Hardness results for maximum agreement problems have close connections to hardness results for proper learning in computational learning theory. In this paper we prove two hardness results for the problem of finding a low degree polynomial threshold function (PTF) which has the maximum possible agreement with a given set of labeled examples in Rn 							
						
							
					 															
					Ilias Diakonikolas, Ryan O'Donnell, Rocco A. Serve