黎曼

Congratulations your paper is very BRIGHT and even encompasses all the precedings ones by its clarity about the functional equation, the definition of the unctions, etc.

祝贺，你的论文（陈一文注：指蒋春暄最新的论文《Riemann paper (1859) is false》，即《黎曼的论文（1859）是错误的》）非常聪明，在函数方程式、函数定义方面的清晰性方面涵盖了所有以前的论文。

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

& [6] &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。

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。

The problem of sub-Riemannian geodesics is a Lagrange problem with constraint. How to describe the constraint condition "γ'∈ D, a. e." is a difficult problem.

次黎曼测地线问题是变分学中的一个有约束的Lagrange问题，但在变分的过程中有个难点―如何推出约束条件&γ'∈D，在上几乎处处成立&的解析式。

In the case of general relativity Einstein did not himself invent new mathematical tools, but applied ideas on non-Euclidean geometry developed by Riemann, Ricci, Livi-Civita and others.

在广义相对论方面，他并没有发明新的数学工具，只是运用了由黎曼、里奇、勒维-契维塔以及其他一些人发展起来的非欧几里德几何方面的思想。他在数学方面并不突出，比不上牛顿。

It is embodied in the three research programs of modern physics:(1) According to the program of geometrization of physics, the essence of the Curved Space in gravitational field needs to be explicated by Riemannian geometry, differential geometry, tensor analysis;(2)According to the program of quantum field theory, the generation and annihilation operator can represen...

它分别体现在现代物理学的三大研究纲领中：(1)根据物理学的几何化纲领，引力场弯曲空间的奥秘需要通过黎曼几何、微分几何与张量分析来解读；(2)根据量子场论纲领，场理论的&产生和湮灭&算符，能方便而精确地表征和重构相关的微观作用机制；&场的本体论&和&生成辩证法&同时得到体现。

DoCarmo, Riemannian Geometry.

标准的黎曼几何教材

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。

I can imagine a clever person who proves the Riemann hypothesis, only to be disappointed not to find new important applications.

我可以想象一个证明了黎曼假设的聪明的人因为未能发现新的重要应用儿失望。

It is a significant and challenging subject to apply the theory of Riemann Geometry into the fields of digital image processing.

将黎曼几何学的理论应用到数字图像处理学之中，是一个非常有意义、并且富有挑战性的课题。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。