The present invention relates to a method for making a direct emulsion of a copolymer in water, characterized in that it comprises the polymerization of at least, expressed as a percentage by weight of each of the monomers based upon the total weight of the monomers: a) 10 to 80% by weight of methacrylic acid and, optionally, of acrylic acid; b) 15 to 80% by weight of at least one non-ionic vinyl monomer; c) 0.05 to 9.5% by weight of 2-acrylamido-2-methylpropane sulfonic acid or a salt thereof; d) 0.5 to 30% by weight of at least one monomer containing at least one hydrophobic group; and e) 0.01 to 5% by weight of at least one crosslinking monomer; said polymerization being carried out in the presence of at least one surfactant It also relates to the corresporiding new copolymer emulsion in water, a method for thickening an aqueous composition comprising such an emulsion of copolymer and to an aqueous composition comprising such a copolymer emulsion.