What's a reliable way to detect math mode (including align*)?

Question

I thought ifmmode detected math mode, but clearly it does not:
documentclass{article}
usepackage{amsmath}
begin{document}
[
    ifmmode math else not math fi
]
$ifmmode math else not math fi$
begin{align*}
  ifmmode math else not math fi
end{align*}
end{document}

How do I reliably detect math mode, including within align*?

Phelype Oleinik · Accepted Answer

Adding relax, as you noted in the comment, is the solution basically.  If you look at the LaTeX sources you'll see that most uses of ifmmode are preceded by relax, exactly for that reason:
defverb{relaxifmmodehboxelseleavevmodenullfi %[...]

At the beginning of a table cell (roughly what align uses) TeX is expanding macros looking for omit or noalign, and at this point it's not in math mode, and expands ifmmode which is then false.
Adding relax (or any non-expandable token) stops that scanning, and the column template is inserted, effectively starting math mode.

What's a reliable way to detect math mode (including align*)?

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