Bernhard Riemann


by David F. Coppedge

Let’s turn now to another remarkable Christian mathematician who, like Blaise Pascal, changed the world but never reached his 40th birthday: Georg Friedrich Bernhard Riemann (pronounced REE-mon).

Mathematics is the language of science and the two are almost useless without one another.  There are textbooks both in mathematical physics and physical mathematics.  Sometimes the scientist presses the mathematician to produce better tools for computation, but sometimes the mathematician opens up new vistas for the scientist to explore.  Riemann was such a man.  He liberated mathematics from the strictures of Euclidean geometry that for 2,000 years had seemed intuitively obvious and inviolable.  In so doing, he created a new space for Einstein to apply his mental powers.  Howard Anton called Riemann’s work “brilliant and of fundamental importance,” and lamented that “his early death was a great loss to mathematics.”  Yet such achievement would have seemed unlikely for a boy who wanted to become a preacher.

Like Leonhard Euler in the previous century, Riemann was the son of a Protestant minister.  Wanting to follow in his father’s footsteps, Bernhard had a trait that would not have suited the preaching profession, according to John Hudson Tiner: he was excessively shy.  Nevertheless, throughout his life, he was devoutly religious and sincere in his Christian faith.  Early on, his propensity for mathematics became obvious.  Dan Graves says that he outpaced his teacher at age ten, and at age 16 “he mastered Legendre’s (1752-1833) massive and difficult Theory of Numbers—in just six days.”  He breezed through Euler’s works on calculus and studied under the great Carl Friedrich Gauss, under whom he received his PhD with a thesis on complex functions.

In order to obtain an assistant professorship, Riemann had to deliver a lecture on one of three topics.  Gauss selected the topic for which his student was least prepared: the foundations of geometry.  After hastening to prepare, he delivered a paper so brilliant it astonished his aging master.  Riemann’s work led to a bizarre concept hard for many to grasp: curved space, in which Euclid’s rules of geometry broke down.

One of Euclid’s primary assumptions was that parallel lines never meet; another was that the shortest distance between two points is a straight line.  A few, including Gauss, had speculated whether it would be possible to question these assumptions, and thereon build a non-Euclidean geometry.  By proposing that space was curved, Riemann’s method succeeded far better than earlier attempts.  In curved space, parallel lines could meet, and the shortest distance between two points would be a curve on the curved surface.  These ideas, mere curiosities among the learned in the 1850s, were fundamental to Einstein’s theories of relativity 50 years later.  Riemann also formalized the modern understanding of the definite integral and made other important contributions in both physics and mathematics, yet he did not achieve fame or recognition in his lifetime.

Personally, Riemann was bashful, reserved, and a perfectionist.  These traits led to two breakdowns from overwork, and contributed toward ill health much of his life.  For most of his short career he had low-paying jobs.  Though poor himself, he unselfishly supported his unmarried sisters.  Within a month of marrying at age 36, he suffered respiratory diseases that sent him into a downward spiral.  Through all his troubles, he maintained a steadfast faith and conducted daily spiritual examination.  As he was succumbing to tuberculosis, the Lord’s prayer comprised the last words on his lips.  His tombstone bears the inscription of Romans 8:28, “All things work together for good to them that love God.”

Calculus students today learn about Riemann sums, Riemann surfaces and Riemann integrals.  Knowing a little about the person behind the terms is definitely integral to appreciating them.

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