"Confronting Science's Logical Limits," by John L. Casti. Scientific American, October 1996.
This article explores the question of whether or not the kind of logical limitations exposed by such results as G\"odel's incompleteness theorem imply analogous limitations on our ability to understand nature. Casti presents three examples that illustrate this question: the solar system, protein folding, and the efficiency of financial markets. There are mathematical models that attempt to address important questions in each of these systems but that end up providing strange or ineffective answers. Is this due to the fact that a mathematical model cannot be an entirely faithful representation of the original problem, or is it due to inherent limitations in mathematics? Casti explores this question and concludes the article with musings about whether the creativity of the human mind is subject to the same limitations as the calculating ability of a computer.