A score of 600 on the quantitative section of the GRE is considered too low for admission into a math graduate program, especially for someone in a math honor society. A verbal score of 390 raises concerns, particularly for a native English speaker. Retaking the GRE is strongly recommended to improve these scores, as they significantly impact the perception of the applicant's capabilities. While some graduate programs do not require GRE scores, many still consider them important. The applicant's overall profile, including GPA and recommendations, is also crucial. Being a woman in math may provide some advantages in the application process, as diversity is valued by many programs, but challenges remain in securing long-term positions in the field. The discussion also touches on the relevance of verbal scores for non-native English speakers, indicating that lower scores may be more acceptable in those cases.