35%。 According to the query, what is displayed on the Internet is youth. In the national mathematics competition for college students, the number of winners of the first prize accounts for 8% of the total number of participants, the number of winners of the second prize accounts for 12% of the total number of participants, and the number of winners of the third prize accounts for 15% of the total number of participants, with a total winning ratio of 35%. Therefore, the winning proportion of the national college students' mathematics competition is 35%.