A mathematician , like a painter or a poet, is a maker of patterns ……The mathematician ’s patterns, like the painter’s or poet’s ,must be beautiful……Beauty is the first test:there is no permanent place in the world for ugly mathematics.
（数学家如画家或诗人一样，是款式的制造者．．．．．．数学家的款式，如同画家或诗人的款式，必须是美的……世上没有丑陋数学的永久立身之地。）
——哈代   
A peculiar beauty reigns in the realm of mathematics, a beauty which resembles not so much the beauty of art as the beauty of nature and which affects the reflective mind , which has acquired an appreciation of it , very much like the later.
（一种奇特的美统治着数学王国，这种美不像艺术之美与自然之美那么相类似，但她深深地感染着人们的心灵，激起人们对她的欣赏，与艺术之美是十分相象的。）
——库默 　 
May not Music be described as Mathematics of sence, Mathematics as Music of the reason? The soul of each the same! Thus the musician feels Mathematics, the mathematician thinks Music—Music the dream, Mathematics—the working life—each to receive its consummation from the other when the human intelligence, elevated to its perfect type, shall shine forth glorified in some future Mozart—Dirichlet or Beethoven—Gauss—a union already not indistinctly foreshadowed in the genius and lobours of a Helmholtz.
(难道不可以把音乐描绘成感觉的数学，而把数学描绘成理性的音乐吗？这样，音乐家感觉到数学，数学家想到音乐——音乐是梦想，数学是工作的一生——每一方都经由对方达到尽善尽美的境地，那时，人类的智慧达到完美的典型，将在某个未来的莫扎特——狄利克雷或贝多芬——高斯的歌颂下而光彩夺目。这种联合已经在一个赫姆霍尔兹的天才和工作中清楚地预示出来了。）
——西尔弗斯特

I like to look at mathematics almost more as an art than as a science, for the activity of the mathematician, constantly creating as he is , guided though not controlled by the external world of the senses, bears a resemblance, not fanciful I believe but real, to the activity of an artist, of a painter let us say. Rigorous deductive reasoning on the part of the mathematician may be likened here to technical skill in drawing on the part of the painter. Just as no one can become a good painter without a certain amount of skill, so no one can become a mathematician without the power to reason accurately up to a certain point. Yet these qualities, fundamental though they are , do not make a painter or mathematician worthy of the name, no indeed are they the most important factors in the case. Other qualities of a far more subtle sort, chief among which in both cases is imagination, go to the making of a good artist of good mathematician.
（一般地说，我更想把数学视为是艺术，而不是科学。因为我们可以说，数学家的活动，当他受外部的理性世界所引导，而不是被控制时，不断地进行创造性的活动，与一个艺术家、一个画家的活动相类似，有着实在的，不是虚幻的相似点。数学家这一方面的严密演绎推理可以比喻为画家那一方面的绘画技巧。恰如没有一定技巧的人不能成为一位好画家一样，没有一定的精密推理能力的人不能成为一位好的数学家。但是，这些尽管是他们的基本特质，还不足以使一个画家或数学家名副其实，画图技巧与推理能力，说实在的，终究不是最重要的因素。远为敏感的，为二者都是主要的一类特质是想象力，它才能造就一名杰出的艺术家或杰出的数学家。）
——博歇   
 We can hope that as education and leisure develop more people will enjoy music and painting. But the number of people who really enjoy mathematics is very small.
(我们能够期待，随着教育与娱乐的发展，将有更多的人欣赏音乐与绘画。但是，能够真正欣赏数学的人数是很少的。)
——贝尔斯