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)

 

 

 

 

 

    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)

 

 

 



 

   A true mathematician who is not also something of a poet will never be a perfect mathematician.
    一个没有几分诗人气质的数学家永远不可能成为十全十美的数学家。
             ——魏尔斯特拉斯(Weierstrass)







    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.
   < 拙译> 数学,当你正确地看待它时,不仅拥有真,而且拥有非凡的美 —— 一种犹如雕塑般冷峻而素朴的美,一种不引诱任何我们的较软弱天性的美,一种没有绘画和音乐那样富丽花俏的装饰的纯净之至的美,同时又能达到一种唯有最伟大的艺术才能表达的严格的完美。
               ——罗素(Bertrand Russell








   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.
   < 拙译> 正如在诗歌中一样,在数学中同样能找到真正的欢乐的精神,升华的快感,那种超越凡俗接近神祗的美妙感觉——它是最高等级的卓越成就的试金石。
               ——罗素(Bertrand Russell







    Besides language and music, it [mathematics] is one of the primary manifestations of the free creative power of the human mind, and it is the universal organ for world-understanding through theoretical construction. Mathematics must therefore remain an essential element of the knowledge and abilities which we have to teach, of the culture we have to transmit, to the next generation.
    < 拙译> 数学是除了语言与音乐之外,人类心灵自由创造力的主要表达方式之一,而且它是通过理论的构建理解宇宙万物的普适工具。因此,数学必须始终是我们得传授给下一代的知识和技能的要素和我们要传承给下一代的文化的要素。
                   ——外尔(Hermann Weyl)

     

 








    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.

    < 拙译> 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

         ——摘自《一个数学家的辩白》

            (A Mathematician's Apology)


 

 

 

 


 

数学传奇故事·英汉双语阅读 (4) 

英文原文 (Original English Text)

哈密尔顿自叙发现四元数的美妙瞬间

    谢国芳(Roy Xie)译

  roixie@163.com

“明天将是四元数诞生十五周年的记念日,它们是一八四三年十月十六日以完全长成的姿态横空出世,或者说得见天日的,当时我正携夫人步行去都柏林,刚好走到布鲁穆桥上。 这就是说,我在那个地方在那一瞬间感到思想的电路接通了,从中迸发出的火花就是 i,j,k 之间的基本关系式,一如我自那以后一直在使用的那样。我当场抽出一个随身携带的笔记本——这个本子现在还在——记下了它, 在那一刻,我觉得发现它也许值得我耗费至少十年(甚或十五年)的辛苦劳动。然而公正地说,这是因为我觉得在那一刻一个难题被解决了,一种知性上的渴求得到了满足,在这之前,它已经纠缠了我至少有十五个年头了。”

“……我同样抑止不住一种强烈的冲动用一把小刀在布鲁穆桥的一块石头上刻下符号 i,j,k 满足的基本公式,那就是 i² = j² = k² = ijk = -1.” 

 

--- 摘译自哈密尔顿写给朋友和儿子的两封信  

 

布鲁穆桥上的四元数石碑

注:哈密尔顿原来的石刻已被岁月消蚀,此碑为后来爱尔兰人为纪念哈密尔顿而刻,

现在已成为旅游景点,有机会去都柏林不可不看。

 

纪念哈密尔顿的邮票

 

Hamilton’s Own Account of the Discovery of Quaternions

"Tomorrow will be the fifteenth birthday of the Quaternions. They started into life, or light, full grown, on the 16th of October, 1843, as I was walking with Lady Hamilton to Dublin, and came up to Brougham Bridge. That is to say, I then and there felt the galvanic circuit of thought closed, and the sparks which fell from it were the fundamental equations between i, j, k, exactly such as I have used them ever since. I pulled out, on the spot, a pocketbook, which still exists, and made an entry, on which, at the very moment, I felt that it might be worth my while to expend the labour of at least ten (or it might be fifteen) years to come. But then it is fair to say that this was because I felt a problem to have been at the moment solved, an intellectual want relieved, which had haunted me for as least fifteen years before."

".... Nor could I resist the impulse to cut with a knife on a stone of Brougham Bridge, as we passed by it, the fundamental formula with the symbols i, j, k; namely, i² = j² = k² = ijk = -1."

--- Extracts from Hamilton's letters to a friend and his son