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)

 

 



 

 

    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)

     

 

 

 

     The only way to learn mathematics is to do mathematics.
    学习数学的惟一方法是做数学。


           —— 哈尔莫斯(Paul Halmos)

 

 

 



 

   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)


 

 

 

 

 

  

    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.

     <拙译> 如果理智的好奇,职业的自豪和抱负心是研究工作的主要激励,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

 

        ——摘自《一个数学家的辩白》

            (A Mathematician's Apology)



 

 



    But on the whole the history of science is fair, and this is particularly true in mathematics. No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay it, is one of the soundest and steadiest of investments.
   
<拙译> 但在总体上讲,科学的历史是公平的,对数学尤然。没有一门其他的学科象数学一样有着如此清晰明确和被一致公认的标准,而那些被铭记的人几乎都是当之无愧的。数学上的荣誉,如果你有支付得起的现金的话,是最合理最稳固的投资之一。

                       ——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 (3) 

英文原文 (Original English Text)

巴拿赫与苏格兰咖啡馆和苏格兰笔记本

  作者:John Tabak      谢国芳(Roy Xie)译

  roixie@163.com

斯蒂凡·巴拿赫可以说是一个怪才,他很少花时间记下他的思想,读研究生期间他经常旷课,当他的一个老师认识到他所考虑的问题的深度时,就派学生伴随他,伺机问他问题,巴拿赫有问必答,执行此任务的学生回头将他的答复写成数学论文的形式,在投稿前交巴拿赫过目,以保证内容精确无误。

在取得数学博士学位后,巴拿赫继续他的与众不同的工作习惯,他在一个叫苏格兰咖啡馆的地方接待他的仰慕者,这是当时波兰的利维夫市——现在是乌克兰的利沃夫市的一个平庸无奇的场所,在整个十九世纪三十年代,当地的学者名流和外来的访客在这个咖啡馆里聚会,其中包括一些欧洲最优秀的数学家。

“课”于晚餐时分开始,参加者们常常活动到深夜,讨论数学,辩论各种思想,有时候也下下象棋。一度他们曾把他们的数学思想写在桌面和餐巾上,但桌面和餐巾并不是永久性的媒质,尤其是桌面,每晚都会被擦干净。一些数学家抱怨重要的工作在苏格兰咖啡馆被发现又被遗忘。后来终于有人买了一个笔记本,存放在咖啡馆里,人们提出数学问题并展开讨论,如果那一晚的参加者认为一个问题有价值,它就会被记录在笔记本里,连同其解答一起——假如能找到解答的话。

这个笔记本幸存到了第二次世界大战之后,尽管当时在苏格兰咖啡馆聚会的一些人没有,特别是巴拿赫在战争期间该城市被德军占领时吃足了苦头,他于一九四五年、就在苏联红军将德军逐出该城后不久去世。今天,这本珍贵的苏格兰笔记本被翻译成了多种语言。

--- 摘译自 John Tabak 的科普新著《超越几何——一种关于空间和形状的新数学》  

 

斯蒂凡·巴拿赫(Stefan  Banach, 1892-1945)

苏格兰咖啡馆(Scottish Café )

Banach, the Scottish Café and the Scottish Book

Stefan Banach was something of an eccentric. He rarely took the time to write down his ideas. During graduate school, he was often absent from classes. When one of his teachers realized the level at which Banach was thinking, students were assigned to accompany Banach and ask him questions. Banach answered the questions, and the students wrote his responses in the form of mathematics papers that Banach reviewed for accuracy prior to submitting them for publication. After receiving a Ph.D. in mathematics, Banach continued his unusual work habits by “holding court” in a place called the Scottish Café, a nondescript place in L’viv, Poland, now Lvov, Ukraine. Throughout the 1930s, local academics and guests --- and some of the finest mathematicians in Europe --- spent time at the café.

“Class” began about dinnertime. Participants often worked late into the night discussing mathematics, debating ideas, and sometimes playing chess. For a while they wrote their mathematical ideas on tabletops and napkins, but tabletops and napkins are not “permanent” media --- the tabletops, in particular, were wiped clean each night. Some mathematicians complained that important work was being discovered and forgotten at the Scottish Café. Eventually, someone bought a notebook, which was kept at the cafe. Mathematics problems were proposed and discussed, and if that night’s participants thought a problem worthwhile, it was recorded in the notebook along with any solutions if solutions could be found.

The Scottish Notebook survived World War 2, although some of the participants at the Scottish Café did not. Banach, in particular, suffered terrible hardships during the war when the city was under German occupation. He died in 1945, shortly after the Sovient army drove the German army from the city. Today the Scottish Notebook has been translated into numerous languages.

--- John Tabak, Beyond Geometry – A New Mathematics of Space and Form