Conjecture: Mathematical English (ME) and the symbolic language of math (SL) are two distinct languages, not dialects of the same language.

I have asserted this in several places (Handbook, abstractmath.org) but I am not a linguist and it could be that linguists would disagree with this conjecture, or that the study of a mathematical corpus would reveal that another theoretical take on the situation would be more appropriate.

Some relevant points are listed below. I intend to expand on them in later posts.

1) Is ME a dialect of English or a register of English? Or does it have some other relationship to English?

2) ME appears to have several dialects or registers. One register is that used for what mathematicians call “formal proofs”. These are not formal in the sense of first order predicate logic, but their language is constrained, with the intent of making it easier to see the logical structure of the argument. Another register is that of “intuitive [or informal] explanations”. This is more like standard English.

3) The SL is clearly not a spoken language. It is a two-dimensional written language using symbols from English and other languages and some symbols native only to math. People do try to speak formulas aloud occasionally but this is well known to be difficult and can be done successfully only for fairly simple expressions.

4) There are other non-spoken languages such as ASL for example. I don’t know whether there are other non-spoken languages that are written. I don’t think dead languages count.

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