A common trope in post-apocalyptic science fiction has crowds of peasants hunting down scientists to lynch them. Those damn eggheads got it wrong and wrecked the old culture, leaving us in this mess! Check out Edgar Pangborns
Davy for a readable example. In the fifties and sixties this was just a plausible plot point.
Today, even without a collapse, science is under assault from many directions. Some from power players who dont want those damn eggheads interfering with profit. Dont talk to me about extinctions and ecological ruination when there is money to be made! Mostly its from scientific illiterates who dont want to examine their preconceptions. According to Wikipedia
A 2009 poll by Pew Research Center found that "Nearly all scientists (97%) say humans and other living things have evolved over time 87% say evolution is due to natural processes, such as natural selection. The dominant position among scientists that living things have evolved due to natural processes is shared by only about third (32%) of the public." http://en.wikipedia.org/wiki/Level_of_support_for_evolution Include other examples like the anti vaccination idiots and the moon landing is a fake clowns and the numbers add up.
How many scientists know how to build a fire and rig a shelter? How many We dont need no stinking science good old boys do? Outside of secure enclaves guarded by the military, scientists may become an endangered species.
If America becomes a land of
The Road or
The Book of Eli, thats one thing. The scientifically based high tech culture will continue elsewhere.
If its a worldwide collapse, we might need hidden caches for science books and priest holes for scientists.