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Carl Friedrich Gauss

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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.'

 
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.

 
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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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Euclid manages to obtain a rigorous proof without ever dealing with infinity, by reducing the problem [of the infinitude of primes] to the study of finite numbers. This is exactly what contemporary mathematical analysis does.

 
Lucio Russo
 

It is a contradiction in terms and ideas to call anything a revelation that comes to us at second hand, either verbally or in writing. Revelation is necessarily limited to the first communication. After this, it is only an account of something which that person says was a revelation made to him; and though he may find himself obliged to believe it, it cannot be incumbent on me to believe it in the same manner, for it was not a revelation made to me, and I have only his word for it that it was made to him.

 
Thomas Paine
 

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...

 
Henry John Stephen Smith
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