mjhjmtu

Why is underbrace (and similar commands) in the form

underbracemy formula_some text under my formula

?

Shouldn't a standard macro be in the form

underbrace[some text under my formula]my formula

since the text to put under is optional?

Why is it treated like a math operator?

documentclassarticle
usepackageamsmath
begindocument
[
underbracea+b=c
]
[
underbracea+b=c_textsomething
]
[
lim_xto a x= a
]
enddocument

The underbrace macro is exactly the same in LaTeX as in plain: it's one of those things which came with the original 'load on top of plain' approach, well before latex.ltx. Moreover, the _ 'argument' isn't an argument at all, it's a TeX core subscript. It looks like an argument, but the construction uses low-level TeX math mode primitives.

Re-implemented today, one would likely set up such that the alignment is done without the primitives, and thus the text part would be an argument. But that's a completely different question!

When you look at the definition of underbrace (or overbrace) you'll see the following:

> underbrace=macro:
#1->mathop vtop m@th ialign ##crcr $hfil displaystyle #1hfil $crcr
noalign kern 3p@ nointerlineskip upbracefill crcr noalign kern 3p@ 
limits .

It shows that the first (and only) argument to underbrace is set as a math operator and closes with limits. And, math operators have their limits (superscripts and subscripts) set on top/below it. It's therefore no surprise that you can do:

$underbraceabcd_dcba underbraceabcd^dcba$

It's treated like a math operator because that's the primitive way of stacking elements below/above something so that it doesn't displace the someting vertically.

I think it's much easier to iterate with the underscore syntax. For example

documentclassarticle
usepackageamsmath
begindocument
beginequation*
 underbraceleft(frac12+frac13right)_
 >underbracefrac14+frac14_
 underbrace2cdot frac14_
 frac12
 
 
 
 quad + quad
 underbraceleft(frac14+frac15+frac16+frac17right)_
 >underbracefrac18+frac18+frac18+frac18_
 underbrace4cdot frac18_
 frac12
 
 
 
 quad > quad frac12+frac12
endequation*

enddocument

Try to do the same with the "option" syntax. The point is that with the "underscore" syntax, you write the code for the iteration sequentially, from left to right, similarly to what the output will look like, while with the option syntax, you'd end up writing from right to left, so the bottom 1/2 in the output will be the leftmost formula after the three underbrace commands.