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1·Can mathematicians prove the Riemann hypothesis?

数学家可以证明黎曼猜想吗？

2·So, do not cry, there is healthy life without the Riemann hypothesis.

所以，不要哭，没有黎曼假设依然能够有健康的生活。

3·Analytic number theory is fortunate to have one of the most famous unsolved problems, the Riemann hypothesis.

解析数论非常幸运还有一个最为有名的未解决的问题，即黎曼假设。

4·In concluding this talk I wish to emphasize my advocacy for analytic number theory by saying again that the theory flourishes with or without the Riemann hypothesis.

在结束这次讲话时，我愿通过再次说明，数论将在无论有还是没有黎曼假设的情况下继续繁荣，来强调我对于解析数论的拥护。

5·Actually, many brilliant ideas have evolved while one was trying to avoid the Riemann hypothesis, and results were found which cannot be derived from the Riemann hypothesis.

事实上，在人们试图回避黎曼假设时，许多有才气的想法获得进展，发现了一些绝对不可能得自黎曼假设的结果。