Prime Obsession Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) / Chapter Skim
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16. Climbing the Critical Line
16. Climbing the Critical Line
Pages 252-264
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From page 252... ...
The title of the speech was "Logic and the Understanding of Nature." Hilbert's purpose was to express some opinions about the relationship between our inner lives our mental processes, including those that help us to create and prove mathematical truths and the physical universe. This was, of course, a topic with a long philosophical pedigree, one in which the name of another of Konigsberg's native sons, the eighteenth-century philosopher Immanuel Kant, has particular prominence.
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From page 253... ...
Those wor(ls are the last in his Konigsberg address. Hilbert believed firmly in the unbounded power of the human mind to uncover the truths of Nature and mathematics.
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From page 254... ...
I say"was intended" because the old Field Marshal, Paul van Hindenburg, was still presi(lent of the German Republic and had to be (leferre(1 to. He insiste that there be two categories of exemption to the April 7 decree: first, any Jew who had performed military service in World War I, and second, any who had aIrea(ly held a civil service position before August 1914, when that war began.
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From page 255... ...
Uniformed storm troopers prevented Landau's students from entering the lecture hall. With singular courage, Landau asked the Council lea(ler, a 20-year
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From page 256... ...
There were a few overseas lecturing trips, which seemed to give him great pleasure, but he would not leave his native land to live permanently abroad and died from natural causes at his Berlin home in 1938. Hilbert himself flied in wartime Gottingen on February 14, 1943, three weeks after his 81st birthday, from complications following a fall in the street.
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From page 257... ...
Van de Lune went on to carry his investigation to 5 billion zeros at the en(1 of 2000, and to 10 billion by October 2001. In the mean
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From page 258... ...
van de Lune et al. 1986 1,500,000,001 time, in August 2001, Sebastian Wedeniwski, using idle time on 550 office PCs at IBM Corp., Germany, began a project to advance computation yet further.
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From page 259... ...
In 1960, working on second-generation mainframe computers at the universities of Cambridge and Manchester, in England, HaseIgrove and his colleagues tabulated the first 1,600 zeros, accurate to six (lecimal places, and published the table. Andrew Odlyzko told me that when he began his work on the zeta zeros in the late 1970s, HaseIgrove's tables were the only ones he knew of, though he thinks that Lehman, as part of his 1966 work, might have done accurate computation of more zeros.
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From page 260... ...
Andrew O(llyzko has also leapt ahead to examine small, isolated ranges very high up. He has published the highest non-trivial zero of the zeta function known to (late, the 10,000,000,000,000,000,010,000-th.
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From page 261... ...
i: Turing's work on the "zeta function machine" stopped abruptly n 1939, when World War II broke out. He joined the Government Code and Cypher School at BletchIey Park and spent the war years breaking enemy codes.
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From page 262... ...
He went on to write a classic mathematical text on the zeta function.96 All this mechanical work came to an end with the advent of electronic computers after WorI(1 War II, of course. Other stories, too .
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From page 263... ...
This was computational hard labor; values of the zeta function are not easy to compute. The basic technique was one named "EulerMacIaurin summation," developed around 1740 by Leonhard Euler and the Scottish mathematician Colin MacIaurin, working indepen(lently.
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From page 264... ...
Car] Siegel, by the way, was not Tewish and was not directly affected by the restrictive laws of the early Nazi period.
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