On section 2.1.3 of the manual (at http://mirrors.ctan.org/macros/generic/markdown/markdown.html#latex), I use the provided code:

\documentclass{article}
\usepackage{markdown}
\begin{document}

\begin{markdown}
$\sqrt{-1}$ *equals* $i$
\end{markdown}

\begin{markdown}[texMathDollars]
$\sqrt{-1}$ *equals* $i$
\end{markdown}

\end{document}

Expected output (according to the manual):

(yes, this is the display in my browser, see below, at the end!)

Real output:

But the real expected output is (if I understand correctly):

What is wrong? If I misunderstand anything, please add some information in the manual, thanks.

Why is this manual in HTML form? The output of pdfLaTeX (and other engines) is PDF, so PDF is probably a better format for the manual. With PDF output, there is no problem: the PDF is always the same. Here, the Safari browser wrongly display the mathml code (which is strange, because the page https://webkit.org/demos/mathml/MathMLDemo.xhtml is correctly displayed).

In the web inspector:

Comparison on the webkit page:

Perhaps because <msqrt> is the right tag for square root, and <mroot> is for cubic root etc. And embedding in is wrong? See the usage of <mroot> here: https://developer.mozilla.org/en-US/docs/Web/MathML/Element/mroot, and the usage of <msqrt> here: https://developer.mozilla.org/en-US/docs/Web/MathML/Element/msqrt.

Conclusion: the PDF format is more safe.

But, more important: how to obtain the right output with LaTeX?