The influential physicist Richard Feynman became interested in the relationship between religion and science during a mid-career phase. He proposed that their interface was embroiled in unresolvable difficulties. He felt that science demanded an attitude of uncertainty for its claims, while religion contrarily required certain belief in its core doctrines. Though possessing several non-contradictory dimensions, Feynman felt that the nature of the truth claims of science and religion suffered from insurmountable elemental conflicts. This was by contrast to Karl Popper, the leading critical rationalist of the 20th century, who argued that there could be no tension between science and religion. This paper will argue that the ‘Feynman Problem’ is not as insoluble as it appears. Rather, several Solutions exist within critical rationalism. Two will be presented-the first revolves around the conjectural basis of knowledge and is already a well characterised critical rationalist notion. The second is a novel solution based on the separate categorisation of psychological, pragmatic, and epistemological attitudes to religion and science. Karl Popper’s view of religion-science dissimilarity was a minimalist point of departure for critical rationalists, who have developed increasingly sophisticated frameworks for investigating the relationship between faith and reason. Critical rationalism represents an equally inspirational methodology for the pursuit of scientific and religious truth. Though both Feynman and Popper’s views on religion were underdeveloped, they foreshadowed the religion-science frameworks advocated by many late 20th century scientists, especially in the form of New Atheism and Gould’s NOMA theory.