What is the character used in letters in math mode?

Question

There are a lot of questions about the fonts used by default in latex. However I didn't manage to find exactly the font I'm looking for. Specifically, I'm looking for the font used by latex when producing something like this:

that is, the characters used in math mode.

In particular, I'm looking not much for the numbers as for the that kind of n. Using italic Latin Modern Math, which, if I understood correctly, is the default math font, I obtain the following:

which is clearly different from what latex reproduces (that is, the first image above).

What is the font that latex is using to produce characters like the n above? And where can I find it?

Answer 1

If you run the test file

\documentclass{article}
\usepackage{lmodern}
\begin{document}
\showoutput
$n=2$
\end{document}

and look in the log file, you'll find

....\mathon
....\OML/lmm/m/it/10 n
....\glue(\thickmuskip) 2.77771 plus 2.77771
....\OT1/lmr/m/n/10 =
....\penalty 500
....\glue(\thickmuskip) 2.77771 plus 2.77771
....\OT1/lmr/m/n/10 2
....\mathoff

You see that actually two different fonts are used: \OML/lmm/m/it/10 and \OT1/lmr/m/n/10. Now the problem is: what physical font is being used?

There are at least two ways for discovering it: one is to do, from the command line,

cat $(kpsewhich omllmm.fd)

that displays

% This file belongs to the Latin Modern package. The work is released
% under the GUST Font License. See the MANIFEST-Latin-Modern.txt and
% README-Latin-Modern.txt files for the details. For the most recent version of
% this license see http://www.gust.org.pl/fonts/licenses/GUST-FONT-LICENSE.txt
% or http://tug.org/fonts/licenses/GUST-FONT-LICENSE.txt

\ProvidesFile{omllmm.fd}[2009/10/30 v1.6 Font defs for Latin Modern]

\DeclareFontFamily{OML}{lmm}{\skewchar\font127 }
\DeclareFontShape{OML}{lmm}{m}{it}%
     {<-5.5>    lmmi5     <5.5-6.5> lmmi6
      <6.5-7.5> lmmi7     <7.5-8.5> lmmi8
      <8.5-9.5> lmmi9     <9.5-11>  lmmi10
      <11->   lmmi12
      }{}
\DeclareFontShape{OML}{lmm}{b}{it}{%
       <-6> lmmib5     
      <6-8> lmmib7     
      <8->  lmmib10
      }{}
\DeclareFontShape{OML}{lmm}{bx}{it}%
     {<->ssub*lmm/b/it}{}
\endinput

Looking for {OML}{m}{it} and the specification for 10pt, we find lmmi10. For the other font, we do

cat $(kpsewhich ot1lmr.fd)

and we see (showing just the relevant part)

\DeclareFontShape{OT1}{lmr}{m}{n}%
     {<-5.5>    rm-lmr5     <5.5-6.5> rm-lmr6
      <6.5-7.5> rm-lmr7     <7.5-8.5> rm-lmr8
      <8.5-9.5> rm-lmr9     <9.5-11>  rm-lmr10
      <11-15>   rm-lmr12
      <15-> rm-lmr17
      }{}

so the font is rm-lmr10.

Second way: modify the test file to be

\documentclass{article}
\usepackage{lmodern}
\begin{document}
\showoutput
$n=2$

\texttt{\fontname\csname OML/lmm/m/it/10\endcsname}

\texttt{\fontname\csname OT1/lmr/m/n/10\endcsname}
\end{document}

and the output will be

However, you may want to use the OpenType fonts. Then modify the test file again to be

\documentclass{article}
\usepackage{unicode-math}
\begin{document}
\showoutput
$n=2$
\end{document}

The log file, after running LuaLaTeX on the file, will show

....\EU2/latinmodern-math.otf(0)/m/n/10 𝑛
....\glue(\thickmuskip) 2.77771 plus 2.77771
....\EU2/latinmodern-math.otf(0)/m/n/10 =
....\penalty 500
....\glue(\thickmuskip) 2.77771 plus 2.77771
....\EU2/latinmodern-math.otf(0)/m/n/10 2
....\mathoff

So modify it again essentially as before:

\documentclass{article}
\usepackage{unicode-math}
\begin{document}
\showoutput
$n=2$

\texttt{\fontname\csname EU2/latinmodern-math.otf(0)/m/n/10\endcsname}

\end{document}

and the output will be

Now you know what font you should load in the external program.

Indeed, if I copy from the log file the 𝑛 glyph and paste in a word processing application I get

Answer 2

It seems that the default font used by latex in math mode is not latin modern, which is what I erroneously understood from, for example, this answer, but Computer Modern Serif, in Italic form (EDIT: this is not exactly true, see comments below).

This font can be downloaded on sourceforge, and produces the following output:

as well as all the other correct letters. The number can be instead reproduced with plain Latin Modern Math (downloadable for example here):

For the equal sign there is yet some other font, to me unknown, being used.