观点 2：认为应用数学差劲的人是差劲的数学家
Doron Zeilberger: 1995 年 5 月 2 日。
我只是在开玩笑。他们不是差劲的数学家，因为他们根本就不是数学家。真正的数学家尊重数学的所有部分，他们不相信诸如"纯粹的"、"应用的"、"理论的"、"实践的"、"概念的"、"计算的 "等对数学的武断划分。数学是一张网，是一张无限维度的织锦，一切都交织在一起。
有些人，如 G.H.Hardy 和 Paul Halmos，像柏拉图和亚里士多德一样自欺欺人，认为 "纯粹的"，不管它意味着什么，都比"应用的"，不管它意味着什么，更纯粹。柏拉图式数学的命运如今正迅速加入柏拉图式、先验的、非实验的物理学的命运。
我的胡言乱语是针对哈尔莫斯的文章《AppliedMathematics is Bad Mathematics》，转载于他的《Selecta》一书。矛盾的是，正如 Peter Doyle 向我指出的，他在那里举的纯数学的例子 :Tutte 等人的 "squaring the square"，是由 "应用"数学，即电路，所激发的。
转念一想，Hardy 和 Halmos 都是数学家。Hardy 尽管有哲学上的错误，但仍然是一位伟大的数学家，即便是最广泛的意义上而言。Halmos 也是一位不错的数学家，他只是有时会说些胡话。
对观点的观点：
仅以此送给所有认为数学存在鄙视链，并以此鄙视其他人的伪数学家；一并送给营造学术壁垒，垄断话语权的学阀。再并送给羞于实践并以实践为耻，端坐在海市蜃楼上颐指气使，为千秋万代努力编织神话的肉食者。
观点 98: 不要爱上你的模型。我最近证明 P=NP 的警示故事
Doron Zeilberger: 2009 年 4 月 1 日
人类将是人类。物理和数学世界是无限复杂的，我们这些卑微的人类不可能希望对正在发生的事情有任何真正的了解。当然，我们有"令人印象深刻"的科学和数学知识的外表，但与上帝的思想相比，这一切都是完全微不足道的，也是完全错误的，我们的预测之所以"经常"出现"正确"，是一种光学幻觉和一厢情愿。
因为科学、数学和经济学是如此困难，事实上是难以解决的，所以人类想出了非常简单的、完全天真的模型。它们在开始时都有一个"免责声明"：这只是一个模型，不应过于认真。但是这些人类一说完这些敷衍的话--就像外科医生的警告一样--他们就忘了这一切，真正相信这些模型是准确的，可以在现实世界中使用。
我们都知道所有这些来自华尔街的量化奇才的下场，他们宁愿拥有 30 万的起薪（奖金前），而不是 5 万，作为一个客座助理教授，（好像你的工资乘以 6 会让你快乐 6 倍，恰恰相反！），并开发了所有那些有缺陷的模型。看看他们现在在哪里？现在他们正在申请数学研究生院，因为，他们突然意识到"他们真正的爱和力量是纯数学"。
但这并不是这篇文章的主要观点。主要的一点是评论我最近的"突破"，即 P=NP。我之所以不大肆宣扬（肯定也不会去领克莱基金会的一百万美元奖金，因为正如我上面所说，钱越多越悲惨，而我宁愿继续快乐地分文不取），是因为这个解决方案结果是非常反常的。它所做的只是证明这个问题是愚蠢的，因为它是基于当代计算机科学有缺陷的教条，将简单等同于"多项式时间"。我的证明中的 "多项式 "算法有一个巨大的指数和一个巨大的常数，这使得它在今天（以及任何一天）的计算机上远远不可行。
但我真的希望我的解决方案不是徒劳的。谁知道呢，也许至少有人会意识到，人类试图做科学和数学是多么的徒劳，即使有计算机的帮助，因为，不幸的是，计算机仍然是由人类编程的，而这些人类不能被信任去开发现实的模型。也不能相信他们会开发玩具模型，因为他们很快就会忘记这些是修补玩具，这样就会危及我们所有人。
所以，让我们谦虚一点，忘记科学和数学，回到旧时代的宗教，崇拜上帝，只有他知道发生了什么。
对观点的观点：
华尔街的金融家博取学术地位的事例不由得让人联想到新兴的资产阶级暴发户购买贵族头衔，而囊中羞涩的破落贵族也正需要钱来装点门户，于是他们达成可鄙的交易，用加入对方来承认彼此的合法性。多么伟大的双赢！诺贝尔获得了金币，而斯坦福则获得了声誉，只有群众蒙在鼓里！这是一个社会玩具，一场社会游戏。
P vs NP 则是一个学术玩具。但相当有欺骗性。它的出发点是好的：开始我们只关心问题“是否有解”，后来“是否可解”，再次“如何解”，现在“解算过程多复杂”。可以看到，提问越来越接近实践。（这里呈现的是逻辑过程，历史过程则大多相反）但正是这个本该面向工程、面向实践的问题，理论探索偏离了实践轨道。一个高次的多项式算法和一个指数复杂的算法，只能在无穷意义上被区分开来，而无穷是理论的一种假设，它无法在实践中得到呈现。在实践中，计算机并不包容一切多项式算法，他们只偏爱 O(n)，最多带几个 log n 罢了。因此，当理论计算机学家高兴地宣布把 O(n3)降为 O(n2.9)，算法工程师找来他们的证明，翻拣他们丢进垃圾桶 O 里的东西后，失望的离开。比起理论证明，他们更愿意相信“启发式”，因为面前的邪恶机器并不允许他们拥有那个万能的垃圾桶。
倒退回上帝并非谦虚，反而是一种傲慢，因为上帝也是人类创造的玩具，或者说是人类创造的乐园，而人们甘愿成为其中的玩具。这正如面对机器轰鸣的旧贵族试图倒退回田园牧歌一样愚蠢。承认人类的无知、上帝的幻灭、世界的崩坏，抑或世界本身就是矛盾的，我们要做的正是拥抱它。
（原谅我的一股子翻译腔，这种题材我实在不知如何遣词造句，包括这句话）
附录是原文
Opinion 2:People who believe that Applied Math is Bad Math are Bad Mathematicians
By: DoronZeilberger
Written:May 2, 1995.
I was justkidding. They are not bad mathematicians, because they are not mathematiciansat all. A true mathematician has respect for all parts of mathematics, and doesnot believe in arbitrary divisions into 'Pure', 'Applied','Theoretical','Practical', 'Conceptual', 'Computational'. Mathematics is a Web,an infinite dimensional tapestry with everything intertwined.
Somepeople, like G.H.Hardy and Paul Halmos, deceive themselves, like Plato andAristotle, that 'pure', whatever it means, is purer than 'applied', whatever itmeans. The fate of Platonic mathematics is nowadays quickly joining the fate ofPlatonic, a priori, non-experimental, physics.
My rantingand raving is a propos Halmos's article 'Applied Mathematics is BadMathematics' reproduced in his'Selecta' volume. Paradoxically, as Peter Doylepointed out to me, the example of pure math he gives there: Tutte et. al's'squaring the square', was motivated by 'applied' math, i.e. ElectricalCircuits.
On secondthought, both Hardy and Halmos are mathematicians. Hardy, in spite of hisphilosophical errors, is still a great mathematician, even in the broad senseof the word. Halmos is also a good mathematician, he just sometimes saysnonsense.
Opinion 98:Don't Fall In Love With Your Model: The Cautionary Tale of my Recent proof that P=NP
By DoronZeilberger
Written:April 1(!), 2009
Humans willbe humans. The physical and mathematical worlds are infinitely complex, andthere is no way that we, lowly humans, can ever hope to have any realunderstanding of what is going on. Sure enough, we have the appearance of an"impressive" body of scientific and mathematical knowledge, butcompared to the mind of G-d, it is all utterly trivial, and also totally wrong,and the reason that "often" our predictions come out"right" is an optical illusion and wishful thinking.
Becausescience, math, and economics are so hard, in fact intractable, human beingscame up with very simplistic, utterly naive, models. They all start out with a"disclaimer": this is only a model, and should not be taken tooseriously. But as soon as these humans finish these perfunctory words-just likethe Surgeon General's warning- they forget all about it, and truly believe thatthese models are accurate and can be used in the real world.
We all knowwhat happened to all these quants whiz-kids from Wall Street, who preferred tohave a starting salary (before bonuses) of 300K, as opposed to 50K, as avisiting assistant professor, (as though multiplying your salary by six wouldmake you six times happier, quite the contrary!), and developed all thoseflawed models. Look where they are now! Now they are applying to mathematicsgraduate school, because, all of a sudden they realized that "their reallove and strength is pure mathematics".
But this isnot the main point of this post. The main point is to comment on my recent"breakthrough" that P=NP. The reason that I am not making such a bigdeal about it (and definitely I am not going to claim the one million dollarprize from the Clay Foundation, since, as I said above, the more money youhave, the more miserable you are, and I prefer to continue to be happilypenny-less) is that the solution turned out to be very anti-climactic. All itdid was prove that the question was stupid, because it was based on the flaweddogma of contemporary computer science that equates easy with "polynomialtime". The "polynomial" algorithm in my proof has such a hugeexponent, and such a huge constant, that makes it far from feasible, on today's(and any day's) computers.
But I trulyhope that my solution was not in vain. Who knows?, maybe at least some peoplewill realize how futile it is for humans to attempt to do science and mathematics, even with computers' help, because, unfortunately, the computersare still programmed by humans, and these humans can't be trusted to developrealistic models. They can't be trusted with developing toy models either,since they soon forget that these are tinker toys, and this way endanger all ofus.
So, let's be humble, forget about science and mathematics, and go back to old-time religion and worshiping God, who alone knows what is going on.