You may be interested in the “logical languages”, conlangs like Lojban and Toaq.
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math as perceived by mathematicians: Formulating arguments in a non-ambiguous and universal language.
math as perceived by everybody else: Writing simple ideas in an unnecessarily complicated way.
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non ambiguous, universal I agree but not only. It has to be concise as possible.
Math is a weird science that I loved and hated at the same time.
Not at all, as long as it’s correct the length won’t matter. Perhaps being concise is recommended if you want people to enjoy reading your ideas.
In fact, I regularly find the more concise articles to be annoying, since it means you have to figure out the majority of the details yourself.
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who don’t want to communicate his ideas?
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Believe me that enough mathematicians don’t really care about communicating their ideas 
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that don’t give them reason.
I’m not talking about hidden details you have to figure out as you said. I’m talking I prefer when you can generate all the theorem of a field with 5 axioms instead of 6. I prefer a well done symbol or notation (excuse my English) or a well organized demonstration.
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Please don’t make even this thread about math, k thanx bye
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This is indeed a good goal, since it shows that the 6th axiom is unnecessary to prove the theorem. But it generally comes at the cost that the proof becomes a whole lot more complicated, sometimes by a huge amount. (There’s even a theorem by Gödel that such statements that become enormously more complicated necessarily exist, called the speed-up theorems).
It also really depends on the application. If your 6th axiom is given anyways, why not use it then? It will only become important if you want to apply the theory to contexts where the 6th axiom is not present.
As for wanting to communicate ideas: last week’s seminar we touched upon a subject that was apparently quite developed by Woodin, except that he never wrote any papers or books about it, nor did he assign any of his students to do so. Essentially there’s this theory that several results are known from, since they were communicated in a seminar, but never really worked out anywhere in the literature. It’s not just details missing, the whole ideas themselves were never properly communicated.
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Tired already? Sorry for that, but you did put yourself in it from the start.
To come back to the topic, I sincerely think that languages (not computing languages but human) are at the opposite end of maths in most aspects. Now it’s old memories and such so I would enjoy some more reading, like some epistemology of maths? Any suggestion would be greatly appreciated.
Native english, and some ASL, American sign language.
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Italian, English, Spanish and French. I understand Portuguese quite well and can say something in German and modern Greek. I studied Latin in high school but I think I have forgotten almost everything 
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Russian native, English advanced+business+scientific, Japanese upper intermediate, Italian lower intermediate (been some time, maybe lower than this), Interslavic “familiarised”.
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Not sure I’ve ever heard of Interslavic before. I see it’s an auxiliary language only about 10-15 years old, based on Old Church Slavonic and Slavic communication traditions.
What’s the speakership like?
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text that can be understood by people of different languages is nice idea, but who will learn how to write that text? So just google translate seems more practical.
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Native American English, California accent, inflection and slang
School Student Castilian Spanish (Latin American Spanish language learner. Functionally competent)
Japanese 3rd level test passer, two years in Fukuoka, married to a Nagoyan (Very fluent culturally and conversationally, literate at a grade school level for reading, writing? Why bother? No hope whatsoever as in 300 characters, plus various kana, Ka na?)
Chinese: Bing Che Ling. 
Don’t kill me.
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If you are saying math isn’t language, I’m sorry to disagree…
Interslavic heard for the first time…
(Being told by bot I can reply to several posts at once with @ symbol. fine. I will observe protocol next time…)
English and Chinese (HSK 6).
Japanese A2 in reading/listening, A1 in speaking/writing.
Mother tongue is Croatian, which means I can understand most south slavic languages, but I cannot speak them.
I also studied German, Spanish, Latin and old-Greek in high school, to no avail.
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