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January 5, 2020 54 min
主播 小果汁 (https://fom.fm/hosts/ijoy) 帽子君 (https://fom.fm/guests/hat) 嘉宾介绍 为什么喜欢数学? 数学系都学些什么? 数学家的思维方式是怎样的? 数的直觉-自然语言的抽象化 最早的计数可能出现在文字之前 语言出现以后,依靠量词用来表示真实世界的属性,数词渐渐抽象出来 人类把数作为共同性质抽象出来,并采用与大多数具体事物无关的某个语音来替代它 数学产生的标志 人类社会属性的认知,就是一个把真实世界抽象化的过程 形的直觉-几何 几何-尼罗河的馈赠 对自然的观察 古埃及&古巴比伦文明的数学发展 希腊人的出场 思想环境:宗教和祭祀不再限制思想,城邦社会的唯理主义,可以去两大河谷文明学习 毕达哥拉斯 柏拉图-最早对证明的强调 柏拉图和他建立的学园,在数学史上有什么贡献 无理数的认识,人对未知的定义 数学家舍弃全盘的勇气——反证法 什么是演绎推理? 芝诺悖论 从应用题到证明题的认知蜕变 能看到的不是真实-表现与本质的分离 观察者对世界认识的偏差 柏拉图之后的古希腊数学家 亚里士多德 欧几里得与《几何原本》 非欧几何的发现 同时代的中国算数 质数无穷多的证明 人对∞的想象 在朴素唯物主义中一枝独秀的理性主义 尾声&下期预告 联系我们 (mailto:hi@fom.fm) 订阅方式 (https://fom.fm/subscribe) Special Guest: 帽子君.
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