Process for producing a water-absorbing polymer, characterized in that the process comprises the following steps: ( i) mixing (α1) 0.1 to 99.99% by weight of polymerized, ethylenically unsaturated monomers containing acid groups or salts thereof, or polymerized, ethylenically unsaturated monomers including a protonated or quaternized nitrogen, or mixtures thereof, optionally in partly neutralized form, (α2) 0 to 70% by weight of polymerized, ethylenically unsaturated monomers copolymerizable with (α1), (α3) 0.001 to 10% by weight of one or more crosslinkers, (α4) 0 to 30% by weight of water-soluble polymers, and (α5) 0 to 20% by weight of one or more assistants, where the sum of the weights (α1) to (α5) is 100% by weight; (ii) free-radical polymerization with crosslinking to form a water-insoluble aqueous untreated hydrogel polymer; (iii) coarse comminution of the untreated hydrogel polymer to give pieces having a diameter in the range from 0.1 mm to 5.0 cm; ( iv) cooling the precomminuted untreated hydrogel polymer in the cooling region having at least one cooling zone over a period of 30 sec to 3600 sec, wherein the cooling region has a temperature gradient and additionally, in the end region of the cooling region, a cooled apparatus for grinding the comminuted untreated hydrogel polymer and the coolants used are inert solid or liquid refrigerants from the group of CO, carbon dioxide, inert hydrocarbons such as short-chain aliphatics (methane, ethane, propane), halogenated hydrocarbons, nitrogen, helium, argon, or other inert gases which liquefy at temperatures below -30°C, or mixtures thereof, and grinding the cooled untreated hydrogen polymer; (v) drying the comminuted untreated hydrogel polymer after grinding at a temperature in the range from 85°C to 260°C, and sieving the dried pieces in the range from 150 μm to 850 μm; (vi) postcrosslinking the hydrogel polymer and (vii) drying and finishing the water-absorbing polymer, wherein, after step (ii), the hydrogel polymer still at reaction temperature is comminuted in a first step (iii) and then cooled in a cooling region to -30°C to -200°C and comminuted further (iv), wherein the cryogenic grinding takes place before the drying. ( i) mixing (α1) 0.1 to 99.99% by weight of polymerized, ethylenically unsaturated monomers containing acid groups or salts thereof, or polymerized, ethylenically unsaturated monomers including a protonated or quaternized nitrogen, or mixtures thereof, optionally in partly neutralized form, (α2) 0 to 70% by weight of polymerized, ethylenically unsaturated monomers copolymerizable with (α1), (α3) 0.001 to 10% by weight of one or more crosslinkers, (α4) 0 to 30% by weight of water-soluble polymers, and (α5) 0 to 20% by weight of one or more assistants, where the sum of the weights (α1) to (α5) is 100% by weight; (α1) 0.1 to 99.99% by weight of polymerized, ethylenically unsaturated monomers containing acid groups or salts thereof, or polymerized, ethylenically unsaturated monomers including a protonated or quaternized nitrogen, or mixtures thereof, optionally in partly neutralized form, (α2) 0 to 70% by weight of polymerized, ethylenically unsaturated monomers copolymerizable with (α1), (α3) 0.001 to 10% by weight of one or more crosslinkers, (α4) 0 to 30% by weight of water-soluble polymers, and (α5) 0 to 20% by weight of one or more assistants, where the sum of the weights (α1) to (α5) is 100% by weight; (ii) free-radical polymerization with crosslinking to form a water-insoluble aqueous untreated hydrogel polymer; (iii) coarse comminution of the untreated hydrogel polymer to give pieces having a diameter in the range from 0.1 mm to 5.0 cm; ( iv) cooling the precomminuted untreated hydrogel polymer in the cooling region having at least one cooling zone over a period of 30 sec to 3600 sec, wherein the cooling region has a temperature gradient and additionally, in the end region of the cooling region, a cooled apparatus for grinding the comminuted untreated hydrogel polymer and the coolants used are inert solid or liquid refrigerants from the group of CO, carbon dioxide, inert hydrocarbons such as short-chain aliphatics (methane, ethane, propane), halogenated hydrocarbons, nitrogen, helium, argon, or other inert gases which liquefy at temperatures below -30°C, or mixtures thereof, and grinding the cooled untreated hydrogen polymer; (v) drying the comminuted untreated hydrogel polymer after grinding at a temperature in the range from 85°C to 260°C, and sieving the dried pieces in the range from 150 μm to 850 μm; (vi) postcrosslinking the hydrogel polymer and (vii) drying and finishing the water-absorbing polymer,