Looking for drama where the lead lives his/her life by some weird philosophy. or has an odd worldview. For example, like in Misaeng(Incomplete Life) where he sees the world as a game of Go. Or I guess, Cinderella and the four knights where she says she lives according to Sun Tzu's Art of War, however she never really does, so it doesn't really match what I'm looking for.

Thanks :D
hard nut (she pretty much views the world as a collection of math problems. In any case she's rather unique)
otenki onee-san (she is also pretty unique and has an odd personality)

These are all Japanese dramas:
Fake Couple
Guren Onna
Date- Koi to Wa Donna Mono Kashire
ST Aka to Shiro no Sousa File
Hotaru no Hikaru 1 & 2
Lucky romance (she lives her life according to superstitions)
Koe Koi
the male lead wears a paper bag

Mr. Nietzsche in the Convenience Store
the male lead live by the rules of monks

Death Note (either drama or movies or both, you'll never get tired of this plot)
both male leads are odd in their way and it's not really clear who the villain is supposed to be

and maybe Bloody Monday, the villain wants to destroy everything and build something new


+1 Lucky Romance & Mr. Nietzsche in the Convenience Store

Meitantei no Okite (this show is a parody of detective dramas with the male lead being aware of that fact and who breaks the 4th wall)
Shopping King Louie (his life revolves around shopping, his emotions & thoughts can be "seen" or "heard" through his shopping)
Matching! Boys Archery (she is a BL manga writer and she sees every day occurrences as BL moments in her head)