最近聊天时，自己偶尔提到了以前在网上看到的关于数学家的段子。讲完后担心讲错了，便查证了一下。这一查不得了，发现这些段子竟然来自一篇论文。论文里有大量关于数学家的段子，但在我这个外行人的眼里，大部分段子的笑点都过于奇怪，不好玩。这里摘录一部分我觉得还行的段子，以备忘。
葡萄
- Q: What’s purple and commutes?
- A: An abelian grape.
英文中葡萄（grape）和群（group）谐音，但中文二者不谐音。为了保留谐音梗效果，试译为：
不过，无论是原文还是译文，都很生硬，不太好玩。后面还有一大堆关于阿贝尔群的段子，都不好玩。
飞机
A bunch of Polish scientists decided to flee their repressive government by hijacking an airliner and forcing the pilot to fly them to a western country. They drove to the airport, forced their way on board a large passenger jet, and found there was no pilot on board. Terrified, they listened as the sirens got louder. Finally, one of the scientists suggested that since he was an experimentalist, he would try to fly the aircraft. He sat down at the controls and tried to figure them out. The sirens got louder and louder. Armed men surrounded the jet. The would-be pilot’s friends cried out, “Please, please take off now!!! Hurry!!!” The experimentalist calmly replied, “Have patience. I’m just a simple pole in a complex plane.”
一群波兰科学家决定劫机逃亡到西方国家。他们驱车赶往机场，冲上一架大型客机，却发现没有飞行员。警报声响起，他们慌了手脚。终于，一位科学家站出来说，他可以试着驾驶飞机，因为他是一名实验科学家。于是他坐下来开始摆弄那些控制杆。警报声越来越大，武警包围了客机。这位准飞行员的同伴们哭喊：「快起飞啊！快啊！」实验科学家淡定地说：「耐心一点，我只是一个复杂飞机里的普通波兰人（一个复平面上的简单极点）。」
A group of Polish tourists is flying on a small airplane through the Grand Canyon on a sightseeing tour. The tour guide announces: “On the right of the airplane, you can see the famous Bright Angle Falls.” The tourists leap out of their seats and crowd to the windows on the right side. This causes a dynamic imbalance, and the plane violently rolls to the side and crashes into the canyon wall. All aboard are lost. The moral of this episode is: always keep your poles off the right side of the plane.
一群波兰游客乘坐一架小型飞机穿越大峡谷。导游说：「在飞机右侧，大家可以看到著名的亮角瀑布。」游客们纷纷离开座位，挤到右侧窗户去看。飞机失去平衡，朝一侧翻滚，最终坠毁在大峡谷。机上所有人全部遇难。这件事给我们的教训是：始终保持所有的波兰人都远离飞机的右侧（所有的极点都不在平面的右侧）。
灯泡
- Q: How many topologists does it take to change a lightbulb?
- A: Just one, but what will you do with the doughnut?
- 问：换一个灯泡需要几个拓扑学家？
- 答：只要一个，但你拿着甜甜圈干什么？
- Q: How many number theorists does it take to change a lightbulb?
- A: This is not known, but it is conjectured to be an elegant prime.
- 问：换一个灯泡需要几个数论学家？
- 答：不知道，据推测会是一个优雅的素数。
- Q: How many geometers does it take to screw in a lightbulb?
- A: None. You can’t do it with a straightedge and compass.
- 问：换一个灯泡需要几个几何学家？
- 答：零。你不可能用尺规作图完成。
- Q: How many analysts does it take to screw in a lightbulb?
- A: Three. One to prove existence, one to prove uniqueness, and one to derive a nonconstructive algorithm to do it.
- 问：换一个灯泡需要几个分析家？
- 答：三个。一个证明解的存在性，一个证明解的唯一性，还有一个推导一种非构造算法来实现它。
- Q: How many Bourbakists does it take to replace a lightbulb?
- A: Changing a lightbulb is a special case of a more general theorem concerning the maintenance and repair of an electrical system. To establish upper and lower bounds for the number of personnel required, we must determine whether the sufficient conditions of Lemma 2.1 (Availability of personnel) and those of Corollary 2.3.55 (Motivation of personnel) apply. If and only if these conditions are met, we derive the result by an application of the theorems in Sections 3.1123. The resulting upper bound is, of course, a result in an abstract measure space, in the weak-topology.
- 问：换一个灯泡需要几个 Bourbakists？
- 答：换灯泡是关于维护和修理一个电气系统这个一般性定理的一个特例。为了确立该问题所需员工人数的上下限，我们必须确保引理 2.1（人员可用性） 以及推论 2.3.55（人员积极性）的充分条件成立。当且仅当这些条件成立时，我们可应用第 3.1123 节的定理求解。当然，此上限是在弱拓扑学中一个抽象测度空间的结果。
- Q: How many mathematicians does it take to screw in a lightbulb?
- A: 0.999999…
- 问：换一个灯泡需要几个数学家？
- 答：0.999999… 个。
- Q: How many lightbulbs does it take to change a lightbulb?
- A: One, if it knows its own Gödel number.
- 问：换一个灯泡需要几个灯泡？
- 答：一个，如果这个灯泡知道它的哥德尔编码的话。
马路
- Q: Why did the chicken cross the road?
- A: Gödel: It cannot be proved whether the chicken crossed the road.
- 问：鸡为什么过马路？
- 答：哥德尔：无法证明鸡有没有过马路。
- Q: Why did the chicken cross the road?
- A: Erdös: It was forced to do so by the chicken-hole principle.
- 问：鸡为什么过马路？
- 答：埃尔多斯：根据鸡洞原则，它必须这么做。
- Q: Why did the chicken cross the road?
- A: Riemann: The answer appears in Dirichlet’s lectures.
- 问：鸡为什么过马路？
- 答：黎曼：答案见狄利克雷讲义。
- Q: Why did the chicken cross the road?
- A: Fermat: It did not fit on the margin on this side.
- 问：鸡为什么过马路？
- 答：费马：因为路这边的空间不够了。
- Q: Why did the chicken cross the Möbius strip?
- A: To get to the other-er…
- Q: Why did the chicken cross the Möbius strip?
- A: To get to the same side.
现实
Engineers think that equations approximate the real world. Physicists think that the real world approximates equations. Mathematicians are unable to make the connection.
工程师认为公式是对现实世界的近似。物理学家认为现实世界是对公式的近似。数学家不知道二者有什么联系。
救火
An engineer, a physicist, and a mathematician are staying in a hotel. The engineer wakes up and smells smoke. He goes out into the hallway and sees a fire, so he fills a trash can from his room with water and douses the fire. He goes back to bed. Later, the physicist wakes up and smells the smoke. He opens his door and sees a fire in the hallway. He walks down the hall to a fire hose and after calculating the flame velocity, distance, water pressure, trajectory, and so forth, extinguishes the fire with the minimum amount of water and energy needed. Later the mathematician wakes up and smells smoke. He goes to the hall, sees the fire and then the fire hose. He thinks for a moment and then exclaims, “Ah, a solution exists!” and then goes back to bed.
一个工程师，一个物理学家，和一个数学家住酒店。工程师醒来，闻到烟味，到走廊一看，发现着火了。他拿起房间里的垃圾桶，灌满水，把火浇灭，然后回到床上继续睡觉。然后，物理学家醒来，闻到烟味，到走廊一看，发现着火了。他顺着走廊走，找到消防栓，计算火焰速度，距离，水压，弹道等等，然后用最少的水和能量将火扑灭。后来，数学家醒来，闻到烟味，到走廊一看，发现着火了，并且发现了消防栓。他想了一会儿，宣称：「解是存在的。」然后回到床上继续睡觉。
篱笆
One day a farmer called up an engineer, a physicist, and a mathematician and asked them to fence in the largest possible area with the least amount of fence. The engineer made the fence in a circle and proclaimed that he had the most efficient design. The physicist made a long, straight line and proclaimed “We can assume the length is infinite…” and pointed out that fencing off half of the Earth was certainly a more efficient way to do it. The mathematician just laughed at them. He built a tiny fence around himself and said, “I declare myself to be on the outside.”
一个农夫叫来一个工程师，一个物理学家，和一个数学家，让他们用最少的篱笆围出最大的面积。工程师将篱笆围成一个圆，声称这是最佳设计。物理学家将篱笆扎成一条长长的直线，说：假设这条直线无限延伸，就能围出半个地球的面积。数学家微微一笑，只用很少的篱笆把自己围起来，说：「我在外面。」
空楼
A biologist, a physicist, and a mathematician were sitting in a street café watching the crowd. Across the street they saw a man and a woman entering a building. Ten minutes later they reappeared together with a third person. “They have multiplied,” said the biologist. “Oh no, an error in measurement,” the physicist sighed. “If exactly one person enters the building now, it will be empty again,” the mathematician concluded.
一个生物学家，一个物理学家，和一个数学家坐在咖啡馆里看着街上的人群。他们看到街对面有一男一女走进一座大楼。十分钟后，这对男女和第三个人一同走出了大楼。生物学家说：「他们繁殖了。」物理学家说：「哦不，测量误差。」数学家说：「如果再进去一个人，这栋楼就又空了。」
黑羊
A mathematician, a physicist, and an engineer were traveling through Scotland when they saw a black sheep through the window of the train. “Aha,” says the engineer, “I see that Scottish sheep are black.” “Hmm,” says the physicist, “You mean that some Scottish sheep are black.” “No,” says the mathematician, “All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black!”
一个工程师，一个物理学家和一个数学家路过苏格兰时，透过火车窗户看到一只黑色的羊。工程师说：「啊哈，我看到苏格兰的羊是黑色的。」物理学家说：「唔，只能说有些苏格兰羊是黑色的。」数学家说：「不，我们仅仅知道苏格兰至少有一只羊，且这只羊的至少一面是黑色的。」
热气球
Three men are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. One of the three men says, “I’ve got an idea. We can call for help in this canyon and the echo will carry our voices far.” So he leans over the basket and yells out, “Helloooooo! Where are we?” (They hear the echo several times.) Fifteen minutes later, they hear this echoing voice: “Hellooooo! You’re lost!!” One of the men says, “That must have been a mathematician.” Puzzled, one of the other men asks, “Why do you say that?” The reply: “For three reasons: (1) He took a long time to answer, (2) he was absolutely correct, and (3) his answer was absolutely useless.”
三人乘坐热气球，在山谷中迷失了方向。其中一个对着山谷喊：「喂，我们在哪？」十五分钟后，他们听到一个声音说：「喂，你们在热气球上。」一个人说：「这肯定是个数学家。」另一个人问：「为什么？」答：「因为他用了很长时间，给出了一个完全正确的结论，但结论毫无用处。」
搬家
One day the Wiener family was scheduled to move into a new house. Mrs. Wiener, mindful of her husband’s propensity for forgetting, wrote the new address on a slip of paper and handed it to him. He scoffed, saying, “I wouldn’t forget such an important thing,” but he took the slip of paper and put it in his pocket. Later that same day at the university a colleague came by his office with an interesting problem. Wiener searched for a piece of paper and took the slip from his pocket to use to write some mathematical equations. When he finished, he crumpled up the slip of paper and threw it away. That evening, he remembered there was something about a new house but he couldn’t find the slip of paper with the address on it. Without any alternative course of action, he returned to his old home, where he spotted a little girl on the sidewalk. “Say, little girl,” he said, “Do you know where the Wieners live?” The girl replied, “That’s o.k., Daddy, Mommy sent me to get you.”
维纳家准备搬家。维纳夫人知道丈夫健忘，便将新家地址写在纸上交给他。维纳先生笑说：「这么重要的事情我怎么可能忘记？」然后将纸装进了口袋。在大学里，一位同事找维纳先生讨论一个有趣的问题。维纳先生从口袋里掏出纸，在上面写了许多公式，然后把纸扔了。晚上，维纳先生才想起关于新家的事，却找不到写了地址的纸。他只好走回原来的住址，看到路边站着一个小女孩，便上前问：「小姑娘，你知道维纳家住在哪里吗？」小女孩说：「没事，爸爸，妈妈让我来接你。」
