The logical positivist movement stemming from the Vienna Circle is famous for its empiricist approach to scientific rationality and a theory of meaning based around the principle of verification. Karl Popper was initially sympathetic to some of the positivist concerns regarding scientific knowledge, but became increasingly disenchanted with the doctrine of verificationism, and began to focus his attention on developing a precise logical account of the demarcation between science and non-science. In The Logic of Scientific Discovery (1933) he put forward a radical and controversial argument about the process he believed we must use to justify scientific knowledge claims.
The crucial point for Popper was that theories, in order to be scientific, must be constructed in terms of propositions that are logically falsifiable (and are thus empirically testable). As a consequence, Popper argues that we can find a logical resolution to the problem of induction - an ancient debate into the very foundations of human knowledge, dating back as far as the skeptical philosophy of the Pyhrronian Greeks.
While the problem of induction may have turned out to be of less practical importance for scientists than Popper claimed, there are still significant aspects of this work that remain extremely relevant today. The principle of error correction is essential to understanding how we can develop a rational system of knowledge that is able to evolve and grow with increasingly deeper inquiry into the nature of the universe. Popper's notion of self-correction being an inbuilt part of science is sorely underrepresented in contemporary debates on science education where the problem of demarcating between science and non-science has become a central issue in recent controversies regarding the alleged scientific status of Intelligent Design. Due to the obviously unfalsifiable state of the doctrines presented under the banner of Intelligent Design, it's easy to think this a non-issue more to do with rhetoric and religion, but the severity of this assault on science cannot be underestimated.
In the face of such challenges, it is more important than ever for scientists and philosophers to emphasize the role of evolution in the context of our ever-changing scientific knowledge, not just as a doctrine of biology. Popper's work stands as a foundational guide in understanding how even the best of our theories can turn out to be wrong, and that our most fundamental understanding of nature can always be improved upon.