@barbarabeeton I consider you as an expert in all this, but a text written almost exclusively without italics is cumbersome to read and expensive to understand

@yo' -- consider napier -- after all, it's got a good math connection, with logarithms. and it's not flashy.

@egreg I starred this comment because it is true..

@barbarabeeton looks nice

@manooooh -- yes. i already addressed that -- a mathematician is expected to define the notation used, and then be consistent. different mathematicians have different ideas about what to use even in similar circumstances, and as long as their exposition is satisfactory, ...

@barbarabeeton I will read that Guide -- I love talking about notations!

@barbarabeeton I do not understand. If a mathematician has his own style, why write a guide on recommended styles?

@egreg -- there's also no distinction when a manuscript was prepared on an ordinary typewriter, which is why so much that was published on the cheap in the 1960s is so unattractive, and sometimes subject to ambiguityl

It would be against their will

@manooooh -- the guide is actually for copyeditors, not directly for authors of mathematical papers and books (although they might benefit from it).

@barbarabeeton for whom do the editors write?

@manooooh they check it when in doubt about how something shall be done

@barbarabeeton if it is for a general public then that general public will not be interested in the notation used; and if it is for a mathematical audience then there will be discrepancies between the notation used by the editors and the one used by mathematicians

@manooooh -- copyeditors or the members of the editorial board of a journal?

@yo' @barbarabeeton it is a fact that I speak without knowing, since I do not participate in meetings of mathematicians or meetings of editors. Sorry

@manooooh -- the "professional" editors (the ones who are responsible for determining whether a particular submission will or will not be published) will (at least are supposed to) judge a submission on the merit of its content. copyeditors will adhere closely to a publisher's style guide, which does allow for personal expression, as long as notation is consistent and all the commas are in the right place.

@barbarabeeton I am an engineering student with the desire to look like a mathematician. With this in mind, what do you recommend, \mathrm d or d?

@manooooh -- as an engineering stident, i would look for a reputable journal that covers the subject matter you are writing about, and follow their lead. (it may be that an upright d is appropriate in this situation, but if you are writing about an abstract mathematical topic, then the italic form would be more appropriate. my opinion. i should check some of my old engineering textbooks to see what was done there, but they are currently being used as "bricks" for the supports of bookshelves.)

@barbarabeeton I know we have different opinions on that. This is a paper by a fields medalist from Princeton. If you look at equation (2.5) of his paper, you will see an upright differential d. Like this gentleman, many have very good reasons to prefer upright d's.

@barbarabeeton thanks for your opinion, it is very important for me. Unfortunately, I do not know Argentine engineers who write articles related to mathematics -- and the ones that exist, they are liar. What is written about mathematics in engineering does not go beyond the notation of a guide to mathematical exercises, or books written by Argentine engineers, which are also liars

@marmot -- i will try to check this out from home later this evening. right now it's time to go find something to eat.

@marmot This is physics.

@barbarabeeton ^^^ enjoy your meal

@marmot LOL is @egreg the meal?

@egreg And the fields medal? Also physics?

@marmot Coauthors? Note that the differential is at the beginning, contrary to what mathematicians do: only physicists are so perversed.

@egreg And how about the excellent IOP or Cambrigde mathematics books?

@egreg I thought that, too. But if you look closely you will see that there is no variable that depends on x, so they are a constant and can be written outside the integral (in particular, it can be on the right)

@marmot What do you expect from Britons?

@manooooh “dx” is the name of a linear form, precisely the linear form corresponding to the first coordinate in the dual basis.

@egreg Good point. I also agree with you on the integral notation. But definitely not on the differential d's Too often d denotes, say, a distance, and my eyes bleed if someone writes \frac{dd}{dt}.

@manooooh And the functions depend on x; physicists usually don't write the variable.

@egreg Well well well. "Usually" is an overstatement, but "often" is (unfortunately) true.

@egreg I do not know what are you talking about, but I trust you. I thought d^4x was referring to "The fourth derivative with respect of the variable x"

@egreg I did not know it, but it seems that @marmot is (almost) in agreement with you

@marmot And didn't you notice that the paper uses both indentation and paragraph skip?

@manooooh No, the integral is a four-dimensional one, with the functions depending on four variables, collectively denoted by x. So d^4x actually means dx_1 dx_2 dx_3 dx_4

These are details. Imagine you had a car without wheels. Would you complain about the color? I'd rather have a car with wheels but wrong color.

@egreg ^^^^^ (I'm sitting in a talk with terrible slides.)

@marmot I think @egreg is right... please chek out this paper, p. 9, "2.2 Potential Theory"; the differential is "dt"...

@manooooh I can assure you that what the authors of this paper does not define the best conventions.

@marmot do not pay attention to the other convention notations, but pay attention to that integral notation (and the others integral). I think that article is a math article, and they write the differential with non-upright ds. It is just an example

@barbarabeeton if you have to write "Example:" in italics, would you include ":" into the italics?

Or for example "Theorem." or "Definition:", etc.