The title of Paul Dirac’s lecture is a very general one, but in Lindau he immediately announced that he would use some of the time to describe a still unpublished discovery of so-called super-heavy elements, elements heavier than uranium. These should recently have been found at his home university in Florida in certain minerals. This announcement fits very well into Dirac’s general theme of beliefs and prejudices, since we know today that the announcement turned out to be false and that the first known super-heavy elements eventually were produced in large accelerators. Dirac’s main point, though, is that a scientist may have certain beliefs, but that these easily might become prejudices to be discarded as soon as the beliefs are shown to be wrong. He tells of his own belief in the 1920’s that the Bohr orbits of the electrons in atoms would explain everything in atomic physics. This belief (turned into a prejudice) he discarded when Heisenberg showed that it made no sense to think about one Bohr orbit, but that everything actually was based on so called matrix elements connecting two Bohr orbits. Another of his examples concerns the existence of so-called magnetic monopoles. From ordinary experience we know that a magnet always has a north pole and a south pole. But the equations describing electromagnetism seem to allow also magnets that have only one pole. These hypothetical particles were studied by Dirac already in the 1930’s. In his lecture he describes the (then) recent experimental search for monopoles in the cosmic radiation at high altitudes. A balloon experiment had detected a particle track in a plastic detector and the experimenters interpreted the track as resulting from a magnetic monopole. The result was published, but met strong criticism. At the time of the lecture, Dirac still kept an open mind, but we know today that (again) the discovery was false. Even today there has been no trace of magnetic monopoles.