# 混沌，又一次数学之旅

http://songshuhui.net/archives/78893

# 失而复得

“一切相互影响，因为时间，一切将会相遇。而在自由延伸的空间，以及无限延续的运动中，所有物质缠绕着，幻作所有形状，映出所有轮廓。一切且近且远，且聚且散，且合且离，且生且死。而这全因那些或吸引或排斥的力，只有它们是永恒的。它们不知疲倦地摇摆着，使宇宙焕出活力，成为一座舞台，用不断重生的实物演着常新的戏码。”

# 影片在线观看地址

Youku（中文字幕）:

http://v.youku.com/v_show/id_XNTAwNzg1MzI4.html

http://v.youku.com/v_show/id_XNTAwNzg3NDIw.html

http://v.youku.com/v_show/id_XNTAwNzk0NjQ0.html

http://v.youku.com/v_show/id_XNTAwOTMyMjUy.html

http://v.youku.com/v_show/id_XNTAwOTQ5MTIw.html

http://v.youku.com/v_show/id_XNTAxMDMyNjQ4.html

http://v.youku.com/v_show/id_XNTAxMDQ5Nzg0.html

http://v.youku.com/v_show/id_XNTAxMDYxOTUy.html

http://v.youku.com/v_show/id_XNTAxMDgwMjE2.html

# 素数并不孤独

http://songshuhui.net/archives/82114

——高斯

# 素数何时成双对

2、3、5、7、11、13……最初的几个素数，要找出来并不困难，但随着数字增大，如果一个一个数字按照定义去筛选是否素数，工作量会很快变得十分庞大。同为古希腊数学家的埃拉托色尼，给出了一个比较省力的算法，后人称之为埃拉托色尼筛法。

【埃拉托色尼筛法，图片出处：维基百科】

# 漫天星河难理清

【画在平面上的素数分布，图片出处：维基百科】

【霸气的哈代，图片出处：维基百科】

# 狂沙淘尽始得金

【出问题的那款芯片，图片出处：维基百科】

【陈景润的雕像，图片出处：维基百科】

# 梅花香自苦寒来

【张益唐，图片出处：新罕布什尔大学】

# 路漫漫其修远兮

6月5号，40万，连原来的百分之一都不到。

Bounded gaps between primes, Yitang Zhang, Annals of Mathematics

Open question: The parity problem in sieve theory, Terence Tao,http://terrytao.wordpress.com/2007/06/05/open-question-the-parity-problem-in-sieve-theory/

Are there infinitely many twin primes?, D. A. Goldston,http://www.math.sjsu.edu/~goldston/twinprimes.pdf

# 哈洛德•贺欧夫各特：彻底证明弱哥德巴赫猜想

http://songshuhui.net/archives/85342

“任一大于 2 的整数都可以写成三个质数之和。”271 年前，德国人哥德巴赫告诉欧拉这句话时，可能自己也没想到一下就在解析数论这个领域挖了一个东非大裂谷级别的“坑”。

1937 年，苏联数学家伊万•维诺格拉多夫更进一步，在无需广义黎曼猜想的情形下，直接证明了充分大的奇数可以表示为三个素数之和，被称为“三素数定理”。不过他无法给出“充分大”的界限。他的学生博罗兹金于 1939 年确定了一个“充分大”的下限：314348907。这个数字有 6846169 位，要验证比该数小的所有数完全不可行。

1995 年，法国数学家奥利维耶•拉马雷证明，不小于 4 的偶数都可以表示为最多六个素数之和。莱塞克•卡涅茨基证明了在黎曼猜想成立的前提下，奇数都可表示为最多五个素数之和。2012年，陶哲轩在无需黎曼猜想的情形下证明了这一结论。

2013年5月13日，法国国家科学研究院和巴黎高等师范学院的数论领域的研究员哈洛德•贺欧夫各特，在线发表两篇论文宣布彻底证明了弱哥德巴赫猜想。贺欧夫各特在文章“Minor arcs for Goldbach’s problem”中，给出了指数和形式的一个新界。在文章“Major arcs for Goldbach’s theorem”中，贺欧夫各特综合使用了哈迪-利特伍德-维诺格拉多夫圆法、筛法和指数和等传统方法，把下界降低到了1030左右，贺欧夫各特的同事 David Platt 用计算机验证在此之下的所有奇数都符合猜想，从而完成了弱哥德巴赫猜想的全部证明。

# 谈谈张益唐

【摄影：方弦】

Platt做的就是用计算机完成这样的计算，而且是以严格的方式。对于数学验证而言，严谨性很重要。我们知道，计算机只能表达有理数，它不能直接处理像圆周率这样的无理数。所以，实际上计算机不能处理实数，它只能处理一个区间[a,b]，其中a和b都是有理数。而你只能问你的计算机，能不能给出一个尽量短的区间[c,d]，使得区间[a,b]中的实数的正弦值（或者别的什么函数值）都落在区间[c,d]中。这就是所谓的区间算术。

# 丘成桐香港中文大学演讲：如何成就科学大师

（丘成桐 1949年出生于广东汕头。1983年获得素有数学诺贝尔奖之称的菲尔兹奖，迄今仍是华人数学家中唯一的获奖者。1979年后，丘成桐把主要精力转向振兴祖国数学事业上，先后创建了香港中文大学数学所、中科院晨兴数学中心、浙江大学数学中心和清华大学数学中心，并亲自担任这些研究机构的负责人。现任美国哈佛大学讲座教授、国际顶尖数学杂志《微分几何杂志》主编。）（原标题：数学与生活）

# 13 Math Jokes That Every Math Geek Will Find Hilarious

Back when the internet was young, the primary users were its builders, math and tech-oriented academics spread around the country.

As a result, math jokes have an elemental role in the history of the internet.

From the earliest Usenet threads to the techiest subreddits, geeky math jokes — some implicit swipes at less-pure disciplines, other puns or plays on words of different concepts — have been a major part of the modern history of math.

What’s more, these japes also have the effect of making those who didn’t get the joke to look into what makes it funny, teaching people some of the more obscure concepts.

Here are just a few of the best ones. Where necessary, we’ll do the unthinkable and the tacky and explain the joke.

### JOKE #1

Three statisticians go out hunting together. After a while they spot a solitary rabbit. The first statistician takes aim and overshoots. The second aims and undershoots. The third shouts out “We got him!”

Source: chjilloutdamnit / Reddit

### JOKE #2

Two random variables were talking in a bar. They thought they were being discrete but I heard their chatter continuously.

Source: armchairdetective /  reddit

Explanation: When you roll a die, you either get a 1, 2, 3, 4, 5, or 6. Since there are a finite number of possibilities, the statistic involved is called a discrete random variable. When you select any real number from between 0 and 1, there are an infinite number of possible draws. The statistic involved is called a continuous random variable.

### JOKE #3

There was a statistician that drowned crossing a river… It was 3 feet deep on average.

Source: anatiferous_outlaw / reddit

### JOKE #4

Write the expression for the volume of a thick crust pizza with height “a” and radius “z”.

Source: Reddit

Explanation: The formula for volume is π·(radius)2·(height). In this case, pi·z·z·a.

### JOKE #5

A: “What is the integral of 1/cabin?”

B: “log cabin.”

A: “Nope, houseboat–you forgot the C.”

Source: Reddit

Explanation: We’re treating “cabin” is a variable.

The integral of 1/x is loge(x).

However, since it’s integration, you’ve got to add a constant.

So ∫(1/cabin) = loge(cabin) + c, or “a log cabin plus the sea.”

### JOKE #6

Q: Why did the chicken cross the road?

A: The answer is trivial and is left as an exercise for the reader.

Source: Reddit

Explanation:

This is a common refrain found in mathematics texts.

It is widely considered a cruel professor’s malicious cop-out by particularly lazy students of mathematics.

### JOKE #7

Q: How many mathematicians does it take to change a light bulb?

A: One: she gives it to three physicists, thus reducing it to a problem that has already been solved.

Source: MathOverflow

Explanation: Mathematicians try to reduce an unsolved problem to a form which has already been solved before. Once that’s done it’s considered complete, as the previously derived formula is taken as written.

There are many light bulb jokes about physicists. Finding several are left as an exercises to the reader.

### JOKE #8

A physicist, a biologist, and a mathematician are sitting on a bench across from a house. They watch as two people go into the house, and then a little later, three people walk out.

The physicist says, “The initial measurement was incorrect.”

The biologist says, “They must have reproduced.”

And the mathematician says, “If exactly one person enters that house, it will be empty.”

Source: Reddit

### JOKE #9

The B in Benoît B. Mandelbrot stand for Benoît B. Mandelbrot.

Source: Reddit

Explanation: The Mandelbrot set is a fractal. As you zoom in on portions of the fractal, you ee a self replicating image. So the infinite paradox in the joke is a shoutout to the problem. Here’s an example of what we’re talking about with a gif of zooming in on a point of infinite complexity in the Mandelbrot set:

### JOKE #10

Infinitely many mathematicians walk into a bar. The first says, “I’ll have a beer.” The second says, “I’ll have half a beer.” The third says, “I’ll have a quarter of a beer.” The barman pulls out just two beers. The mathematicians are all like, “That’s all you’re giving us? How drunk do you expect us to get on that?” The bartender says, “Come on guys. Know your limits.”

Source: Reddit

Explanation: This is a reference to a converging infinite series.

The limit of this:

from n=0 to ∞   Σ (1/2n) = 1 + 1/2 + 1/4 + 1/8 + …  = 2

### JOKE #11

An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third orders a third of a beer. The bartender bellows, “Get the hell out of here, are you trying to ruin me?”

Source: Reddit

Explanation: This is another hilarious reference to an infinite series — the harmonic series — which is not convergent but instead diverges to infinity.

from n=1 to ∞   Σ (1/n) = 1 + 1/2 + 1/3 + 1/4 + …  =

See a full explanation in this slideshow >

### JOKE #12

When a statistician passes the airport security check, they discover a bomb in his bag. He explains. “Statistics shows that the probability of a bomb being on an airplane is 1/1000. However, the chance that there are two bombs at one plane is 1/1000000. So, I am much safer…”

Source: Andrej and Elena Cherkaev

Explanation: While this statistician is correct that the joint probability there are two bombs on a plane is 1/1,000,000, his bringing one on doesn’t change the prior probability that there is still a 1/1,000 chance of his flight being the one with a random bomb.

### JOKE #13

What do you get when you cross a mosquito with a mountain climber?

Nothing. You can’t cross a vector and a scalar.

Source: Reddit

Explanation: A vector is a mathematical entity with both magnitude and direction in any number of dimensions. You can take the cross product of two vectors to form a new vector, similar to multiplication of real numbers.

A scalar is just a real number, a directionless magnitude in vector space. You cannot take a cross product of a scalar and a vector.

Hence, you can’t cross a mosquito (disease vector) and a mountain climber (a scalar).

That is one terrible pun. I’m sorry.