A MikTeX update may remove amslatex / amsmath as obsolete - how to fix it

On several TeX sites users wrote that in the recent days a problem occured after they updated their MiKTeX installation: amsmath could not be used any more since MiKTeX has marked amslatex as obsolete, so it was uninstalled.
The first time I read about this was in the matheplanet.com LaTeX forum on February 2, 2013: after an update, amsmathamscd and amsthm were missing and not available via the package manager. amslatex has been marked as obsolete:
MiKTeX: amslatex is obsolete
It's caused by a reorganization of MiKTeX, as Heiko Oberdieck wrote on TeX Stack Exchange, he also provided all three screenshots. The maintainer of MiKTeX splitted amslatex into amsmath and amscls, similar to the packaging in TeX Live.
MiKTeX: amsmath, amscls, amslatex
Sadly, it doesn't automatically reinstall those packages. You need to synchronize the local repository database, in the package manager, done via the menu: Repository→Synchronize. Afterwards it would be reinstalled on-the-fly, if this option is activated, or you can do it manually, in the package manager.
MiKTeX: amsmath and amscls
Also amsthm is affected, which belongs to the amscls package, which contains AMS classes such as amsartamsbook and amsproc for publishing in journals of the American Mathematical Society.
I also think, it's better to separate AMS classes from the amsmath package, since the classes are only needed when writing for AMS journals or books. And consistency with TeX Live is another good point. An improvement lead to this small problem, I hope this post may helps users who stumbled across it.

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