A method for making a polyurethane in the substantial absence of metallic and/or low molecular weight amine urethane catalysts is desired. The method should produce a polyurethane having good properties and good elevated temperature stability, in a reasonably short curing time. The polyurethane produced in the process preferably has good high temperature properties. This invention is in one aspect a polyurethane polymer having a density of at least 750 kg/m$^{8}$that is the reaction product of reactants that comprise: b-1) one or more polyols having a hydroxyl equivalent weight of greater than 250 g/mol and a nominal hydroxyl functionality of 2 to 4 and b-2) one or more polyols having a hydroxyl equivalent weight of up to 250, wherein at least 50% by weight of b-2) is at least one alkoxylated Mannich base having an average hydroxyl functionality of 2 to 7; wherein the hard segment content of the polyurethane polymer is 20 to 80% by weight of the polyurethane polymer. The invention is also a process for making a polyurethane polymer, comprising reacting, in one or more steps that include a final curing step in which the isocyanate index is 90 to 150, reactants comprising b) polyols comprising b-1) at least one polyol having a hydroxyl equivalent weight of greater than 260 g/mol, and b-2) one or more polyols having a hydroxyl equivalent weight of up to 260, wherein at least 60% by weight of b-2) is at least one alkoxylated Mannich base having an average hydroxyl functionality of 2 to 7; wherein the hard segment content of the polyurethane polymer is 20 to 80% by weight of the polyurethane polymer and the density of the polyurethane polymer is at least 750 kg/m$^{3}$. The invention has important advantages. The reaction of the alkoxylated Mannich base towards isocyanate groups proceeds at commercially useful rates even in the absence of a metallic and/or amine urethane catalysts; accordingly such catalysts can be eliminated or used only in very small quantities. The polyurethane polymer has good mechanical and thermal properties, in some cases better than otherwise like polymers that are made with other crosslinking agents or curatives that do not contain amine groups. Polyurethanes having very a) at least one organic polyisocyanate; and a) at least one organic polyisocyanate and b) polyols comprising