The f.64 group was founded by Ansel Adams and his peers in the early 1930s. The group promoted the art of the "clearness and definition of the photographic image" (quote of their words), with photos of sharply-focused on and carefully framed images showing actual fine detail (portraying reality) as opposed to the then popular pictorialist style, as for example, imitating artist brush paintings.

Stopping down to f/64 for better depth of field was one of their approaches, however, realize that to maximize detail, they were generally using large view cameras, perhaps like Ansel Adams using 8x10 inch sheet film, requiring corresponding longer lenses like perhaps 300 mm (or longer) as a normal lens. However f/64 required a long exposure.

Because of diffraction, one side effect was an old rule of thumb to NOT exceed a f/stop greater than focal length / 4. This just computes a minimum aperture diameter of 4 mm. Those old limits compute as:

600 mm f/150
300 mm f/75
200 mm f/50
100 mm f/25
50 mm f/12.5
24 mm f/6
12 mm f/3

Still not a bad plan for routine work (although it does not take sensor size or print enlargement into account, but both are fundamentally important to depth of field). However today, we do realize that in some cases, the greater depth of field can often benefit much more than losses of diffraction can hurt, so this old rule disappeared. We no longer hear it said that way.

So things are bit different today with the tiny digital sensors requiring a very short focal length (like 3 mm on a phone camera). F/64 would not often be a proper idea with todays small cameras.