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I'm pretty sure this applies to most typesetting languages for math. When entering a formula, do you insert a hard space between symbols? For example, if I have 'a' for acceleration and 't' for time, would I typeset like this:$$d=\frac{1}{2}at^2$$and let the typesetting language figure it out, or do I explicitly set them apart:$$d=\frac{1}{2}\space a\space t^2$$because $at$ could either be the product of $a$ and $t$, or a new variable called $at$, and the space removes the ambiguity.

Quark Soup
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    Let the typesetter figure it out. If you want $at$ as a new variable you will confuse your reader. – Ethan Bolker Oct 29 '21 at 21:44
  • It depends. Sometimes, I want a space, and sometimes I don't. After composing, I read what I have written and ask myself which typesetting makes the concept more clear. Sometimes the inserted hard space is best, and sometimes it isn't. As you proofread, you have to pretend that this material is brand new to you. Also, if the problem involves undergraduate math, then I pretend that the reader is a senior in high school, and try to compose so that it is impossible for the 17 year old to be in any way confused. – user2661923 Oct 29 '21 at 21:54
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    Traditionally variables in mathematics are denoted by single letters, with subscripts or superscripts or other kinds of decoration to allow more variety. Longer identifiers (which are usually not variables) like $\sin$ and $\exp$ are written using a distinctive font. The layout of your formula with extra spaces looks quite wrong. – Rob Arthan Oct 29 '21 at 21:54
  • @RobArthan Generally I agree with you, with one caveat. To me, the issue isn't whether it looks wrong to the experienced reader but rather whether it is crystal clear to the 17 year old. – user2661923 Oct 29 '21 at 21:56
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    @RobArthan - I'm sure you're right about tradition, but for people like me that learned math on Mathematica, seeing a variable called 'at' uses the same neurons that identify a variable called 'a'. The distinction is artificial for me. My mind tends to parse computer languages and math formulas in the same way now. Not disagreeing, just asking if tradition is changing yet. – Quark Soup Oct 29 '21 at 21:58
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    @user2661923: I take your point, but the 17 year old who is going on to make or use mathematics needs to learn how to read the literature. To the OP: I take your point too. In fact, I have worked for many years with computational logic systems of many kinds that adopt the conventions of programming languages for variable names (and typically don't allow juxtaposition $ab$ as a short-hand for an operation $a \times b$). Does $a,t$ mean $a \times t$ in Mathematica? I would have expected it to mean $a(t)$ (function application). Your question is a very nuanced one. – Rob Arthan Oct 29 '21 at 22:09
  • @RobArthan Most of the college math books that I have been exposed to have whole sections that are confusing (i.e. poorly written). So, the 17 year old will be forced to grapple with literature soon enough. An exception might be if the 17 year old has arrhythmia, since then, the shock of crystal clear writing could be dangerous. – user2661923 Oct 29 '21 at 22:14
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    Note that TeX automatically removes normal spaces between variable names that you put in your code. If you want a space to appear, you have to use something more explicit like ˋ,or~`. Most mathematicians simply do what TeX does by default. (Also, most of TeX’s defaults are based on conventions that existed in professional mathematical typesetting before its advent. I believe this is one of them.) – Eike Schulte Oct 30 '21 at 12:57

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