Looking for fantasy/alien beings?

Try The Humans by Matt Haig.

The aliens are purple filaments, from another dimension I think, that possess humans.

They're also very good with mathematics.

Sounds like the Quaslings in Wesley Chu's The Lives of Tao - gaseous aliens forced to live in human host bodies to protect them from our atmosphere, who learn to control us and use hosts to wage a secret war.

Also some shades of the changeling/sleeper agents from Rick Yancey's The 5th Wave trilogy.

I tried to read Stephanie Myers The Host as well, once, during the Twilight years. Could not get into it enough to tell you what the aliens were, but you could look at that as well.

Fantasy rather than sci-fi, but there was a Japanese series of light novels by Mizuna Kuwabara that dealt with "Possessors." Basically, it's individuals from the feudal time period forcibly taking over other people's bodies through time to allow themselves and their souls a continued existence on earth to continue their conflict--- and bringing along all their drama and hostility and baggage with them. So A is a noble lord, and X, Y, and Z are vassals, and various individuals have different abilities they bring to their respective sides, and there's a whole lotta undead extras who had been their respective armies who hadn't been lucky enough to enjoy a continued earthly existence, but are waiting patiently and eagerly to be summoned back into action. And in the process of remembering or not-remembering their memories from the past, there's also questions about identity, and guilt about obliterating the soul of the person they hijacked, and jealousies, and hostages, and blah blah blah.

So, depending on what kind of lifespan your aliens have, and how short or how long they spend time dwelling with a particular host, and what happens to the host once they've chosen to move in--- "Mirage of Blaze" was fun and angsty and layered and complicated. The novels only exist in fragmented fan translations in English, but there were a few episodes of animation that were licensed ages ago and are easy to find.

Patty said:

I tried to read Stephanie Myers The Host as well, once, during the Twilight years. Could not get into it enough to tell you what the aliens were, but you could look at that as well.

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I recall some muttered accusations of it ripping off Animorphs. The Yeerks in the Animorphs were parasitic sluglike aliens that enveloped a host's brain to control them.