Number rules the universe.

    数支配着宇宙。
              ——毕达哥拉斯(Pythagoras)

 

    Reason is immortal, all else mortal.

    理性是不朽的,其余一切都会消亡。
              ——毕达哥拉斯(Pythagoras)

 

 

    The highest form of pure thought is in mathematics”.

    数学是纯粹思维的最高形式。

                                  ——柏拉图(Plato)

 

     

    Nature’s great book is written in mathematical symbol.
    自然这本大书是用数学符号写的。
                             ——伽里略(Galileo)

 

    

    Mathematics is the Queen of the Sciences,and Arithmetic the Queen of Mathematics.

  数学是科学的皇后,而数论是数学的皇后。

                              ——高斯 Gauss

 

 

    Wir müssen wissen, wir werden wissen.

    We must know, we will know.

    我们必须知道,我们必将知道。

       ——希尔伯特(Hilbert)

 

 

    Pure mathematics is,in its way,the poetry of logical ideas.
    纯粹数学,就其本质而言,是逻辑思维的诗篇。
             ——爱因斯坦(Einstein)

 

 

    The science of mathematics presents the most brilliant example of how pure reason may successfully enlarge its domain without the aid of experience.
    数学科学呈现出一个最辉煌的例子,表明纯粹的理性如何能不借助实验而成功地扩大其领域。
                                    ——康德(Kant)

   

 

    Histories make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; moral, grave; logic and rhetoric, able to contend.

     历史使人聪明,诗歌使人机智,数学使人精细,哲学使人深邃,道德使人严肃,逻辑与修辞使人善辩。

              ——培根(Francis Bacon)

     

    Mathematics, rightly viewed, possesses not only truth, but supreme beauty, a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.
                
——罗素(Bertrand Russel)

 


 I believe in intuition and inspiration. Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution.

想像力比知识更重要,因为知识是有限的,而想象力则包罗万象,推动着进步,是进化的源泉。

       ——爱因斯坦(Einstein)


Logic will get you from A to B. Imagination will take you everywhere.
逻辑会把你从A引导到B,而想象力会把你引向任何地方。
       ——爱因斯坦
(Einstein)


 

    Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. "Immortality" may be a silly word, but probably a mathematician has the best chance of whatever it may mean.

    当埃斯库罗斯被人遗忘之际阿基米德仍会被人铭记,因为语言会死亡而数学思想不会。“长生不死”是一个愚蠢的词,但不管它实际上何所指,数学家当属首选。
   

                            ——哈代G.H.Hardy

   

 

    If intellectual curiosity , professional pride , and ambition are the dominant incentives to research , then assuredly no one has a fairer chance of gratifying them than a mathematician. His subject is the most curious of all --- there is none in which truth plays such odd pranks. It has the most elaborate and the most fascinating technique, and gives unrivalled openings for the display of sheer professional skill. Finally , as history proves abundantly , mathematical achievement, whatever its intrinsic worth , is the most enduring of all.

     如果理智上的好奇,职业上的自豪,和抱负心是研究工作的主要激励物,那么可以肯定没有谁比数学家享有更好地满足这些欲望的机会了。他的研究对象是世上最激发好奇心的——没有哪一个领域里的真理爱跟人耍如此奇诡的把戏。它具有最完善精致和最有趣迷人的工具,它给人表现纯粹的职业技巧无可匹敌的良机。最后,正如历史充分证明的那样,数学上的成就,无论它的内在价值如何,是世间最永久恒常的。
                  ——哈代G.H.Hardy

   

                                  数学大师原稿译注 ·  黎曼原稿 [1] 

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