Riemann’s On the Hypotheses Which Lie at the Foundations of Geometry

One must be truly enamored of the internet that it allows one to find and read a copy of Bernhard Riemann’s doctoral thesis Habilitation Lecture (in English translation) at the University of Göttingen from 1854!

His brief paper has created a tsunami of mathematical work and research in the ensuing 156 years. It has ultimately become one of the seminal works in the development of the algebra and calculus of n-dimensional manifolds.

Paul Halmos on Prerequisites

Definitely the quote of the day:

Paul Halmos (1916 – 2006, Hungarian-born American mathematician
in Measure Theory (1950)

 

This is essentially the mathematician’s equivalent of the adage “Fake it ’til you make it.”