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Is science dead? Quantum gadfly Sabrine Hossenfelder covers a lot of ground in this clip, discussing "the end of science" from various angles.

If I understand her correctly, science "shouldn´t" end, since there are still unsolved problems. Such as? Well, we may be missing one law of nature or two! For instance, laws governing chaos and complexity. Since we seem to understand, at least in principle, where to start looking for such laws, science as an enterprise doesn´t have to end. Indeed, major discoveries may be just around the corner.

Or they may not - but not for the reasons you think. While humans are in theory clever enough to build an advanced computer to "do the math", we may in practice be too stupid to organize scientific work efficiently enough to create the conditions for such a breakthrough. It could even be a kind of "catch 22" situation: in order to understand complexity, we need to organize science in an incredibly complex way...which we can´t do, since we don´t understand complexity in the first place! 

My personal take is that finite beings can´t - neither in theory nor in practice - understand the infinite. However, our dynamic intelligence will keep trying, and in that sense, science will never end...