I’m going to go against what appears to be the consensus. I think it is possible that at some point science will be generally done. There is not really an infinite amount of scientific information out there: science is about understanding what a hydrogen atom is, not about cataloging each individual hydrogen atom. At some point I feel we’ll understand all the basic principles of how the universe works and at that point we’ll just be discovering new examples of things we already knew.
Whether or not there is a finite amount of information in the universe, one must consider the potential of mankind’s ability to detect and process the information. It’s quite possible that humanity will reach its pinnacle of data-gathering capabilities long before we scratch the surface of the universe. We just can’t see inside a black hole and that’s that.
Of course, another short answer is that science will end once all life goes extinct.
I agree. At some point we’ll know everything that can be known, and after that it’s just cataloguing examples of things that were already predicted, or at least fully predictable.