Math terminology: What are rules regarding hyphens? (Nonzero vs. nonzero)
Solution 1
Since many (or a nonnegligible amount) of authors just do not care, I guess it's up to personal preference. However, there is a semantic code, like pointed out here. Thereafter, the prefix non is not hyphenated. And I really think this should be consistent. I had nonzero, nonempty and nonholonomic occuring in my thesis and it was "corrected" by different supervisors into different versions, mostly where nonholonomic was hyphenated and the rest not. I really think this is bad practice, since consistency is lost by this "to highlight" mentality. If on tries to highlight something, why not explain it and treat it consistently in semantics.
To underline my point consider using $X$ for vectors in one direction. For some other vector, to hightlight that it's not in this direction you use $\alpha$. But why not $Y$ with an explanation?! Therefore, semantics is consistent and the highlights are where they belong, in the "comments".
What got me to enforce this was that every title I cited contained the nonhyphenated versions of all those words. Thus, (from a far too small sample, but of good works) I conclude that this is common practice in this field (between robotics and automation).
Oxford Dictionary also advises to use hyphens for prefixes, which lead to vowel collisions, like preadvised, although nothing further is stated there.
Solution 2
Donald Knuth says we should drop the hyphens.
Here is the link to his post in which he says so:
https://cs.stanford.edu/~knuth/email.html
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Xoque55
Updated on August 01, 2022Comments

Xoque55 over 1 year
This question is geared toward clarifying terminology in writing math.
Which terms are correct and why?
 A set $E$ is nonempty.
 A set $E$ is nonempty.
 The number $x$ is nonnegative.
 The number $x$ is nonnegative.
 The number $y$ is nonpositive.
 The number $y$ is nonpositive.
 The number $z$ is nonzero.
 The number $z$ is nonzero.
As a personal preference, I like the way nonzero looks but I prefer to use nonempty so I don't know what the consistency with hyphens is when prefixing "non". I also like the way nonnegative reads but I feel like nonpositive looks better than without a hyphen. I don't have any rhyme or reason why I have these preferences and that's why I'm curious to learn if there is a correct version of each term listed above.

Fizz almost 9 yearsThis would be more suitable on english.stackexchange.com as the wordformation rules probably don't have much to do with actual math.

Git Gud almost 9 yearsI'd be surprised if the technicality of the terms is relevant to answer this question. Have you tried asking at English Language S.E. or English Language Learners S.E.?

Xoque55 almost 9 years@RespawnedFluff I considered that SE but I figured that mathematicians would have more familiarity seeing these terms and have a better sense of which one is more common or be able to give reasons why they prefer/avoid hyphens.

achille hui almost 9 yearsI'll just do whatever that pleases the spell checker I'm using and concentrate on the real math. Only when it get to the point to get something published, you ask your secretary or English major friend for proof reading.

Fizz almost 9 yearsMaybe someone can actually provide info if the major math publishing houses, like AMS, Springer etc., have any rules or preferences expressed in some style document of theirs.

Brian M. Scott almost 9 yearsBoth are generally accepted. I much prefer and always use the hyphenated versions.

bof over 7 yearsI use hyphens before capital letters, so "nonAbelian" instead of "nonAbelian".

Admin over 7 yearsRelevant question on the English SE: Hyphens after the prefixes “non” and “anti” in mathematics

GEdgar over 7 yearsOnce long ago, an AMS journal corrected "nonnegtive" to "nonnegative" in a paper of mine, so I have used it (and similar spellings) ever since.

Calmarius about 4 yearsMy spellchecker underlines nonzero and suggests fixing it to nonzero.

john c. j. over 3 yearsThis link says it is better to write "nonempty", no hyphen or space: groups.google.com/forum/#!topic/misc.education.language.english/…

Fizz almost 9 yearsIf I search in Google Books "nonnegative" vs. "nonnegative" they're about tied, and the top hits are all math books for both searches.

bof over 7 yearsWhat does "nonnegatable" mean?

mike over 7 yearsI was stuck between languages and just wrote some mixture, what I meant was nonnegligible.

T. Eskin about 7 yearsPositive and nonnegative are not the same though, as 'nonnegative' implies zero or positive, while 'positive' only implies positive.

Antonio Hernandez Maquivar about 7 yearsI did not know this. I have always taken zero to be a positive whole even number.

Roberto Rastapopoulos over 4 years@AntonioHernandezMaquivar This is just a convention. In French positive also includes zero, and I suppose the same holds for Spanish?

Antonio Hernandez Maquivar over 4 years@RobertoRastapopoulos I was taught that in school, yes. Is there a sound mathematical reason why $0$ would not be a positive number ?