Establishing an independent academic identity is a central yet insufficiently understood challenge for early-career researchers. However, limited resources and mentor-driven research agendas often constrain early efforts toward autonomy. To provide large-scale quantitative evidence on how junior researchers develop independence, we introduce a framework that traces how mentees diverge from their mentors in both research topics and collaboration networks, and how these divergences relate to long-term scientific impact. Analyzing over 500,000 mentee-mentor pairs in Chemistry, Neuroscience, and Physics across six decades, we find that high-impact scientists often initiate work in secondary areas of their mentors' expertise while adaptively establishing distinct research trajectories. This pattern is most pronounced among mentees who eventually surpass their mentors' impact. We identify an inverted U-shaped relationship between topic divergence and mentees' enduring impact, with moderate divergence yielding the highest scientific impact, revealing an independence paradox in scientific careers. This pattern holds whether topic divergence is measured by citation network or semantic thematic distance. We further reveal that excessive direct mentor-mentee collaborations correlate with lower mentee impact, whereas expanding professional networks to include mentors' collaborators is beneficial. These findings not only offer actionable guidance for early-career researchers navigating independence but also inform institutional policies that promote mentorship structures supporting intellectual innovation and recognizing original contributions in promotion evaluations.

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