientific paper once they come to the mathematical parts.

When I was a boy, we were taught the literary languages, like Latin and Greek, extremely well, but mathematics atrociously badly. Beginning with the multiplication table, we learned a series of operations by rote which, if remembered correctly, gave the “right” answer, but about any basic principles, like the concept of number, we were told nothing. Typical of the teaching methods then in vogue is this mnemonic which I had to learn.

Minus times Minus equals Plus:

The reason for this we need not discuss.

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While it’s true that humanities scholars cannot understand mathematical research, but then neither can many mathematical researchers comprehend humanities scholarship (what the latter lacks in Greek symbols it makes up in abstruse literary theories). Just as many mathematician enjoy reading novels without bothering about literary analysis, similarly many English professors are happy to access their bank accounts with a few mouse clicks without bothering about cyclic groups.

I agree! It seems to me that people in the humanities think that anyone can understand what they write and people in the sciences believe that no one can understand what they write. As you point out, every field (or academic division) has its own theories, techniques, and language. It is often difficult to communicate about deep scholarly issues across the curriculum.

Closely related to this (and relevant to me, since I have to teach a first year seminar next fall), people in the humanities think that anyone can teach a college writing class and lead an academic discussion. These two things don’t come up very often in a math class. I can and do teach how to write mathematics, but not necessarily how to research and write an argumentative essay. And I can lead an interactive mathematics class, but that’s different from leading a discussion about a piece of literature.

To wihch we might add:

A plus times a minus is a minus

Although this rhymn is not as fine as

the original one

Sorry mis-type in that last post *rhyme