Electronic Journal of Differential Equations, Conference 04 (2000), pp. 207-213. Title: The spin-statistics connection; some pedagogical remarks in response to Neuenschwander's question Author: A. S. Wightman (Princeton Univ., Princeton, NJ USA) Abstract: Q: Is there a simple proof of the Spin-Statistics Theorem? A: Not if all that is assumed is invariance under the Euclidean Group. When this hypothesis is supplemented by invariance under restricted Lorentz transformations, the key move is to disregard Henry David Thoreau's advice: "Simplify, simplify" and instead: complexify, complexify. Published July 12, 2000. Math Subject Classifications: 81T05. Key Words: Spin-statistics theorem.