Carl Friedrich Gauss.

The breadth and beauty of his work amazed me when I was a student, and it still inspires me.

He started by building on much less than what many of us take for granted: His doctoral dissertation was the Fundamental Theorem of Algebra. His work covered deep, essential results in many areas, from number theory (quadratic reciprocity, conjecture of prime number theorem) to geometry (Gaussian curvature) to statistics (least squares) to probability (Gaussian distribution). It is difficult to imagine these areas without his fundamental contributions. He also contributed to physics and astronomy.

Even though Gauss explored many areas, he took the time to revisit old results, looking for different and more satisfactory proofs.