Why does equation environment not give an error without the amsmath package?

Question

As far as I understand the equation environment is defined in the amsmath package so one would expect an error while trying to compile the following document with pdflatex:

\documentclass{article}

\begin{document}

\begin{equation}
a=b+c
\end{equation}

\end{document} 

But I don't get any error while running pdflatex on this file an a pdf output with the equation a + b = c is generated. How does that work exactly?

Answer 1

You wrote:

As far as I understand the equation environment is defined in the amsmath package

That's not quite correct. The equation environment is defined in the LaTeX kernel -- and it is redefined if the amsmath package is loaded in the preamble.

---

For completeness, here's the relevant code from the file latex.ltx (the "kernel"):

\@definecounter{equation}
\def\equation{$$\refstepcounter{equation}}
\def\endequation{\eqno \hbox{\@eqnnum}$$\@ignoretrue}
\def\@eqnnum{{\normalfont \normalcolor (\theequation)}}

where \eqno is a so-called "primitive" instruction that takes \hbox{\@eqnnum} as its argument. Basically, \equation initiates display-math mode and increments a counter called equation, while \endequation typesets the equation number (on the far right, by default) and closes display-math mode.

And here's the code from amsmath.sty; note that due to the \renewenvironment instruction, the code replaces what the kernel provides:

\renewenvironment{equation}{%
  \incr@eqnum
  \mathdisplay@push
  \st@rredfalse \global\@eqnswtrue
  \mathdisplay{equation}%
}{%
  \endmathdisplay{equation}%
  \mathdisplay@pop
  \ignorespacesafterend
}

This setup is, quite obviously, rather more elaborate than what's performed in the LaTeX kernel. The most important substantive differences arise from the fact that, if amsmath is loaded, it becomes possible to insert split, aligned, and gathered environments inside an equation environment. In addition, amsmath performs some fancy measuring operations, behind the scenes, to figure out if it's necessary to "shove" the equation number down a bit in order to avoid a collision with an overly long equation.

If you're really interested in the details, I would like to encourage you to examine the information contained in the file amsmath.pdf. Open a command window and type texdoc amsmath.pdf to launch the file in a pdf viewer.