Analysis & CalculusGeometry
Bernhard Riemann
1826 – 1866 · Germany
The man who defined area as 'the sum of thin rectangles'
Bernhard Riemann was a German mathematician who, in a short life, reshaped several branches of mathematics at the root. He defined the area under a curve rigorously as the limit of a sum of thin rectangles (the Riemann integral), giving integration a solid foundation. The 'Riemann hypothesis' he left behind remains the greatest unsolved problem in mathematics.
Key contributions
- Gave integration a rigorous definition via the Riemann integral
- The geometry of curved space (Riemannian geometry)
- The Riemann hypothesis