The argument that the second law of thermodynamics contradicts the theory of evolution has recently been revived by anti-evolutionists. In its basic form, the argument asserts that whereas evolution implies that there has been an increase in biological complexity over time, the second law, a fundamental principle of physics, shows this to be impossible. Scientists have responded primarily by noting that the second law does not rule out increases in complexity in open systems, and since the Earth receives energy from the Sun, it is an open system. This reply is correct as far as it goes, and it adequately rebuts the most crude versions of the second law argument. However, it is insufficient against more sophisticated versions, and it leaves many relevant aspects of thermodynamics unexplained. We shall consider the history of the argument, explain the nuances various anti-evolution writers have brought to it, and offer thorough explanations for why the argument is fallacious. We shall emphasize in particular that the second law is best viewed as a mathematical statement. Since anti-evolutionists never make use of the mathematical structure of thermodynamics, invocations of the second law never contribute anything substantive to their discourse.