Saturday, April 21, 2018 Text is available under the CC BY-SA 3.0 licence.

Carl Friedrich Gauss

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Maybe we have become so hung up on looking at the primes from Gauss's and Riemann's perspective that what we are missing is simply a different way to understand these enigmatic numbers. Gauss gave an estimate for the number of primes, Riemann predicted that the guess is at worst the square root of N off its mark, Littlewood showed that you can't do better than this. Maybe there is an alternative viewpoint that no one has found because we have become so culturally attached to the house that Gauss built.

 
Carl Friedrich Gauss

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Gauss liked to call [number theory] 'the Queen of Mathematics'. For Gauss, the jewels in the crown were the primes, numbers which had fascinated and teased generations of mathematicians.

 
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The revelation that the graph appears to climb so smoothly, even though the primes themselves are so unpredictable, is one of the most miraculous in mathematics and represents one of the high points in the story of the primes. On the back page of his book of logarithms, Gauss recorded the discovery of his formula for the number of primes up to N in terms of the logarithm function. Yet despite the importance of the discovery, Gauss told no one what he had found. The most the world heard of his revelation were the cryptic words, 'You have no idea how much poetry there is in a table of logarithms.'

 
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If we except the great name of Newton (and the exception is one that the great Gauss himself would have been delighted to make) it is probable that no mathematician of any age or country has ever surpassed Gauss in the combination of an abundant fertility of invention with an absolute vigorousness in demonstration...

 
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Carl Friedrich Gauss, often rated the greatest mathematician of all time, played the market. On a salary of 1,000 thalers a year, Euler left an estate of 170,587 thalers in cash and securities. Nothing is known of Gauss's investment methods.

 
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Perhaps the most surprising thing about mathematics is that it is so surprising. The rules which we make up at the beginning seem ordinary and inevitable, but it is impossible to foresee their consequences. These have only been found out by long study, extending over many centuries. Much of our knowledge is due to a comparatively few great mathematicians such as Newton, Euler, Gauss, or Riemann; few careers can have been more satisfying than theirs. They have contributed something to human thought even more lasting than great literature, since it is independent of language.

 
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