有什么好笑的数学笑话吗？
正文翻译
What are some funny mathematics jokes?
有什么好笑的数学笑话吗？
What are some funny mathematics jokes?有什么好笑的数学笑话吗？
评论翻译
Advanced statistics has shown that those who celebrate the most birthdays become the oldest.
先进的统计数据表明，过生日次数最多的人年龄最大。
先进的统计数据表明，过生日次数最多的人年龄最大。
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An engineer, a physicist, and a mathematician are trying to set up a fenced-in area for some cattle, but they have a limited amount of fence. The engineer gets up first and makes a square fence, reasoning that it’s a pretty decent working model. “No, no,” the physicist says, “There’s a better way.” He takes the fence material and creates a circular pen, showing how it encompasses the maximum possible space with the given material.
“No, no, no,” the mathematician speaks up, “There’s an even better way.” He proceeds to construct a tiny fence around himself, then declares: “I define myself to be on the outside.”
一位工程师、一位物理学家和一位数学家试图为一些牛划出最大的围栏区域，但他们的围栏数量有限。工程师首先站起来，做了一个方形的栅栏区域，他认为这是一个很好的养牛区块形状。“不，不，”物理学家说，“有更好的办法。他用栅栏材料围出了一个圆形的区域，展示了如何用给定的材料实现最大可能的空间。
“不，不，不，”数学家大声说，“我有一个更好的方法。他在自己的外面围起一圈小栅栏，然后说:“我现在在外面。”
An engineer, a physicist, and a mathematician are trying to set up a fenced-in area for some cattle, but they have a limited amount of fence. The engineer gets up first and makes a square fence, reasoning that it’s a pretty decent working model. “No, no,” the physicist says, “There’s a better way.” He takes the fence material and creates a circular pen, showing how it encompasses the maximum possible space with the given material.
“No, no, no,” the mathematician speaks up, “There’s an even better way.” He proceeds to construct a tiny fence around himself, then declares: “I define myself to be on the outside.”
一位工程师、一位物理学家和一位数学家试图为一些牛划出最大的围栏区域，但他们的围栏数量有限。工程师首先站起来，做了一个方形的栅栏区域，他认为这是一个很好的养牛区块形状。“不，不，”物理学家说，“有更好的办法。他用栅栏材料围出了一个圆形的区域，展示了如何用给定的材料实现最大可能的空间。
“不，不，不，”数学家大声说，“我有一个更好的方法。他在自己的外面围起一圈小栅栏，然后说:“我现在在外面。”
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It has been proven that ten percent of car theives are left-handed.
It has been proven that all polar bears are left-handed.
Therefore, if your car is stolen, there is a ten percent chance that it was taken by a polar bear.
(Can you figure out why such a conclusion is invalid?)
事实证明，百分之十的司机是左撇子。
另有事实证明，所有的北极熊都是左撇子。
因此，如果你的车被偷了，有百分之十的可能性是被北极熊偷走的。
(你能为什么这样的结论是无效的吗?)
It has been proven that ten percent of car theives are left-handed.
It has been proven that all polar bears are left-handed.
Therefore, if your car is stolen, there is a ten percent chance that it was taken by a polar bear.
(Can you figure out why such a conclusion is invalid?)
事实证明，百分之十的司机是左撇子。
另有事实证明，所有的北极熊都是左撇子。
因此，如果你的车被偷了，有百分之十的可能性是被北极熊偷走的。
(你能为什么这样的结论是无效的吗?)
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What is pi?
The mathematician says, “Pi is the ratio of the circumference of a circle to its diameter.”
The computer programmer says: “Pi is 3.141592653589 in double precision.”
The physicist says: “Pi is 3.14159 plus of minus 0.000003.”
The engineer says: “Pi is about 22/7.”
The nutritionist says: “Pie is a somewhat healthy but still absolutely delicious dessert!”
pi是什么?
数学家说:“π是圆的周长与直径之比。”
计算机程序员说:“π的双精度值是3.141592653589。”
物理学家说:“π是3.14159+- 0.000003。”
工程师说:“π大约是22/7。”
营养学家说:“派是一种健康且绝对美味的甜点!”
What is pi?
The mathematician says, “Pi is the ratio of the circumference of a circle to its diameter.”
The computer programmer says: “Pi is 3.141592653589 in double precision.”
The physicist says: “Pi is 3.14159 plus of minus 0.000003.”
The engineer says: “Pi is about 22/7.”
The nutritionist says: “Pie is a somewhat healthy but still absolutely delicious dessert!”
pi是什么?
数学家说:“π是圆的周长与直径之比。”
计算机程序员说:“π的双精度值是3.141592653589。”
物理学家说:“π是3.14159+- 0.000003。”
工程师说:“π大约是22/7。”
营养学家说:“派是一种健康且绝对美味的甜点!”
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The mother of three is pregnant with her fourth child. One evening, the eldest son says to his father, “Do you know, Daddy, what I figured out?”
“No, Johnny, what did you find out?”
“The new baby will be Chinese!”
“What?!”
“Yes. I’ve read in the paper that statistics shows that every fourth child born nowadays is Chinese…”
一位三个孩子的母亲正怀着她的第四个孩子。一天晚上，大儿子对父亲说:“爸爸，你知道我琢磨出了什么吗?”
“不知道，约翰尼，你发现了什么?”
“妈妈肚子里的小宝宝将是中国人!”
“什么? !”
“是的。我在报上看到有数据显示，现在每四个孩子中就有一个是中国人……”
The mother of three is pregnant with her fourth child. One evening, the eldest son says to his father, “Do you know, Daddy, what I figured out?”
“No, Johnny, what did you find out?”
“The new baby will be Chinese!”
“What?!”
“Yes. I’ve read in the paper that statistics shows that every fourth child born nowadays is Chinese…”
一位三个孩子的母亲正怀着她的第四个孩子。一天晚上，大儿子对父亲说:“爸爸，你知道我琢磨出了什么吗?”
“不知道，约翰尼，你发现了什么?”
“妈妈肚子里的小宝宝将是中国人!”
“什么? !”
“是的。我在报上看到有数据显示，现在每四个孩子中就有一个是中国人……”
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Sherlock Holmes and Watson are sitting in a hot air balloon. For hours, they have been drifting through clouds and are completely lost. Suddenly, the clouds part and the two see the top of a mountain with two other men standing on it.
“Hey! Can you tell us where we are?”
The men don’t reply. Minutes past as the balloon drifts past the mountain. When the balloon is about to be swallowed again by the clouds, a shout is heard from the distance. “You’re in a balloon!”
“They must have been mathematicians,” Sherlock Holmes remarks as the balloon is once again lost in the clouds.
“What makes you think that?”
“Three things, my dear Watson. First, they thought long and hard about what to say. Second, what they eventually said was irrefutably correct. Finally, it was of no use whatsoever.”
Down on the mountain, the two mathematicians are back to their own thoughts and one of them comes to a conclusion. “That must’ve been a couple of physicists.”
“Oh?”
“Well, firstly, they asked an obvious question. Secondly, they were in a horrible hurry to get the answer, and finally, they are unsatisfied with the truth.”
夏洛克·福尔摩斯和华生正坐在一个热气球上。几个小时以来，他们一直在云层中漂流，完全迷失了方向。突然，云层散开了，他们看到山顶上有另外两个人。
“嘿！你能告诉我们，我现在在什么地方吗?”
两个男人没有回答。几分钟后，气球从山上飘过。当气球即将再次被云层吞噬时，远处传来一声喊叫。“你在气球里!”
“他们一定是数学家，”夏洛克·福尔摩斯在气球再次消失在云层中时说道。
“你怎么会这样想?”
“有三个原因，我亲爱的华生。首先，他们想了很久才说了些什么。其次，他们最终所说的是无可辩驳的正确。最后，他们说的屁用没有。”
下山后，两位数学家又回到了自己的思考中，其中一位得出了一个结论。“那气球中肯定是几个物理学家。”
“哦?”
“首先，他们问了一个很明显的问题。其次，他们急于得到答案，最后，他们对真相并不满意。”
Sherlock Holmes and Watson are sitting in a hot air balloon. For hours, they have been drifting through clouds and are completely lost. Suddenly, the clouds part and the two see the top of a mountain with two other men standing on it.
“Hey! Can you tell us where we are?”
The men don’t reply. Minutes past as the balloon drifts past the mountain. When the balloon is about to be swallowed again by the clouds, a shout is heard from the distance. “You’re in a balloon!”
“They must have been mathematicians,” Sherlock Holmes remarks as the balloon is once again lost in the clouds.
“What makes you think that?”
“Three things, my dear Watson. First, they thought long and hard about what to say. Second, what they eventually said was irrefutably correct. Finally, it was of no use whatsoever.”
Down on the mountain, the two mathematicians are back to their own thoughts and one of them comes to a conclusion. “That must’ve been a couple of physicists.”
“Oh?”
“Well, firstly, they asked an obvious question. Secondly, they were in a horrible hurry to get the answer, and finally, they are unsatisfied with the truth.”
夏洛克·福尔摩斯和华生正坐在一个热气球上。几个小时以来，他们一直在云层中漂流，完全迷失了方向。突然，云层散开了，他们看到山顶上有另外两个人。
“嘿！你能告诉我们，我现在在什么地方吗?”
两个男人没有回答。几分钟后，气球从山上飘过。当气球即将再次被云层吞噬时，远处传来一声喊叫。“你在气球里!”
“他们一定是数学家，”夏洛克·福尔摩斯在气球再次消失在云层中时说道。
“你怎么会这样想?”
“有三个原因，我亲爱的华生。首先，他们想了很久才说了些什么。其次，他们最终所说的是无可辩驳的正确。最后，他们说的屁用没有。”
下山后，两位数学家又回到了自己的思考中，其中一位得出了一个结论。“那气球中肯定是几个物理学家。”
“哦?”
“首先，他们问了一个很明显的问题。其次，他们急于得到答案，最后，他们对真相并不满意。”
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An engineer, a physicist and a mathematician are staying in a hotel.
The engineer wakes 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.
A few hours later, the physicist wakes and smells smoke. He opens his door and sees a fire. He walks to a fire hose and, after calculating the flame velocity, distance, water pressure, and trajectory, extinguishes the fire with the minimum amount of water and energy needed.
A few hours after that, the mathematician wakes and smells smoke. He goes to the hall, sees the fire hose, thinks, then exclaims, “Ah, so a solution exists!” He then goes back to bed.
一位工程师、一位物理学家和一位数学家住在一家旅馆里。
工程师醒了，闻到了烟味。他走到走廊，看到了一堆火，于是他从房间里倒了一桶水，浇灭了火。他回到床上继续睡。
几个小时后，物理学家醒了，闻到了烟味。他打开门，看见一堆火。他走到消防水龙前，在计算完火势，距离、水压和曲线后，用最少的水和力量扑灭了火。
几个小时后，数学家醒来闻到了烟味。他走到大厅，看到了消防水管，想了想，然后大叫:“啊，这么说有解！”然后他就回去睡觉了。
An engineer, a physicist and a mathematician are staying in a hotel.
The engineer wakes 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.
A few hours later, the physicist wakes and smells smoke. He opens his door and sees a fire. He walks to a fire hose and, after calculating the flame velocity, distance, water pressure, and trajectory, extinguishes the fire with the minimum amount of water and energy needed.
A few hours after that, the mathematician wakes and smells smoke. He goes to the hall, sees the fire hose, thinks, then exclaims, “Ah, so a solution exists!” He then goes back to bed.
一位工程师、一位物理学家和一位数学家住在一家旅馆里。
工程师醒了，闻到了烟味。他走到走廊，看到了一堆火，于是他从房间里倒了一桶水，浇灭了火。他回到床上继续睡。
几个小时后，物理学家醒了，闻到了烟味。他打开门，看见一堆火。他走到消防水龙前，在计算完火势，距离、水压和曲线后，用最少的水和力量扑灭了火。
几个小时后，数学家醒来闻到了烟味。他走到大厅，看到了消防水管，想了想，然后大叫:“啊，这么说有解！”然后他就回去睡觉了。
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A physicist and a mathematician are sitting in a faculty lounge. Suddenly, the coffee machine catches fire. The physicist grabs a bucket and leaps towards the sink, filling the bucket with water. He then puts out the fire.
The next day, the same two folks are in the lounge. Again, the machine catches fire. This time, the mathematician stands up, gets a bucket, hands the bucket to the physicist, and sits back down, thus reducing the problem to a previously solved one.
一位物理学家和一位数学家坐在教员休息室里。突然，咖啡机着火了。这位物理学家抓起一个水桶，跑到水池边，往桶里灌满了水。然后他扑灭了火。
第二天，这两个人又出现在客厅里。机器再次着火。这一次，数学家站起来，拿了一个桶，把桶递给物理学家，然后坐了下来。这样问题就已经变成了一个已经解决过的问题了。
A physicist and a mathematician are sitting in a faculty lounge. Suddenly, the coffee machine catches fire. The physicist grabs a bucket and leaps towards the sink, filling the bucket with water. He then puts out the fire.
The next day, the same two folks are in the lounge. Again, the machine catches fire. This time, the mathematician stands up, gets a bucket, hands the bucket to the physicist, and sits back down, thus reducing the problem to a previously solved one.
一位物理学家和一位数学家坐在教员休息室里。突然，咖啡机着火了。这位物理学家抓起一个水桶，跑到水池边，往桶里灌满了水。然后他扑灭了火。
第二天，这两个人又出现在客厅里。机器再次着火。这一次，数学家站起来，拿了一个桶，把桶递给物理学家，然后坐了下来。这样问题就已经变成了一个已经解决过的问题了。
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Recently I heard another good one so I’m gonna share it with you.
An experimental physicist, a theoretical physicist and a mathematician are all given a task to paint a wall with green paint. The experimental physicist starts. He paints most of the wall but after a while he runs out of the paint and about a square meter of the wall still isn’t painted. The experimenter is a bit upset, but he realises that this is just a measuring error and is more or less satisfied with the result.
Then it’s the theoretical physicist’s turn. First, he does some percise calculations and realises that he won’t have enough paint to completely cover the wall. He decides to mix the paint with a bit of water and then starts working. After a while the wall is painted, the colour might be a bit too light but the theoretical physicist is still satisfied with his work.
最近我又听到了一个很好的故事，所以我要和大家分享一下。
一位实验物理学家、一位理论物理学家和一位数学家被分配了一项任务，用绿色油漆粉刷墙壁。实验物理学家开始了。他粉刷了大部分墙壁，但过了一段时间，油漆用完了，大约有一平方米的墙壁还没有粉刷。实验物理学家有点沮丧，但他意识到这只是一个测量误差，他对结果多少还是满意的。
然后就轮到理论物理学家了。首先，他做了一些百分比计算，并意识到他没有足够的油漆完全覆盖墙壁。他决定把颜料和一些水混合，然后开始工作。过了一段时间，墙被粉刷完了，但墙的颜色可能有点太浅了，但理论物理学家仍然对他的工作很满意。
Recently I heard another good one so I’m gonna share it with you.
An experimental physicist, a theoretical physicist and a mathematician are all given a task to paint a wall with green paint. The experimental physicist starts. He paints most of the wall but after a while he runs out of the paint and about a square meter of the wall still isn’t painted. The experimenter is a bit upset, but he realises that this is just a measuring error and is more or less satisfied with the result.
Then it’s the theoretical physicist’s turn. First, he does some percise calculations and realises that he won’t have enough paint to completely cover the wall. He decides to mix the paint with a bit of water and then starts working. After a while the wall is painted, the colour might be a bit too light but the theoretical physicist is still satisfied with his work.
最近我又听到了一个很好的故事，所以我要和大家分享一下。
一位实验物理学家、一位理论物理学家和一位数学家被分配了一项任务，用绿色油漆粉刷墙壁。实验物理学家开始了。他粉刷了大部分墙壁，但过了一段时间，油漆用完了，大约有一平方米的墙壁还没有粉刷。实验物理学家有点沮丧，但他意识到这只是一个测量误差，他对结果多少还是满意的。
然后就轮到理论物理学家了。首先，他做了一些百分比计算，并意识到他没有足够的油漆完全覆盖墙壁。他决定把颜料和一些水混合，然后开始工作。过了一段时间，墙被粉刷完了，但墙的颜色可能有点太浅了，但理论物理学家仍然对他的工作很满意。
Finally, the mathematician comes to do the job. His friends leave him in the room because he needs silence to concentrate. After a while the theoretical physicist and the experimenter come to the room and see a wall which is perfectly painted, the colour is not even a bit lighter. Not only that, but after they look at the bucket with paint they find out that it is full. They are shocked so they ask the mathematician how he managed to do this and he responds: “Well, I did the calculations and I realised that I won’t have enough paint to cover the wall completely so I decided to only paint the rational points.”
最后，数学家来做这项工作。他的朋友把他一个人留在房间里，因为他需要安静才能集中注意力。过了一会儿，理论物理学家和实验者来到房间，看到一面墙被完美地粉刷过，颜色完全是正常的颜色，一点也没有变浅。不仅如此，在他们看到装满油漆的桶后，他们发现它是满的。他们很震惊，于是问数学家是怎么做到的，他回答说:“嗯，我计算过了，当我意识到我没有足够的油漆完全覆盖墙壁时，所以我决定只画那些是有理数的点。”（译者加：因为有理数在实数系是稠密的，所以颜色完全正常，又因为在实数系取到有理数的概率为0，所以油漆桶是满的。）
原创翻译：龙腾网 http://www.ltaaa.cn 转载请注明出处
最后，数学家来做这项工作。他的朋友把他一个人留在房间里，因为他需要安静才能集中注意力。过了一会儿，理论物理学家和实验者来到房间，看到一面墙被完美地粉刷过，颜色完全是正常的颜色，一点也没有变浅。不仅如此，在他们看到装满油漆的桶后，他们发现它是满的。他们很震惊，于是问数学家是怎么做到的，他回答说:“嗯，我计算过了，当我意识到我没有足够的油漆完全覆盖墙壁时，所以我决定只画那些是有理数的点。”（译者加：因为有理数在实数系是稠密的，所以颜色完全正常，又因为在实数系取到有理数的概率为0，所以油漆桶是满的。）
原创翻译：龙腾网 http://www.ltaaa.cn 转载请注明出处
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An engineer and a mathematician are taken to one corner of a large lecture hall. Standing in the other corner is a beautiful, sexy woman with bright eyes and an eager smile. Both men are told that this woman has agreed that the first man to reach her will get to go home with her for the night; however, they must follow a rule: they are permitted to cut the distance between themselves and the woman by one half at each and every minute until one of them reaches her. The woman, they are told, will be free to avoid them within the room in any way that she likes, but that she can only move away by a distance of one quarter of her distance to the closest one on each one minute mark.
一位工程师和一位数学家被带到一个大讲堂的一个角落。站在另一个角落的是一个美丽、性感的女人，她有着明亮的眼睛和热切的微笑。两个男人都被告知，这个女人已经同意，第一个找到她的男人可以和她一起回家过夜;但是，他们必须遵守一个规则：他们和女人之间的距离每分钟缩短一半，直到其中一人碰到她。他们被告知，在房间里，女人可以自由地以她喜欢的任何方式避开他们，但在每一分钟内，她只能远离最近的那个人四分之一他们之间的距离。
An engineer and a mathematician are taken to one corner of a large lecture hall. Standing in the other corner is a beautiful, sexy woman with bright eyes and an eager smile. Both men are told that this woman has agreed that the first man to reach her will get to go home with her for the night; however, they must follow a rule: they are permitted to cut the distance between themselves and the woman by one half at each and every minute until one of them reaches her. The woman, they are told, will be free to avoid them within the room in any way that she likes, but that she can only move away by a distance of one quarter of her distance to the closest one on each one minute mark.
一位工程师和一位数学家被带到一个大讲堂的一个角落。站在另一个角落的是一个美丽、性感的女人，她有着明亮的眼睛和热切的微笑。两个男人都被告知，这个女人已经同意，第一个找到她的男人可以和她一起回家过夜;但是，他们必须遵守一个规则：他们和女人之间的距离每分钟缩短一半，直到其中一人碰到她。他们被告知，在房间里，女人可以自由地以她喜欢的任何方式避开他们，但在每一分钟内，她只能远离最近的那个人四分之一他们之间的距离。
They start and the mathematician pulls out his notebook and feverishly starts developing a model to optimize his pursuit of the women. He employs predator and prey calculations, game theory, nonlinear dynamics, and a rapid but impressive array of proofs and derivations.
By the time the third minute passes, the mathematician yells,
"Eureka! It's a fool's errand! Even if she doesn't move, I'll only get infinitely close to her without ever touching because no matter how small the distance I'm still only decreasing the distance by half. Hence, there will always be a space between us. Therefore, I cannot ever reach her, so I won't waste any more of my time on this impossible challenge!" The mathematician then proceeds to storm out of the room and close the door.
他们开始了，数学家拿出他的笔记本，狂热地开始发展一个模型，以优化他追求女人的速度。他运用了捕食者和猎物的计算、博弈论、非线性动力学，以及一系列快速但令人印象深刻的证明和推导。
到了第三分钟，数学家喊道:
“尤里卡！（译者加：类似于bingo，就是突然明白了。）这是件蠢事！即使她不动，我也只能无限地接近她而不会接触到她，因为不管距离有多小，我都只能将距离减半。因此，我们之间总会有一个空间。所以我永远也触碰不到她，所以我不想再在这个不可能的挑战上浪费时间了!”然后，数学家开始冲出房间，关上了门。
原创翻译：龙腾网 http://www.ltaaa.cn 转载请注明出处
By the time the third minute passes, the mathematician yells,
"Eureka! It's a fool's errand! Even if she doesn't move, I'll only get infinitely close to her without ever touching because no matter how small the distance I'm still only decreasing the distance by half. Hence, there will always be a space between us. Therefore, I cannot ever reach her, so I won't waste any more of my time on this impossible challenge!" The mathematician then proceeds to storm out of the room and close the door.
他们开始了，数学家拿出他的笔记本，狂热地开始发展一个模型，以优化他追求女人的速度。他运用了捕食者和猎物的计算、博弈论、非线性动力学，以及一系列快速但令人印象深刻的证明和推导。
到了第三分钟，数学家喊道:
“尤里卡！（译者加：类似于bingo，就是突然明白了。）这是件蠢事！即使她不动，我也只能无限地接近她而不会接触到她，因为不管距离有多小，我都只能将距离减半。因此，我们之间总会有一个空间。所以我永远也触碰不到她，所以我不想再在这个不可能的挑战上浪费时间了!”然后，数学家开始冲出房间，关上了门。
原创翻译：龙腾网 http://www.ltaaa.cn 转载请注明出处
The engineer, smiling, simply turns toward the woman, eyes her up and down and says,
"In a minute or two here, I'm going to start approximating."
工程师微笑着转过身，上下打量着她，然后说，
“再过一两分钟，我就可以开始近似了。”
原创翻译：龙腾网 http://www.ltaaa.cn 转载请注明出处
"In a minute or two here, I'm going to start approximating."
工程师微笑着转过身，上下打量着她，然后说，
“再过一两分钟，我就可以开始近似了。”
原创翻译：龙腾网 http://www.ltaaa.cn 转载请注明出处
-----------------
An astronomer, a physicist and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field. ‘How interesting,’ observed the astronomer, ‘all Scottish sheep are black!’ To which the physicist responded, ‘No, no! Some Scottish sheep are black!’ The mathematician gazed heavenward in supplication, and then intoned, ‘In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black.’
据说一位天文学家、一位物理学家和一位数学家正在苏格兰度假。他们从火车窗口瞥了一眼，发现田野中央有一只黑绵羊。“真有趣，”天文学家说，“苏格兰的绵羊都是黑色的!”这位物理学家回答说:“不，不!是有些苏格兰羊是黑色的!”数学家仰望着天空，然后慢慢说道:“这只能说明在苏格兰的一块地上的一只羊，它的半边是黑色的！”
An astronomer, a physicist and a mathematician (it is said) were holidaying in Scotland. Glancing from a train window, they observed a black sheep in the middle of a field. ‘How interesting,’ observed the astronomer, ‘all Scottish sheep are black!’ To which the physicist responded, ‘No, no! Some Scottish sheep are black!’ The mathematician gazed heavenward in supplication, and then intoned, ‘In Scotland there exists at least one field, containing at least one sheep, at least one side of which is black.’
据说一位天文学家、一位物理学家和一位数学家正在苏格兰度假。他们从火车窗口瞥了一眼，发现田野中央有一只黑绵羊。“真有趣，”天文学家说，“苏格兰的绵羊都是黑色的!”这位物理学家回答说:“不，不!是有些苏格兰羊是黑色的!”数学家仰望着天空，然后慢慢说道:“这只能说明在苏格兰的一块地上的一只羊，它的半边是黑色的！”
----------------
A mathematician is walking, when he comes across a field full of sheep. He approaches the shepherd and asks “If I can tell you how many sheep you have here, may I take one home for my dinner?”
The shepherd agrees, and the mathematician counts the number of sheep in a patch, then counts the number of patches in the field, completes a quick multiplication and says “you have 1063 sheep.”
The shepherd replies “Wow! I just counted them this morning, and there are exactly 1063!”
The mathematician grabs the closest animal and slings it over his shoulder and begins to walk away. The shepherd calls after him “If I can guess your profession, can I have my animal back?”
The mathematician turns, and agrees. The shepherd says “You are a mathematician!”
Dejected the mathematician asks “How did you know that?” and the shepherd replied “If you put down my dog, I’ll tell you”.
一位数学家正在散步，突然他遇到一片满是羊的田野。他走近牧羊人，问:“如果我能快速告诉你这里有多少只羊吗?我可以带一只回家当晚餐吗?”
牧羊人同意了，数学家数了一下每一块地里的羊数，然后又数了一下多少个分割开的地，做完快速的乘法，然后说:“你有1063只羊。”
牧羊人回答:“哇!我今天早上刚数过，正好有1063个!”
这位数学家抓住离他最近的动物，把它甩在肩上，开始走开。牧羊人在他身后叫道:“如果我能猜出你的职业，我能把我的牲口要回来吗?”
数学家转过身，同意了。牧羊人说:“你是个数学家!”
数学家沮丧地问:“你怎么知道的?”牧羊人回答说:“如果你能放下我的狗，我就告诉你。”
A mathematician is walking, when he comes across a field full of sheep. He approaches the shepherd and asks “If I can tell you how many sheep you have here, may I take one home for my dinner?”
The shepherd agrees, and the mathematician counts the number of sheep in a patch, then counts the number of patches in the field, completes a quick multiplication and says “you have 1063 sheep.”
The shepherd replies “Wow! I just counted them this morning, and there are exactly 1063!”
The mathematician grabs the closest animal and slings it over his shoulder and begins to walk away. The shepherd calls after him “If I can guess your profession, can I have my animal back?”
The mathematician turns, and agrees. The shepherd says “You are a mathematician!”
Dejected the mathematician asks “How did you know that?” and the shepherd replied “If you put down my dog, I’ll tell you”.
一位数学家正在散步，突然他遇到一片满是羊的田野。他走近牧羊人，问:“如果我能快速告诉你这里有多少只羊吗?我可以带一只回家当晚餐吗?”
牧羊人同意了，数学家数了一下每一块地里的羊数，然后又数了一下多少个分割开的地，做完快速的乘法，然后说:“你有1063只羊。”
牧羊人回答:“哇!我今天早上刚数过，正好有1063个!”
这位数学家抓住离他最近的动物，把它甩在肩上，开始走开。牧羊人在他身后叫道:“如果我能猜出你的职业，我能把我的牲口要回来吗?”
数学家转过身，同意了。牧羊人说:“你是个数学家!”
数学家沮丧地问:“你怎么知道的?”牧羊人回答说:“如果你能放下我的狗，我就告诉你。”
-----------------
A biologist, a magician and a mathematician are sitting together when someone says:
“See that house? It was empty and two people went in and then three people came out. How could you explain this?”
The biologist says “Easy! One of the people was pregnant and she gave birth in the house”.
The magician says “No, that’s not it. There was a trap door hidden under a rug, and there was a person hiding”
Then the mathematician says “Well, I’d go in to the house to investigate, but then the house would be empty”.
一个生物学家，一个魔术师和一个数学家坐在一起，这时有人说
“看到那个房子了吗?里面是空的，两个人进去了，然后三个人出来了。你怎么解释呢?”
生物学家说:“简单!其中一个人怀孕了，她在房子里生了孩子。”
魔术师说:“不，不是这个原因。是地毯下面藏着一扇活板门，里面还藏着一个人。”
然后数学家说:“好吧，我可以进去调查一下，但是那时候房子里面就是空的了。”
A biologist, a magician and a mathematician are sitting together when someone says:
“See that house? It was empty and two people went in and then three people came out. How could you explain this?”
The biologist says “Easy! One of the people was pregnant and she gave birth in the house”.
The magician says “No, that’s not it. There was a trap door hidden under a rug, and there was a person hiding”
Then the mathematician says “Well, I’d go in to the house to investigate, but then the house would be empty”.
一个生物学家，一个魔术师和一个数学家坐在一起，这时有人说
“看到那个房子了吗?里面是空的，两个人进去了，然后三个人出来了。你怎么解释呢?”
生物学家说:“简单!其中一个人怀孕了，她在房子里生了孩子。”
魔术师说:“不，不是这个原因。是地毯下面藏着一扇活板门，里面还藏着一个人。”
然后数学家说:“好吧，我可以进去调查一下，但是那时候房子里面就是空的了。”
---------------
A mathematician organizes a raffle in which the prize is an infinite amount of money paid over an infinite amount of time. Of course, with the promise of such a prize, his tickets sell like hot cake. When the winning ticket is drawn, and the jubilant winner comes to claim his prize, the mathematician explains the mode of payment: “1 dollar now, 1/2 dollar next week, 1/ 3dollar the week after that…”
一位数学家组织了一个抽奖活动，奖品是在无限长的时间内支付无限次数的钱。当然，有了这样的奖品承诺，他的票卖得很好。当中奖的彩票被抽中，兴高采烈的中奖者前来领奖时，数学家解释了支付方式:“现在1美元，下周1/2美元，下一周1/3美元……”（译者加：这位答主其实回答错了，调和级数是发散的，总和为无穷，应该把1/3换为1/4，这样实际总和为2美元。）
A mathematician organizes a raffle in which the prize is an infinite amount of money paid over an infinite amount of time. Of course, with the promise of such a prize, his tickets sell like hot cake. When the winning ticket is drawn, and the jubilant winner comes to claim his prize, the mathematician explains the mode of payment: “1 dollar now, 1/2 dollar next week, 1/ 3dollar the week after that…”
一位数学家组织了一个抽奖活动，奖品是在无限长的时间内支付无限次数的钱。当然，有了这样的奖品承诺，他的票卖得很好。当中奖的彩票被抽中，兴高采烈的中奖者前来领奖时，数学家解释了支付方式:“现在1美元，下周1/2美元，下一周1/3美元……”（译者加：这位答主其实回答错了，调和级数是发散的，总和为无穷，应该把1/3换为1/4，这样实际总和为2美元。）
----------------
At the end of his course on mathematical methods in optimization, the professor sternly looks at his students and says: “There is one final piece of advice I’m going to give you now: Whatever you have learned in my course – never ever try to apply it to your personal lives!” “Why?” the students ask. “Well, some years ago, I observed my wife preparing breakfast, and I noticed that she wasted a lot of time walking back and forth in the kitchen. So, I went to work, optimized the whole procedure, and told my wife about it.” “And what happened?!” “Before I applied my expert knowledge, my wife needed about half an hour to prepare breakfast for the two of us. And now, it takes me less than fifteen minutes…”
在结束时他的课程在“数学优化方法”后，教授严厉地看着他的学生说:“有一个最终的建议，我想跟你们说：无论你是否学会了我的课程——都不要试图把它应用到你的个人生活!”“为什么?“学生们问。“嗯，几年前，我观察我的妻子准备早餐，我注意到她浪费了很多时间在厨房里走来走去。所以，我开始计算，并优化了整个流程，并告诉了我的妻子。“后来发生了什么事?!”他说:“在我运用我的专业知识之前，我妻子大约需要半个小时为我们俩准备早餐。现在，我，只需要花不到十五分钟……”
At the end of his course on mathematical methods in optimization, the professor sternly looks at his students and says: “There is one final piece of advice I’m going to give you now: Whatever you have learned in my course – never ever try to apply it to your personal lives!” “Why?” the students ask. “Well, some years ago, I observed my wife preparing breakfast, and I noticed that she wasted a lot of time walking back and forth in the kitchen. So, I went to work, optimized the whole procedure, and told my wife about it.” “And what happened?!” “Before I applied my expert knowledge, my wife needed about half an hour to prepare breakfast for the two of us. And now, it takes me less than fifteen minutes…”
在结束时他的课程在“数学优化方法”后，教授严厉地看着他的学生说:“有一个最终的建议，我想跟你们说：无论你是否学会了我的课程——都不要试图把它应用到你的个人生活!”“为什么?“学生们问。“嗯，几年前，我观察我的妻子准备早餐，我注意到她浪费了很多时间在厨房里走来走去。所以，我开始计算，并优化了整个流程，并告诉了我的妻子。“后来发生了什么事?!”他说:“在我运用我的专业知识之前，我妻子大约需要半个小时为我们俩准备早餐。现在，我，只需要花不到十五分钟……”
----------------
Father: If I had five coconuts and I gave you three, how many would I have left?
Child: I don’t know.
Father: Why not?
Child: In our school we do all our arithmetic in apples and oranges.
父亲:如果我有五个椰子，我给你三个，我还剩下几个?
孩子:我不知道。
父亲:为什么不呢?
孩子:在我们学校，我们的算术用的是苹果和橘子。
Father: If I had five coconuts and I gave you three, how many would I have left?
Child: I don’t know.
Father: Why not?
Child: In our school we do all our arithmetic in apples and oranges.
父亲:如果我有五个椰子，我给你三个，我还剩下几个?
孩子:我不知道。
父亲:为什么不呢?
孩子:在我们学校，我们的算术用的是苹果和橘子。
----------------
When the math professor’s wife returns home from work, she finds an envelope on the living room table. She opens it and finds a letter from her husband:
My dearest wife,
We have been married for nearly thirty years, and I still love you as much as on the day I proposed. You must realize, however, that you are now 54 years old and no longer able to satisfy certain needs I still have. I very much hope that you are not hurt to learn that, while you’re reading this, I’m in a hotel room with an 18-year-old freshman girl from my calculus class. I’ll be home before midnight.
Your husband, who will never stop loving you.
当数学教授的妻子下班回家时，她发现客厅的桌子上有一个信封。她打开信封，看到了丈夫的一封信:
我最亲爱的妻子,
“我们结婚快三十年了，但我仍然像求婚那天一样爱你。然而，你必须认识到，你现在已经54岁了，不能再满足我的某些需求。当你读这篇文章的时候，我正在和一个18岁的大一女生一起住在酒店房间里，我非常希望你没有受伤。我将在午夜前回到家。
你的丈夫，永远不会停止爱你。”
When the math professor’s wife returns home from work, she finds an envelope on the living room table. She opens it and finds a letter from her husband:
My dearest wife,
We have been married for nearly thirty years, and I still love you as much as on the day I proposed. You must realize, however, that you are now 54 years old and no longer able to satisfy certain needs I still have. I very much hope that you are not hurt to learn that, while you’re reading this, I’m in a hotel room with an 18-year-old freshman girl from my calculus class. I’ll be home before midnight.
Your husband, who will never stop loving you.
当数学教授的妻子下班回家时，她发现客厅的桌子上有一个信封。她打开信封，看到了丈夫的一封信:
我最亲爱的妻子,
“我们结婚快三十年了，但我仍然像求婚那天一样爱你。然而，你必须认识到，你现在已经54岁了，不能再满足我的某些需求。当你读这篇文章的时候，我正在和一个18岁的大一女生一起住在酒店房间里，我非常希望你没有受伤。我将在午夜前回到家。
你的丈夫，永远不会停止爱你。”
When the professor returns from the hotel shortly before midnight, he also finds an envelope in the living room. He opens it and reads:
My beloved husband,
You may recall that you, too, are 54 years old and no longer able to satisfy certain needs I still have. I thus hope that you are not hurt to learn that, while you’re reading this, I am in a hotel room with the 18-year-old pool boy.
Your loving wife.
P.S. As a mathematician, you are certainly aware of the fact that 18 goes into 54 many more times than 54 goes into 18. Therefore, don’t stay up and wait for me.
当教授在午夜前从酒店回来时，他在客厅里发现了一个信封。他打开信读道:
”我亲爱的丈夫,
你也许还记得，你也已经54岁了，不能再满足我的某些需求。因此，当你读到这篇文章时，我希望你不会受伤，我正和一个18岁的游泳男孩在酒店房间里。
爱你的妻子。
作为一个数学家，你肯定知道，18/54的次数要比54/18的次数，要大很多倍。所以，不要熬夜等我。”（译者加；自己意会。）
My beloved husband,
You may recall that you, too, are 54 years old and no longer able to satisfy certain needs I still have. I thus hope that you are not hurt to learn that, while you’re reading this, I am in a hotel room with the 18-year-old pool boy.
Your loving wife.
P.S. As a mathematician, you are certainly aware of the fact that 18 goes into 54 many more times than 54 goes into 18. Therefore, don’t stay up and wait for me.
当教授在午夜前从酒店回来时，他在客厅里发现了一个信封。他打开信读道:
”我亲爱的丈夫,
你也许还记得，你也已经54岁了，不能再满足我的某些需求。因此，当你读到这篇文章时，我希望你不会受伤，我正和一个18岁的游泳男孩在酒店房间里。
爱你的妻子。
作为一个数学家，你肯定知道，18/54的次数要比54/18的次数，要大很多倍。所以，不要熬夜等我。”（译者加；自己意会。）
----------------
Three men go bow hunting: a physicist, an engineer, and a statistician. After several hours in the forest, they finally see a deer at the other end of the field. The engineer tests his bow, measures how far away the deer is, raises his bow to the correct angle, and fires. But alas, he forgets to account for wind resistance, and his arrow falls 10 feet short.
The physicist then takes his turn. He accounts for air resistance and the force of the bow, aims his arrow, and fires. But this time, an ill-timed gust of wind carries his arrow just 10 feet too far away from the deer.
Suddenly, the statistician jumps into the air, and yells, “We got him!”
三个人用弓箭打猎：一个物理学家，一个工程师和一个统计学家。在森林里走了几个小时后，他们终于在田野的另一头看到了一只鹿。工程师测试他的弓，测量鹿离他有多远，把弓举到正确的角度，然后射出。但是，可惜的是，他忘了考虑风的阻力，他的箭落下时还差鹿10英尺。
然后轮到物理学家。他利用空气阻力和弓的力量，瞄准他的箭，射击。但这一次，一股不合时宜的风把他的箭吹得离鹿又远了10英尺。
但是突然，统计学家跳到空中，大喊道“我们射中他了!”
原创翻译：龙腾网 http://www.ltaaa.cn 转载请注明出处
Three men go bow hunting: a physicist, an engineer, and a statistician. After several hours in the forest, they finally see a deer at the other end of the field. The engineer tests his bow, measures how far away the deer is, raises his bow to the correct angle, and fires. But alas, he forgets to account for wind resistance, and his arrow falls 10 feet short.
The physicist then takes his turn. He accounts for air resistance and the force of the bow, aims his arrow, and fires. But this time, an ill-timed gust of wind carries his arrow just 10 feet too far away from the deer.
Suddenly, the statistician jumps into the air, and yells, “We got him!”
三个人用弓箭打猎：一个物理学家，一个工程师和一个统计学家。在森林里走了几个小时后，他们终于在田野的另一头看到了一只鹿。工程师测试他的弓，测量鹿离他有多远，把弓举到正确的角度，然后射出。但是，可惜的是，他忘了考虑风的阻力，他的箭落下时还差鹿10英尺。
然后轮到物理学家。他利用空气阻力和弓的力量，瞄准他的箭，射击。但这一次，一股不合时宜的风把他的箭吹得离鹿又远了10英尺。
但是突然，统计学家跳到空中，大喊道“我们射中他了!”
原创翻译：龙腾网 http://www.ltaaa.cn 转载请注明出处
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A father who is very much concerned about his son's bad grades in math decides to register him at a Catholic school. After his first term there, the son brings home his report card: He's getting "A"s in math. The father is, of course, pleased, but wants to know: "Why are your math grades suddenly so good?" "You know", the son explains, "when I walked into the classroom the first day, and I saw that guy on the wall nailed to a plus sign, I knew one thing: This place means business!"
一位非常关心儿子数学成绩不好的父亲决定把他送到一所天主教学校。在那里的第一个学期结束后，儿子把他的成绩单拿回家:他的数学成绩是“A”。父亲当然很高兴，但想知道:“为什么你的数学成绩突然这么好?”“你知道吗，”儿子解释说，“第一天我走进教室，看到那个家伙被钉在墙上的一个加号上，我就知道一件事:这个地方是玩真的！”
A father who is very much concerned about his son's bad grades in math decides to register him at a Catholic school. After his first term there, the son brings home his report card: He's getting "A"s in math. The father is, of course, pleased, but wants to know: "Why are your math grades suddenly so good?" "You know", the son explains, "when I walked into the classroom the first day, and I saw that guy on the wall nailed to a plus sign, I knew one thing: This place means business!"
一位非常关心儿子数学成绩不好的父亲决定把他送到一所天主教学校。在那里的第一个学期结束后，儿子把他的成绩单拿回家:他的数学成绩是“A”。父亲当然很高兴，但想知道:“为什么你的数学成绩突然这么好?”“你知道吗，”儿子解释说，“第一天我走进教室，看到那个家伙被钉在墙上的一个加号上，我就知道一件事:这个地方是玩真的！”
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An engineer, a mathematician, and a CPA each interviewed for a CFO opening and all three did equally well. So, in order to break the tie, the boss asked each one the same devious question, “What’s 2 + 2?”
The engineer responded quickly “4” - and was told to go home.
The mathematician thought about it and said, “It lies between 3.999… and 4.0001” - and was also let go.
The CPA thought about it for a few minutes, looked around, checked for any hidden microphones and then quietly asked, “What do you want it to be?” He got the job.
一名工程师、一名数学家和一名注册会计师分别参加了首席财务官职位的面试，三人的表现都一样好。所以，为了打破僵局，老板问了每个人同样狡猾的问题:“2 + 2等于多少?”
工程师迅速做出了“4”的反应，并被告知回家吧。
数学家想了想，说:“它介于3.999…和4.0001之间。”
会计师想了几分钟，环顾四周，看看有没有隐藏的麦克风，然后平静地问:“你想要多少?”然后他得到了这份工作。
An engineer, a mathematician, and a CPA each interviewed for a CFO opening and all three did equally well. So, in order to break the tie, the boss asked each one the same devious question, “What’s 2 + 2?”
The engineer responded quickly “4” - and was told to go home.
The mathematician thought about it and said, “It lies between 3.999… and 4.0001” - and was also let go.
The CPA thought about it for a few minutes, looked around, checked for any hidden microphones and then quietly asked, “What do you want it to be?” He got the job.
一名工程师、一名数学家和一名注册会计师分别参加了首席财务官职位的面试，三人的表现都一样好。所以，为了打破僵局，老板问了每个人同样狡猾的问题:“2 + 2等于多少?”
工程师迅速做出了“4”的反应，并被告知回家吧。
数学家想了想，说:“它介于3.999…和4.0001之间。”
会计师想了几分钟，环顾四周，看看有没有隐藏的麦克风，然后平静地问:“你想要多少?”然后他得到了这份工作。
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Mother is 21 years older than her son.
In six years she will be five times older than her son.
Question: Where is Dad?
母亲比儿子大21岁。
六年后她将比她儿子大五倍。
问：爸爸在哪里?
Mother is 21 years older than her son.
In six years she will be five times older than her son.
Question: Where is Dad?
母亲比儿子大21岁。
六年后她将比她儿子大五倍。
问：爸爸在哪里?
Solution:
Age of son at this moment = x
Age of mother at this moment = y = x + 21.
Age of son after 6 years = x + 6
Age of mother after 6 years = x + 21 + 6
After six years mother is five times older than son = (x + 6) * 5
We solve this system of equations:
解：
此时儿子的年龄x
此时母亲年龄 y = x + 21。
六岁后儿子年龄 x + 6
母亲6岁后的年龄 x + 21 + 6
六年后，母亲比儿子大五倍(x + 6) * 5
我们求解这个方程组:
Age of son at this moment = x
Age of mother at this moment = y = x + 21.
Age of son after 6 years = x + 6
Age of mother after 6 years = x + 21 + 6
After six years mother is five times older than son = (x + 6) * 5
We solve this system of equations:
解：
此时儿子的年龄x
此时母亲年龄 y = x + 21。
六岁后儿子年龄 x + 6
母亲6岁后的年龄 x + 21 + 6
六年后，母亲比儿子大五倍(x + 6) * 5
我们求解这个方程组:
5 * (x + 6) = y + 6
5 * (x + 6) = x + 21 + 6
5x + 30 = x + 27
4 x = -3
x = - 3/4
At this moment son's age is - 3/4 of the year, which is -9 months, which means at this moment daddy is on mother.
5 * (x + 6) = y + 6
5 * (x + 6) = x + 21 + 6
5x + 30 = x + 27
4x = -3
x = - 3/4
在这个时候，儿子的年龄是- 3/4，也就是-9个月，这意味着在这个时候爸爸在妈妈身上。
5 * (x + 6) = x + 21 + 6
5x + 30 = x + 27
4 x = -3
x = - 3/4
At this moment son's age is - 3/4 of the year, which is -9 months, which means at this moment daddy is on mother.
5 * (x + 6) = y + 6
5 * (x + 6) = x + 21 + 6
5x + 30 = x + 27
4x = -3
x = - 3/4
在这个时候，儿子的年龄是- 3/4，也就是-9个月，这意味着在这个时候爸爸在妈妈身上。
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Once a Mathematician was giving an interview.
Interviewer : Suppose you had an urgent and important meeting in your office and you are late and running fast to reach the office as early as possible and at the same time you see a building caught by fire with some people in serious problem in that building.Then what will you do??
Mathematician: Mam I will help the people caught in fire in the building by calling fire brigade.
Interviewer: Ok, same question but now there is no fire in the building.
Mathematician: Mam , I will set fire in the building and then the solution of this problem became same as the previous one.
有一次，一位数学家在接受采访。
面试官：假设你在办公室里有一个紧急而重要的会议，你迟到了，赶紧尽可能早地赶到办公室，同时你看到一栋大楼着火了，大楼里的一些人都遭遇了严重的问题。然后你会做什么?
数学家：嗯...我会打电话给消防队帮助大楼里失火的人。
记者：好的，同样的问题，但是现在大楼里没有着火。
数学家：嗯...我要到大楼里放火，然后这个问题的答案就变成和前一个一样了。
Once a Mathematician was giving an interview.
Interviewer : Suppose you had an urgent and important meeting in your office and you are late and running fast to reach the office as early as possible and at the same time you see a building caught by fire with some people in serious problem in that building.Then what will you do??
Mathematician: Mam I will help the people caught in fire in the building by calling fire brigade.
Interviewer: Ok, same question but now there is no fire in the building.
Mathematician: Mam , I will set fire in the building and then the solution of this problem became same as the previous one.
有一次，一位数学家在接受采访。
面试官：假设你在办公室里有一个紧急而重要的会议，你迟到了，赶紧尽可能早地赶到办公室，同时你看到一栋大楼着火了，大楼里的一些人都遭遇了严重的问题。然后你会做什么?
数学家：嗯...我会打电话给消防队帮助大楼里失火的人。
记者：好的，同样的问题，但是现在大楼里没有着火。
数学家：嗯...我要到大楼里放火，然后这个问题的答案就变成和前一个一样了。
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A mathematician is waiting for his pregnant wife to give birth. His mother in law calls: “Is it a boy or a girl?”
The mathematician replies: True
一位数学家正在等待他怀孕的妻子生孩子。岳母打电话问:“是男孩还是（或）女孩?”
数学家回答:是的。
A mathematician is waiting for his pregnant wife to give birth. His mother in law calls: “Is it a boy or a girl?”
The mathematician replies: True
一位数学家正在等待他怀孕的妻子生孩子。岳母打电话问:“是男孩还是（或）女孩?”
数学家回答:是的。
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Married couple, dealing with an issue …
"You love your mathematics more than you love me!"
"Not so, darling, I love you much more."
"Then prove it!"
"OK. Let R be the set of all lovable obxts..."
已婚夫妇，处理一个问题…
“你爱你的数学胜过爱我!”
“不是这样的，亲爱的，我更爱你。”
“那就证明它!”
“好吧。先令R是所有可爱东西的集合……”
原创翻译：龙腾网 http://www.ltaaa.cn 转载请注明出处
Married couple, dealing with an issue …
"You love your mathematics more than you love me!"
"Not so, darling, I love you much more."
"Then prove it!"
"OK. Let R be the set of all lovable obxts..."
已婚夫妇，处理一个问题…
“你爱你的数学胜过爱我!”
“不是这样的，亲爱的，我更爱你。”
“那就证明它!”
“好吧。先令R是所有可爱东西的集合……”
原创翻译：龙腾网 http://www.ltaaa.cn 转载请注明出处
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