元数学！
Meta Math!
Gregory Chaitin · 初版 2005 年
11人推荐
17位读者提及
23次提及
为什么值得读
- 将哥德尔不完备定理与图灵停机问题紧密串联
- 从极简主义视角探讨优秀数学概念的评价标准
- 风格比硬核专著更平易近人，读来轻松有趣
在 Meta Math! 中，世界顶尖数学家之一 Gregory Chaitin 带领我们踏上了一段引人入胜的科学发现之旅，并阐明了他得出开创性理论的过程。所有的科学都建立在数学基础之上，但数学家们已经痛苦地意识到，数学本身存在着严重的局限性。这一观念最早在二十世纪数学界的两位泰斗 Kurt Godel 与 Alan Turing 的研究中显现出来。如今，他们的后继者 Gregory Chaitin 进一步深入挖掘数学的基础，证明了数学中充斥着……
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……讨论的不是‘自然’，而是我们关于‘自然’的信息。但物理学当时还没有能够在那个层面表达思想的词汇，因此只能不断摸索。” >我们对“无限”理解得很透彻啊。我挺喜欢 Gregory Chaitin 的《Meta Math》：http://arxiv.org/abs/math/0404335 “所以实数集虽然在几何上是很自然的——甚至是直观直接给出的——却依然相当难以捉摸：我凭什么要相信……
…discussing not Nature, but our information about Nature. But physics did not have the vocabulary for expressing ideas on that level, hence the groping." >we understand "infinity" just fine. I enjoyed "Meta Math" by Gregory Chaitin: http://arxiv.org/abs/math/0404335 "So the set of real numbers, while natural—indeed, immediately given— geometrically, nevertheless remains quite elusive: Why should I believe in…
我不确定“除非真的非用不可，否则尽量别用[反证法]”是不是最好的结论。在《Meta Math》[1]中，Gregory Chaitin 探讨了这样一个问题：“是什么让一个数学概念变得令人向往？”答案是简单性。最好的定理事后看来都很显然，因为它们被简化成了……之间的关系
I'm not sure "try not to use [proof by contradiction] unless you really need it" is the optimal conclusion. In "Meta Math"[1], Gregory Chaitin explores the question: "What makes a mathematical concept desirable?" Simplicity was the solution. The best theorems seem obvious in retrospect, because they are reduced into relationships…
我大概每年都会重读一遍《Gödel's Proof》。你可能也会对 Gregory Chaitin 的《Meta Math! The Quest For Omega》感兴趣，它（除了其他内容外）把停机问题和哥德尔联系了起来。不过先提醒一句，这本书风格相当独特/古怪，你可能从书名就能看出来了。
I try to read Godel's Proof once a year or so. You might also be interested in Gregory Chaitin's Meta Math! The Quest For Omega, which relates the halting problem (among other things) to Godel. A word of warning though, the book is rather idiosyncratic, as you might have seen from the title.
Chaitin 的《Meta Math》也挺值得一读。读起来没《G.E.B.》那么累。
Chaitin's "meta math" is also a good read. Less arduous than G.E.B.
……http://www.amazon.com/Concrete-Mathematics-Foundation-Comput... ）由 Graham、Knuth 和 Patashnik 合著——它是基于自 1970 年以来在斯坦福教授的课程编写的，真的非常非常棒。我觉得你还应该入手的另一本书是 Gregory Chaitin 写的《Meta Math: The quest for Omega》（http://www.amazon.com/Meta-Math-Quest-Gregory-Chaitin/dp/140... ）。它不太算是一本数学教材，主要是作者对自己最喜欢的……话题的见解
…http://www.amazon.com/Concrete-Mathematics-Foundation-Comput... ) by Graham, Knuth & Patashnik - It's based on the course taught at Stanford since 1970 & it's really really good. Another book I think you should get is Meta Math: The quest for Omega( http://www.amazon.com/Meta-Math-Quest-Gregory-Chaitin/dp/140... ) by Gregory Chaitin. It's not really a math course book, and is mostly the authors take on his favorite topics in…
对这个感兴趣的人肯定会非常喜欢 Gregory Chaitin 写的《Meta Math!》。基本上，他论证了存在一些随机为真的定理：它们为真并没有什么特别的理由。当然，这与哥德尔的工作有着深刻的联系。如果有人……
Anyone interested in this would immensely enjoy Meta Math! by Gregory Chaitin. Basically, he demonstrates that there are theorems which are randomly true: they're true for no particular reason. It's, of course, deeply connected with Gödel's work. If anyone's…