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; ande) 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 corresponding 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.