[庞加莱] Mathematical Creation-01.pdfVIP

Mathematical Creation 数学创造 庞加莱 How is mathematics made? What sort of brain is it that can compose the propositions and systems of mathematics? How do the mental processes of the geometer or algebraist compare with those of the musician, the poet, the painter, the chess player? In mathematical creation which are the key elements? Intuition? An exquisite sense of space and time? The precision of a calculating machine? A powerful memory? Formidable skill in following complex logical sequences? A supreme capacity for concentration? 数学是由什么构成 的？哪种类型的大 脑能够创造数学的 定理和系统？几何 学家或是代数学家 的思维活动和音乐 家、是人画家和象棋 选手有什么不同？ 数学创造中，哪些是 关键元素？直觉？ 空间和时间的精确 感觉？机器一般的 计算准确性？超强 的记忆力？复杂逻 辑 推 导 的 超 强 技 能 ？ 极 好 的 注 意 力？ The essay below, delivered in 下面的文章，是本世 2 the first years of this century as a lecture before the Psychological Society in Paris, is the most celebrated of the attempts to describe what goes on in the mathematicians brain. Its author, Henri Poincaré, cousin of Raymond, the politician, was peculiarly fitted to undertake the task. One of the foremost mathematicians of all time, unrivaled as an analyst and mathematical physicist, Poincaré was known also as a brilliantly lucid expositor of the philosophy of science. These writings are of the first importance as professional treatises for scientists and are at the same time accessible, in large part, to the understanding of the thoughtful layman. 纪（20 世纪）初期 在巴黎心理学会上 做的一次报告，是描 述关于数学家大脑 如何运转的最著名 的尝试。该报告的作 者，亨利·庞加莱 （是政治家雷蒙德 的表亲），是承担该 任务的极其适当的 人选。作为历史上最 重要的数学家之一， 一位无可匹敌的分 析和数学物理学家， 庞加莱同样擅长对 科学哲学作出清晰 准确的阐释。这份报 告对于科学家们而 言是一极其重要的 专业论述，同时在很 大程度上，也可以为 非专业人士所理解。 Poincaré on Mathematical Creation 庞加莱 关于数学创 造 3 The genesis of mathematical creation is a problem which should intensely interest the psychologist. It is the activity in which the human mind seems to take least from the outside world, in which it acts or seems to act only of itself and on itself, so that in studying the procedure of