I see post and math rock to be very influenced by other genres, post rock more so.
There are mellow bands such as 3epkano, The Album Leaf, The Drift, ef, Eluvium, From Monument to Masses, Toe, Manual, The Mercury Programme, Moonlit Sailor, Signal Hill, Unwed Sailor
Folky such as Beast Please Be Still, Tarwater, Balmorreha, Remember Remember, Ritual
Electronica such as 65daysofstatic, BlackMothSuperRainbow, Daedelus, Errors, Four Tet, Hella, Holy ****
Pop/rock such as The American Dollar, Couch, Yippah, Do Make Say Think, Dorena, Parlour, Salvatore
Punk/new wave/indie such as ASIWYFA, Battles, Cougar, Don Caballero, Three Trapped Tigers, Scraps Of Tape, El Ten Eleven, Fridge, Giraffs? Giraffs!, The Redneck Manifesto
Anthemic such as Explosions in The Sky, Mogwai, This Will Destroy You, Jakob, Collapse Under The Empire, Laura, Long Distance Calling, Maserati, MONO, Saxon Shore
Metal such as Animals As Leaders, Grails, Turing Machine, Caspian, Maybeshewill
Prog rock/psychedelic such as Cul De Sac, Dntel, Microfilm, Oresund Space Collective
and within each there are crossovers and other influences unique to each band.