Bernhard Riemann vs. Carl Friedrich Gauss
Side-by-side comparison of two thinkers
Bernhard Riemann
1826 – 1866
Georg Friedrich Bernhard Riemann was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rigorous formulation of the integral, the Riemann integral, and his work on Fourier series. His contributions to complex analysis include most notably the introduction of Riemann surfaces, breaking new ground in a natural, geometric treatment of complex analysis.
"Measure-relations can only be studied in abstract notions of quantity, and their dependence on one another can only be represented by formulæ. On certain assump…"
Carl Friedrich Gauss
1777 – 1855
Johann Carl Friedrich Gauss was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. His mathematical contributions spanned the branches of number theory, algebra, analysis, geometry, statistics, and probability. Gauss was director of the Göttingen Observatory in Germany and professor of astronomy from 1807 until his death in 1855.
"Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density."