数学精英

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  2011-11-29
  In short he (Archimedes) used his mechanics to advance his mathematics. This is one of his titles to a modern mind: he used anything and everything that suggested itself as a weapon to attack his problems.
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  2011-11-29
  Archimedes made his own occasions. Sitting before the fire he would rake out the ashes and draw in them. After stepping from the bath he would anoint himself with olive oil, according to the custom of the time, and then, instead of putting on his clothes, proceed to lose himself in the diagrams which he traced with a finger-nail on his own oily skin.
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  2011-11-29
  ... the common whole numbers 1,2,3 ... are insufficient for the construction of mathematics even in the rudimentary form in which he (Pythagoras) knew it. [...] This was what knocked his theory flat: it is impossible to find two whole numbers such that the square of one of them is equal to twice the square of the other. [...] Actually Pythagoras found his stumbling-block in geometry: the ratio of the side of a square to one of its diagonals cannot be expressed as the ratio of any two whole numbers. This is equivalent to the statement above about squares of whole numbers. In another form we would say that the square root of 2 is irrational, that is, is not equal to any whole number or decimal fraction, or sum of the two, got by dividing one whole number by another.
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  2011-11-29
  Of all the ancients Archimedes is the only one who habitually thought with the unfettered freedom that the greater mathematicians permit themselves to-day with all the hard-won gains of twenty-five centuries to smooth their way, for he alone of all the Greeks had sufficient stature and strength to stride clear over the obstacles thrown in the path of mathematical progress by frightened geometers who had listened to the philosophers. [...] Had the Greek mathematicians and scientists followed Archimedes rather than Euclid, Plato, and Aristotle, they might easily have anticipated the age of modern mathematics, which began with Descartes (1596~1650) and Newton in the seventeenth century, and the age of modern physical science inaugurated by Galileo (1564~1642) in the same century, by 2,000 yea...
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  2011-11-29
  Mathematics then has had four great ages: the Babylonian, the Greek, the Newtonian (to give the period around 1700 a name), and the recent, beginning about 1800 and continuing to the present day. Competent judges have called the last the Golden Age of Mathematics.
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  2011-11-29
  The nineteenth century, on this scale, contributed to mathematical knowledge about five times as much as was done in the whole of preceding history.More important than the technical algebra of these ancient Babylonians is their recognition - as shown by their work - of the necessity for proof in mathematics. Until recently it had been supposed that the Greeks were the first to recognize that proof is demanded for mathematical propositions.
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  2011-11-29
  It is probably correct to say that as a class they (mathematicians) have tended slightly to the left in their political opinions.An impartial account of western mathematics, including the award to each man and to each nation of its just share in the intricate development, could be written only by a Chinese historian. He alone would have the patience and the detached cynicism necessary for disentangling the curiously perverted pattern to discover whatever truth may be concealed in our variegated occidental boasting.... the nineteenth century, prolonged into the twentieth, was, and is, the greatest age of mathematics the world has ever known. Compared to what glorious Greece did in mathematics the nineteenth century is a bonfire beside a penny candle.From the earliest times two opposing t...
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  2011-11-29
  After all, the whole purpose of science is not technology - God knows we have gadgets enough already; science also explores depths of a universe that will never, by any stretch of the imagination, be visited by human beings or affect our material existence. So we shall attend also to some of the things which the great mathematicians have considered worthy of loving understanding for their intrinsic beauty.Lagrange believed that a mathematician has not thoroughly understood his own work till he has made it so clear that he can go out and explain it effectively to the first man he meets on the street.... the first time something new is studied the details seem too numerous and hopelessly confused, and no coherent impression of the whole is left on the mind. Then, on returning after a rest,...
• v_etch

  2011-03-09
  为了避免把复杂的数学论证压缩成简短明了的形式带来的麻烦，他常常删去一切论证，只留下结论和一句乐观的评语“显而易见”。他自己常常会花费几个小时——有时几天——的艰苦劳动，才能把他据以“看出”这些容易的事情的推理再现出来。甚至聪明的读者也很快就染上了只要那句著名的短剧一出现就叹息的习惯，知道十有八九他们又得白费力气的干上一个星期。
• v_etch

  2011-03-09
  丹尼尔年轻的时候，一次在旅行中与一位有趣的陌生人聊天，他客气地自我介绍：“我是丹尼尔.伯努利。”“我吗，”那个人讽刺的说：“艾萨克.牛顿。”丹尼尔终身都为此高兴，把这作为他受到的最真实的称颂。
• 海若

  2014-03-23
  对阿基米德现代性的第二个断定也是基于他的方法。他比牛顿和莱布尼茨领先两千多年发明了积分学。
• 海若

  2014-03-23
  阿基米德不是创作了一件杰作，而是创作了许多杰作。……。简言之，他用了他的力学去推进他的数学。这是称他具有现代头脑的原因之一：他用了可以当做武器的一切东西去攻击他的问题。
• 海若

  2014-03-23
  阿基米德有一个怪癖，与另一个大数学家魏尔斯特拉斯相似。据魏尔斯特拉斯的姐姐说，当她弟弟是一个年轻的中学教师时，要是在他的视线之内有一平方英尺干净的贴墙纸或一个干净的袖头，就不能放心地把一只铅笔交给他。阿基米德打破了这个记录。在他那个时候，一片铺满了沙的地板，或满是尘土的坚硬而光滑的地面，就是一种普通的“黑板”。阿基米德是一只孤独的鹰。
• 海若

  2014-03-23
  根据传说，按照伟大的数学家应该是什么样子流行观念，阿基米德是一个完美的范例。当他沉浸在数学中的时候，他像牛顿和哈密顿一样连吃饭也忘记了（其实还有高斯等等）。在对待穿着的不经意方面，他甚至超过了牛顿。