如果你对 Metamath 的核心教材感兴趣，那就是诺曼·梅吉尔（Norman Megill）和大卫·A·惠勒（David A. Wheeler）合著的《Metamath：数学证明的计算机语言》（Metamath: A Computer Language for Mathematical Proofs）。你可以在这里买到精装版：http://www.lulu.com/shop/norman-megill-and-david-a-wheeler/m... 完整……
If you're interested in the main book on Metamath, it is "Metamath: A Computer Language for Mathematical Proofs" by Norman Megill & David A. Wheeler. You can get the hardcover here: http://www.lulu.com/shop/norman-megill-and-david-a-wheeler/m... Full…
…verifier software, but from the perspective of us humans we don't choose when a proof checks out or not in a formal system, mathematics does. EDIT: if you are into ML and like this idea, certainly check out MetaMath, the book is very accessible, and the author (Norman Megill) is extremely friendly and helpful. It takes perhaps a few days to a week to learn, study, and reimplement the verifier. One does not at all…
Related: Metamath (http://www.metamath.org) is a tiny formal language for writing proofs in symbolic logic, as well as a tiny proof checker for the language. The author, Norm Megill, has used Metamath to formalize many…
Appeal to "actual" authority is still appeal to authority. Consider an unproven theorem in the MetaMath database. Now consider an amateur mathematician, or perhaps a high school student finding and formalizing a proof. Irrespective of how (un)interesting the theorem is, Norman Megill and the users of MetaMath…
Correct. The good news that Elements still works otherwise, you just need to add the missing axiom. But many other "proofs" have been found to be false. The book "Metamath: A Computer Language for Mathematical Proofs" (by Norm Megill and yours truly) is available at: https://us.metamath.org/downloads/metamath.pdf - see section 1.2.2, "Trusting the Mathematician". We list…
如果你对 Metamath 的核心教材感兴趣，那就是诺曼·梅吉尔（Norman Megill）和大卫·A·惠勒（David A. Wheeler）合著的《Metamath：数学证明的计算机语言》（Metamath: A Computer Language for Mathematical Proofs）。你可以在这里买到精装版：http://www.lulu.com/shop/norman-megill-and-david-a-wheeler/m... 完整……
If you're interested in the main book on Metamath, it is "Metamath: A Computer Language for Mathematical Proofs" by Norman Megill & David A. Wheeler. You can get the hardcover here: http://www.lulu.com/shop/norman-megill-and-david-a-wheeler/m... Full…
……验证器软件，但从我们人类的角度来看，在一个形式系统中一个证明是否成立并不是由我们决定的，而是由数学决定的。编辑：如果你对机器学习（ML）感兴趣并且喜欢这个想法，一定要看看 MetaMath，这本书非常通俗易懂，而且作者（Norman Megill）非常友善且乐于助人。大概只要几天到一个星期就能学会、研究透并自己重新实现一个验证器。完全不用……
…verifier software, but from the perspective of us humans we don't choose when a proof checks out or not in a formal system, mathematics does. EDIT: if you are into ML and like this idea, certainly check out MetaMath, the book is very accessible, and the author (Norman Megill) is extremely friendly and helpful. It takes perhaps a few days to a week to learn, study, and reimplement the verifier. One does not at all…
相关：Metamath（http://www.metamath.org）是一种用于在符号逻辑中写证明的微型形式语言，同时也是该语言的一个微型证明检查器。作者 Norm Megill 用 Metamath 形式化了许多……
Related: Metamath (http://www.metamath.org) is a tiny formal language for writing proofs in symbolic logic, as well as a tiny proof checker for the language. The author, Norm Megill, has used Metamath to formalize many…
诉诸“实际的”权威仍然是诉诸权威。想想 MetaMath 数据库里一个未经证明的定理。再想想一个业余数学家，或者也许一个高中生找到并形式化了一个证明。不管这个定理多么（不）有趣，Norman Megill 和 MetaMath 的用户们……
Appeal to "actual" authority is still appeal to authority. Consider an unproven theorem in the MetaMath database. Now consider an amateur mathematician, or perhaps a high school student finding and formalizing a proof. Irrespective of how (un)interesting the theorem is, Norman Megill and the users of MetaMath…
没错。好消息是《几何原本》在其他方面依然成立，你只需要补上缺失的公理就行。但许多其他的“证明”已被发现是错误的。由 Norm Megill 和鄙人合著的《Metamath：数学证明的计算机语言》一书可以在这里获取：https://us.metamath.org/downloads/metamath.pdf —— 请参阅第 1.2.2 节，“信任数学家”。我们列出了……
Correct. The good news that Elements still works otherwise, you just need to add the missing axiom. But many other "proofs" have been found to be false. The book "Metamath: A Computer Language for Mathematical Proofs" (by Norm Megill and yours truly) is available at: https://us.metamath.org/downloads/metamath.pdf - see section 1.2.2, "Trusting the Mathematician". We list…