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Sunday, September 30, 2018

Before his early death, Riemann freed geometry from Euclidean prejudices | Math & Technology - Science News

"The originator of the famous math hypothesis also established the basis for a modern view of spacetime" inform Tom Siegfried, author of the blog Context.

CUT SHORT Bernhard Riemann did a lot more than come up with his eponymous hypothesis, and if he hadn’t died young, he might have rivaled Einstein and Newton.
Photo: Familienarchiv Thomas Schilling/Wikimedia Commons
Bernhard Riemann was a man with a hypothesis.

He was confident that it was true, probably. But he didn’t prove it. And attempts over the last century and a half by others to prove it have failed.

A new claim by the esteemed mathematician Michael Atiyah that Riemann’s hypothesis has now been proved may also be exaggerated. But sadly Riemann’s early death was not. He died at age 39. In his short life, though, he left an intellectual legacy that touched many areas of math and science. He was “one of the most profound and imaginative mathematicians of all time,” as the mathematician Hans Freudenthal once wrote. Riemann recast the mathematical world’s view of algebra, geometry and various mathematical subfields — and set the stage for the 20th century’s understanding of space and time. Riemann’s math made Einstein’s general theory of relativity possible.

“It is quite possible,” wrote the mathematician-biographer E.T. Bell, “that had he been granted 20 or 30 more years of life, he would have become the Newton or Einstein of the nineteenth century.”

Riemann’s genius developed despite unpromising circumstances. Born in Bavaria in 1826 the son of a Protestant minister, he was poor and often sick as a child. Bernhard was homeschooled until his teenage years, when he moved to live with a grandmother where he could attend school. Later his mathematical aptitude caught the attention of a teacher who provided Riemann a nearly 900-page-long textbook by the legendary French mathematician Adrien-Marie Legendre to keep the precocious student occupied. Six days later, Riemann returned the book to the teacher, having mastered its contents.

When he entered the University of Göttingen, Riemann began (at his father’s urging) as a theology student. But Göttingen was the home of the greatest mathematician of the era, Carl Friedrich Gauss. Riemann attended lectures by Gauss and dropped theology for mathematics. More advanced math instruction was available at Berlin, where Riemann studied for two years before returning to Göttingen to finish his math Ph.D...

He made many other contributions to a wide range of technical mathematical issues. And he took great interest in the philosophy of mathematics (as Freudenthal said, had he lived longer, Riemann might eventually have become known as a philosopher). Among his most famous technical ideas was a conjecture concerning the “zeta function,” a complicated mathematical expression with important implications related to the properties of prime numbers. Riemann’s hypothesis about the zeta function, if true, would validate vast numbers of additional mathematical propositions that have been derived from it.
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Source: Science News (Blog)