Gauss invites comparisons only to Isaac Newton or perhaps Johann Wolfgang von Goethe, being the sort of endlessly inventive mind that achieved results when put to any task. His contributions to the fields of pure and applied mathematics were all equally sensational in his day, and equally influential into the 20th century. Gauss' major discoveries reached back to Greek practices, either updating or employing them to novel use. His penchant for publishing only the most rigorous and polished proofs had set a standard for arguments in symbolic logic not seen before. Gauss' formulation of the complex number system advanced number theoryso that all possible operations could be performed on all possible numbers without needing to create new ones. His investigations into algebra and geometry paved the way for the modern disciplines of probability theory, topology, and vector analysis. Among Gauss' inventions and collaborations include the heliotrope(a trigonometric...