How solving one Maths problem can make you a billionaire
EN
What’s the most difficult way to become a millionaire? Probably to solve one of the so- called “Millennium Prize Problems”, a collection of mathematical problems so challenging that the Clay Mathematics Institute in America offers a $1,000,000 prize for anyone who dares to solve them. But solving one of those problems, the “P vs. NP” problem, could earn you a lot more than that, since it contains the key to hacking into every bank account in the world.
The famous “P vs. NP” problem stems from an area of Maths called theoretical computer science, and asks a fundamental question: Are hard problems really just easy problems in disguise? Mathematicians represent this question as “does P=NP?” where P stands for polynomials (which are easy to solve) and NP stands for non-deterministic polynomials (which are difficult to solve).
For example, multiplication is a P problem. If I stopped a stranger on the street and asked them to calculate 3×5, the majority would correctly say 15. Factoring, however, (the technique of breaking big numbers down into smaller numbers) is an NP problem. It isn’t quite as easy to discover that 121 = 11×11, and you would need an hour and a calculator to discover that 232,887 = 521×447!
So what does this have to do with hacking into bank accounts? Well, cryptography, the art of writing or solving code, is an NP problem. Code is just text that computers read, and every bank account in the world is encrypted with it. Breaking down this code is very difficult, thank goodness, hence given the label NP. But suppose a clever Mathematician comes along and proves that P=NP. Suddenly, breaking down the code that protects people’s bank accounts and Internet transactions becomes a P problem, and our financial security is breached.
Why hasn’t someone proved it then? This problem seems so lucrative that every Mathematician in the world must be trying! The thing is, most Mathematicians believe it cannot be solved. In 2002, William Gasarch, a computer scientist at the University of Maryland, asked one hundred Mathematical researchers whether they thought “P=NP?” or not, and found that only 9% believed it was true, and half predicted that the problem would not be solved in this century!

Not everyone agrees though. In Simon Singh’s book, “The Mathematical Secrets of the Simpsons”, he explains that David S. Cohen, one of the writers for “The Simpsons” and an ex computer scientist, has a hunch that P = NP. He gives us a clue in the episode Homer! (1995), where Homer enters a 3-dimensional world and floating behind him is the equation “P=NP”, implying that in our 3-D world, “P=NP” is indeed true. Of course, Mathematics isn’t decided by popularity but rather a rigorous proof. To win $1 million you need either a definite proof of “P=NP”, or a definite proof of “P≠NP”.
The consequences of this problem go far beyond hacking into bank accounts, however. If David S. Cohen turns out to be right then Mathematics will have changed forever. Computers would become so powerful that they could find a proof of almost any Mathematical statement, since every difficult calculation would become easy. Scott Aaronson, a theoretical computer scientist at M.I.T, says “If P=NP then the world would be a profoundly different place than we usually assume it to be”.
So what would you do if you discovered a proof of P=NP? Would you hack into bank accounts and intercept high level military communications, or would you tell the Mathematical world and take the $1,000,000 prize? I don’t know about you but I think that the Clay Mathematics Institute should increase the prize money!
ZH
前言
成为百万富翁的最难方法是什么?可能是解决所谓的“千禧年奖励问题”之一。这是一系列数学难题,其难度之高使美国的克莱数学研究所为敢于解决它们的人提供了1,000,000美元的奖金。但是,解决其中一个问题,“P vs. NP”问题,可能会让你获得比这更多的金钱,因为它包含了全球每一个银行账户的黑客攻击的关键。
著名的“P vs. NP”问题起源于被称为理论计算机科学的数学领域,并提出了一个基本的问题:难题真的只是易于伪装的简单问题吗?数学家表示这个问题为“P=NP吗?”其中P代表多项式(容易解决),NP代表非确定性多项式(难以解决)。
例如,乘法是一个P问题。如果我在街上随便拦住一个陌生人,让他们计算3×5,大多数人会正确地回答15。但是,分解法(将大数字分解为小数字的技术)是一个NP问题。发现121 = 11×11并不那么容易,你可能需要一个小时和一台计算器才能发现232,887 = 521×447!
这与黑客攻击银行账户有什么关系呢?嗯,密码学,即编写或解密代码的技术,是一个NP问题。代码只是计算机阅读的文本,全世界的每一个银行账户都用它加密。幸运的是,破解这些代码非常困难,因此被标记为NP。但假设一个聪明的数学家过来并证明P=NP。突然之间,破解保护人们银行账户和互联网交易的代码变成了一个P问题,我们的财务安全受到了威胁。
为什么还没有人证明它呢?这个问题看起来如此有利可图,世界上的每一个数学家都必须在努力!问题是,大多数数学家相信它不能被解决。2002年,马里兰大学的计算机科学家William Gasarch询问了一百名数学研究者他们是否认为“P=NP?”,发现只有9%的人相信这是真的,有一半的人预测这个问题在这个世纪不会被解决!

然而,并不是每个人都同意。在Simon Singh的书《The Mathematical Secrets of the Simpsons》中,他解释说,《辛普森一家》的编剧之一,前计算机科学家David S. Cohen认为P = NP。他在1995年的“Homer!”一集中给了我们一个线索,其中霍默进入一个三维世界,在他身后浮现出“P=NP”的等式,暗示在我们的三维世界中,“P=NP”确实是真的。当然,数学并不是由流行决定的,而是由严格的证明决定的。要赢得1百万美元,你需要“P=NP”的明确证据,或“P≠NP”的明确证据。
然而,这个问题的后果远不止于黑客攻击银行账户。如果David S. Cohen被证明是对的,那么数学将永远改变。计算机将变得如此强大,以至于它们可以找到
几乎任何数学陈述的证明,因为每一个困难的计算都会变得容易。麻省理工学院的理论计算机科学家Scott Aaronson说:“如果P=NP,那么这个世界将与我们通常认为的大不相同”。
所以,如果你发现了P=NP的证据,你会做什么?你会黑进银行账户并拦截高级军事通讯,还是会告诉数学界并获得1,000,000美元的奖金?我不知道你怎么想,但我认为克莱数学研究所应该增加奖金金额!
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