In this paper we investigate the legitimate and useful role of mathematics in science (and physics in particular). We also investigate the illegitimate and harmful role (or "lure") of mathematics in modern science (and theoretical physics in particular). Thanks to the obsession of contemporary scientists with complex mathematics and the wrong belief (as well as the wrong scientific values and standards) among these scientists that mathematics is the gold standard of excellent science, highly-mathematized and theoretized science (especially in modern physics) reaches these days a shocking level of irrationality and non-sensibility which often approaches the degree of delusion and hallucination. This obsession with complex mathematics and excessive theoretization inflicts serious damages to modern science and results in a huge waste of efforts and resources as well as the emergence of stray trends and bogus scientific theories inside and outside the main stream of science.