Giftedness in mathematics has been characterized by exceptional attributes including strong mathematical memory, formalizing perception, generalization, curtailment, flexibility, and elegance. Focusing on the last attribute, this study examined the following: (a) the criteria which expert mathematicians and mathematically gifted students fleshed out to identify their own most preferred mathematics problem-solving approaches and (b) the extent to which students perceived expert mathematicians' preferences for one approach over the others as aesthetically pleasing. The findings suggested that: (a) unlike expert mathematicians who saw beauty in mathematics as an exhaustive consequence of simplicity and originality, mathematically gifted students found mathematical elegance only in approaches that were efficient in terms of time and number of steps to solve the problems and (b) although expert mathematicians considered mathematically gifted students' most preferred approaches to be the least "beautiful," mathematically gifted students, showing no enthusiasm, considered expert mathematicians' most preferred approaches to be no more attractive than their own approaches.