Recommend a good, relaxing puzzle game like LYNE on Steam

Hexcell games are great idea from luller.
Squarecells, Unium, Paint It Back could be good additions as well

Hook - it's really short (~1h to complete) but fun. :)

Circuits is pretty relaxing. Also, Sokobond is interesting as well.

Have you tried Thomas Was Alone?

How about

• Strata

  or (even if its more of a simulator)

• Poly Bridge

I've not played LYNE, but it looks like Splice has a similar appeal, and it's a game that I quite enjoyed.

Have you played Ichi?

+1 Hexcells. It's fun, and if you can only get 1 version of the game, get the Hexcells Infinite. Imo, it doesn't make me rage, lol.

SpaceChem, though it's far more complex then LYNE

Hmm, have you considered CS:GO?

KAMI

No achievements I think, but still worthwhile because it's a beautifully done game that shouldn't be missed IMO.

If you have an Android device or think you might get one in the future, the HumbleStore gives you a DRM-Free Android copy along with a Steam key:
https://www.humblebundle.com/store/p/kami_storefront

Just thought of another:

Mini Metro

It's not a typical puzzler in that it has elements of randomness and management, but the minimalist interface and thought processes required I think would fit your criteria perhaps.

Zen Bound 2 (I think the chances are high you will love this one)
Type:Rider (Not much of a puzzle game, but more like a relaxing platformer)
Lemma
Mind: Path to Thalamus Enhanced Edition (You can grab it in a bundle right now https://www.onemorebundle.com)
FOTONICA (Also not much of puzzle, more platform, but still great. If you like it, theres also a game named Sinarun which is pretty nice)
EDGE (Another cool one, but not very relaxing)

Cat Goes Fishing
Osmos
Eufloria HD

Hexcell series is awesome.

Just started playing Strata. It's very good.

I need to bookmark this thread so I can get an idea of puzzle games people like that I already f!@#$%^ gosh darn own.

huniepop or the souls series

The HexCells games are pretty good, there's a lot more complexity in the rules than in minesweeper and no guessing necessary. There's also a level generator in HexCells Infinite, so you never need to run out.
Splice is quite good, but unfortunately has a limited number of levels.
If you want a fairly easy game with simple rules, try Strata.
If you want games that are more challenging to turn into algebraic structures, try SpaceChem, Great Permutator, Prelogate, or Tricone Lab.
And I assume you know that Lyne comes out with more level sets daily, yes?
(From a fellow mathematician - I'm an algebraist; you?)