黎曼猜想

随后在1933年，剑桥的一位数学家S.斯奇乌斯表明，如果黎曼猜想是成立的，那么就会在之前找到一个转折点。

Then in 1933 a Cambridge mathematician , S. Skewes , had shown19 that if the Riemann Hypothesis were true , a crossover point would occur before which ,

这个命题被称为黎曼猜想。

This assertion had become known as the Riemann Hypothesis .

我想那一定是“黎曼猜想”。

I think it would be the Riemann Hypothesis .

数学家可以证明黎曼猜想吗？

Can mathematicians prove the Riemann hypothesis ?

这一结果与先前在广义黎曼猜想下得到的结果一样强。

This sharpens Hua 's result and is as good as what was previously derived from the Generalized Riemann Hypothesis ( GRH ) .

他认为黎曼猜想很可能是错误的，因为这么多大量的努力都不能证明它。

Apparently he had decided that the Riemann hypothesis was probably false , if only because such great efforts had failed to prove it .

在研究一般的原根生成算法的基础上，提出了一种不依赖于广义黎曼猜想的概率性多项式时间算法，该算法能够以指定的概率确保输出正确。

By analysing the generation algorithm of primitive root , we put forward a probabilistic algorithm , in which the error probability of this algorithm can be totally controlled .

人们现在要问，这个巨大的范围是否有可能缩小，或者说，是否有可能不依赖于黎曼猜想的正确性而找到一个范围。这就是艾伦现在要研究的问题。

It could be asked whether this enormous bound might be reduced , or whether one could be found that did not depend upon the truth of the Riemann Hypothesis , and these were the problems that Alan now undertook .

如果他觉得这种精度不足以供他研究黎曼猜想，他需要更高的精度，那就需要彻底改造物理设备——用更大的齿轮，或者更精确的平衡。

If he had then found that this accuracy was insufficient for his purpose of investigating the Riemann Hypothesis , and needed another decimal place , then it would have meant a complete reengineering of the physical equipment - with much larger gear-wheels , or a much more delicate balance .

庞加莱猜想和黎曼假设、霍奇猜想、杨-米尔理论等一样，被并列为七大数学世纪难题之一。

The Poincare Conjecture was rated as one of the major mathematical puzzles of the20th century .