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mathtools aims to fix bugs and problems with the AMS package set.

Quote from the AMS site http://www.ams.org/publications/authors/tex/amslatex:

In 2016, LuaTeX version 1 was released, and attempts to use amsmath with LuaLaTeX would fail. To address this problem most effectively, responsibility for maintenance of amsmath was transferred to the LaTeX Project, and the authoritative version of amsmath is now on CTAN and in TeX Live.

Which fix has made it into the AMS package already?

Can the LaTeX Project merge the fixes to amsmath?

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Your question is really two questions. The original adjustments for luatex were done first in amsmath then communicated to the mathtools maintainers to incorporate there, similarly the fix to not need \! before aligned.

mathtools has some extensions and fixes to amsmath and there is a mid to long term aim to incorporate some of them back but mostly that's not done yet. As always the main issues are around document compatibility rather than difficulty in actually making the change.

You can see all the changes made since we picked up amsmath here

https://github.com/latex3/latex2e/commits/master/required/amsmath

Or a more curated top level description of the changes here

https://github.com/latex3/latex2e/blob/master/required/amsmath/changes.txt

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  • Does this mean, it makes no sense to load mathtools in luatex+amsmath, because the fixes were made there first?
    – Jonas Stein
    Apr 25, 2019 at 9:14
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    @JonasStein no it means that mathtools works at all in luatex as the immediate fixes required when luatex changed the behaviour of \mathchardef are incorporated. But as I note above the other unrelated extensions that mathtools adds over amsmath are still just in mathtools. Basically it means that they are in sync whoever the packages claim to be maintained by: any changes made to amsmath will either not break mathtools or we will arrange that compatible update to mathtools happens at the same time.
    – David Carlisle
    Apr 25, 2019 at 9:31

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