Audiophile

Shortanswer as I’m on a phone No. The 80 will also work in most devices (laptops and phones) without needing an amp.

I mean, all headphones need an amp no? I figure what you're asking is whether or not you need a dedicated amp. In this case no, most devices can run a 32 ohm audio device reasonably well. You will find some improvements in audio quality should you decided to fork out cash for a dedicated amp but it is not necessary.

You may however need an adaptor depending on what size connector the cable comes with and what you are plugging it into.

At 32 Ohms anything should be able to drive them just fine. Are these for a computer, phone, or media center?

Nah, those are fine off of regular power. The 80 ohm need a dedicated amp, but the 32s are fine in anything I ever tried them in.

Edit: with the 80s, the amp can be part of a player or whatever, but it'll need to be strong enough, and your average phone or sound card on a pc isn't. My lg g7 can handle the 80 ohm fine, but my oneplus can't, as an example. The oneplus has to be cranked fully to be reasonably audible.