Prime Obsession Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) / Chapter Skim
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4. On the Shoulders of Giants
4. On the Shoulders of Giants
Pages 48-62
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From page 48... ...
Almost instantly, Gauss threw his slate onto the master's table, saying, "Ligget se.f' which in the peasant dialect of that place and time meant, "There it is! " Gauss had mentally listed the numbers horizontally in or(ler (1, 2, 3, .
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From page 49... ...
A keen soldier all his life, he held the rank of field marshal in the Prussian army and was in charge of the joint Prussian-Austrian force that the French stopped at Valmy on September 20, 1792.
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From page 50... ...
To prevent Saxony from becoming a French satellite, the Prussians occupied it, calling the Duke of Brunswick out of retirement he was 71 years old at this point to lead their forces. Napoleon declared war and his army struck northwest through Saxony toward Berlin.
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From page 51... ...
We know from his correspondence, his surviving unpublished papers, and circumstantial evidence in his published worksthat what he presented to the world was only part of what he discovered. Theorems and proofs that would have made another man's reputation, Gauss left languishing in his personal (liaries.
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From page 52... ...
His personal seal showed a tree with only sparse fruit, and the motto, Pauca sed mature "Few, but ripe." This is, as I said, a common failing among mathematicians and often makes the reading of published mathematical papers a very tedious business. In one of the minor classics of modern psychological literature, The Presentation of Self in Everyday Life, Erving Goffman (levelops a theory of"performances," in which a product or activity created in conditions of disorder and opportunity in some "back" environment is presented as a smooth, finished creation at the "front." Restaurants illustrate the point.
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From page 53... ...
III. In December 1849 Gauss exchange(1 letters with the astronomer Johann Franz Encke (after whom a famous comet is named)
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From page 54... ...
By"chiliads" Gauss meant blocks of 1,000 numbers. So beginning in 1792 when he was fifteen years old!
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From page 55... ...
V Because I am surveying here relevant discoveries and conjectures before 1800, and because he was the author of the "Golden Key," of which I am going to make so much in later chapters, this is the right place to introduce the other first-rank mathematical genius born in the eighteenth century, Leonhard Euler (pronounced"oiler"~.
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From page 56... ...
He was especially fond of the company of foreigners, of whom at that time there was a large settlement near Moscow, in the so-called "German suburb." Here, among Scottish mercenaries, Dutch merchants, and German and Swiss engineers, Peter took in European science and culture and indulged his passion for fireworks and boats (in between riotous banquets and all-night drinking bouts)
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From page 57... ...
The ([earth of learning in Russia was in(lee(1 so great that there were no Russians capable of acting as academicians. In fact, since Russia lacked any significant number of elementary or secondary schools, there were not even any Russian youngsters qualifie(1 to attend as students at the attached university.
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From page 58... ...
The St. Petersburg Academy opened its doors in August, 1725too late for Tsar Peter to preside over the ceremony; he had died six months earlier.
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From page 59... ...
Two years later, in a small memorandum on infinite series, Euler discovered the result that I have caHed"the Golden Key," and to which I have devoted the first half of Chapter 7. He was, in short, a principal player in the story I am telling but this will emerge more clearly later, as the mathematical side of the story unfolds.
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From page 60... ...
In 1745-1747 Frederick built the Sans Souci summer palace for himself at Potsdam, 20 miles outside Berlin. (Euler helped design a system of water pumps for the place.)
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From page 61... ...
Euler wrote mainly in Latin, but this is not much of an obstacle to appreciating him, as he had a spare and utilitarian style.22 Euler's crystal-clear Latin makes one realize what western civilization lost when scholars ceased writing in that language. Gauss was the last important mathematician to do so; this was one of those changes that came upon us after the Napoleonic wars.
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From page 62... ...
His wife Catherine died when Euler was 69; a year later he remarried to another Gsell, Catherine's halfsister. He loved children, and it is reported that he could do serious mathematics with infants playing at his feet.
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