Oversimplifying maths and thinking of it as a bunch of equations (which a lot of lay people do) leads to the analogy that it's like a foreign language, in that there is new notation, vocabulary, and "grammar" rules (mathematical operations). This is probably because maths is encountered at a young age, and may be the first time the student is aware they're learning domain-specific vocabulary, so it feels foreign.
Students are often unaware that they should be expressing mathematics in sentences using words, leading them to exclusively use mathematics terminology and notation in their assignments, etc. In reality, good mathematics communication requires constructing sentences and thus language skills, but usually in one's native language. Also, mathematical vocabulary is added to one's native vocabulary, unlike for a foreign language where it replaces your native vocabulary.
In any case, here's my feedback on this analogy (I have a PhD in maths, and I've been actively studying Chinese for years):
Learning X and learning Y will have "learning" in common for any X and Y.
After a certain level, the learning process will always involve learning domain-specific vocabulary and notation, learning how to correctly communicate domain-specific ideas, and learning the key domain-specific concepts and how to apply them. Thus, you could replace "foreign language" and "math" in the analogy with anything, say "Minecraft" and "ancient Roman history", and come up with comparable analogies. The question is: are these analogies useful?
Learning mathematical vocabulary is different to learning foreign vocabulary.
Like a foreign language, math has unfamiliar vocabulary words or terms, which must be put in sentences called expressions or equations.
Learning maths as e.g. a native-English speaker requires learning maths-specific vocabulary ("exponent", "Pythagoras", "cosine"), which is used within English sentences. However, learning e.g. Chinese as a native-English speaker is not merely a matter of introducing a selection of Chinese words into English sentences, you need to produce wholly new sentences, and you learn words which you already know in English (三 "three", 姐妹 "sister", and 蓝色 "blue").
Mathematics is not just equations.
Thinking of maths as a bunch of equations is an oversimplification (you can't just ignore theorem proving; mathematical modelling; etc.). Mathematics is expressed using natural language; writing sentences purely using mathematical notation is advised against in mathematical-writing style guides:
One of the misconceptions students have about writing mathematics (which probably arises from their writing habits in secondary school) is that the writing should be composed mostly of equations and mathematical symbols. This is not true at all. By contrast, a piece of mathematical writing should contain mostly words, supplemented by equations and mathematical symbols. Take any mathematics textbook to verify this. Even in their worked examples, the solutions contain mostly words.
Guide to Writing Mathematics (pdf)
If anything is to be learned here, it's that expressing mathematics requires strong language communication skills, which is often overlooked by mathematics students who often just list out equations. Students (most likely) need to improve their mathematics communication skills in their native language and/or English, not necessarily a foreign language.
Is maths taught in foreign-language courses?
Currently, most universities consider computer and statistics (a form of math) courses as foreign language courses. Some universities have now gone so far as to actually classify math as foreign language.
When I read this, I was perplexed why someone with a PhD would write this? It's just not true. I've been to many universities---I'm not aware of a single example of this. It's illogical: mathematics students and mathematicians will not think to apply to foreign-language departments, and foreign-language students will not want to take mathematics courses.
I looked up the universities listed on his webpage thinking maybe his experience was unusual, but the USF Department of World Languages and the FGCU Department of Language & Literature webpage show no sign of anything related to computers, statistics, or mathematics.
The only conceivable scenario in which I feel this is plausible, is for a small university which does not have enough manpower, and merges otherwise-unrelated disciplines to reduce bookkeeping.
Suppose you and your teacher magically become expert mathematicians, mathematics educators, and mathematics communicators: how does that help you learn Dutch?
Being good at maths tends to help you think logically and break down problems into their essential components and identify key details. Sometimes this confuses people into thinking that some random discipline and mathematics are directly related, whereas mathematics is just how the universe works and is intrinsically related to everything.
Moreover, people who are good at mathematics have the discipline to put in (or the habit of putting in) long hours of study, and so they tend to be people who enjoy spending large amounts of time learning things. Thus, being good at maths often implies having strong general-learning skills, which can be applied to learning a foreign language, as well as learning any other topic.
