This is really a question about the nature of mathematical insight. The ability to see patterns and connections that no one had seen before does not come easily. It is usually the product of months, if not years, of hard work. Little by little, the inkling of a new phenomenon or a theory emerges, and at first you don’t believe it yourself. But then you say: “what if it’s true?” You try to test the idea by doing sample calculations. Sometimes these calculations are hard, and you have to navigate through mountains of heavy formulas. The probability of making a mistake is very high, and if it does not work at first, you try to redo it, over and over again.
More often than not, at the end of the day (or a month, or a year), you realize that your initial idea was wrong, and you have to try some... (查看原文)
Mathematical concepts populate the Kingdom of Mathematics, just like species of animals populating the Animal Kingdom: they are linked to each other, form families and subfamilies, and often two different concepts mate and produce an offspring. (查看原文)
1. Edward Frenkel,UC Berkeley数学系教授,美国艺术与科学院院士,美国数学会会士,Hermann Weyl Prize得主。此外,他又是畅销书《Love&Math》作者,电影短片《Rites of Love&Math》的导演。这本《Love&Math》基本可以算是Edward的半自传,和Yau的《The Shape of Inner Space...
(展开)
18 有用 GoodMorning 2016-06-11 15:44:02
有个学弟和我说 因为这一本书把他从放弃数学的边缘拉了回来
2 有用 ZYN 2021-08-24 14:15:00
四年前一刷这本书,当时或许只感觉对我产生了微小的影响,但如今二刷发现我对数学的很多直觉最初都来自于这里。在我看来Frenkel是花了大功夫在做科普的,我不知道还有什么更好的写法,说他根本没想让人搞懂朗兰兹纲领的人也没错,毕竟Langlands program这些东西在熟知代数几何表示论代数拓扑代数数论前提下去读二三百页的专著都很难看懂。然后感慨一下,Frenkel当年在哈佛同届的好友Resheti... 四年前一刷这本书,当时或许只感觉对我产生了微小的影响,但如今二刷发现我对数学的很多直觉最初都来自于这里。在我看来Frenkel是花了大功夫在做科普的,我不知道还有什么更好的写法,说他根本没想让人搞懂朗兰兹纲领的人也没错,毕竟Langlands program这些东西在熟知代数几何表示论代数拓扑代数数论前提下去读二三百页的专著都很难看懂。然后感慨一下,Frenkel当年在哈佛同届的好友Reshetikhin,Serganova和Tsygan现在分别在Berkeley和Northwestern任教,虽说不是做他们领域的,却也都见了一面,世界可真小。 (展开)
4 有用 greatabel 2016-11-22 17:36:05
作为高中得过数学奥赛奖,觉得喜欢数学,后来数学系读了四年后来考验切换到计算机的人,偶要说:别听那些鸡汤,如果你真想做出点开创新贡献,自己智商觉得不能在100w人之内排到前10名,而且毅力也并非超常,还是最好切换方向吧:不然最多只能做个大学教授起个传承作用,做些修修补补微创新。
11 有用 阅微草堂 2017-03-05 12:51:06
也许我更应该提醒大家的是,某些内容一时看不懂其实无伤大雅。我在从事数学研究时,有90%的时间会有不甚明白的感觉,所以,不必紧张,欢迎来到我的世界。困惑(有时甚至是挫败感)是数学研究的一个必不可少的组成部分。范畴化,集合论转换成范畴论,关注:对象的内部到对象之间的关系(相互作用)的转变。向量空间是数值的范畴化,层是函数(赋值规则)的范畴化。函数式编程的基本概念就是范畴论的例子
1 有用 strider 2021-05-01 17:13:39
书是好书,但到后面真的看不懂,只好抛弃数学,只看爱了。