MAKE RICH

September 4, 2010

TOP 10 WAYS TO MAKE MONEY ONLINE

The internet offers a golden opportunity tomake money. One can make an unlimited money with the help of internet while just sitting at home. There are a lot of legitimate business and money making opportunities available online.  In this article, we will discuss briefly 10 varied ideas that can help in makingmoney online.

1 – Freelancing: Freelancing offers a better opportunity to make money online.  One can opt for writing jobs related to computers, internet marketing, web designing, data entry jobs, form filling jobs etc while sitting at home. This is an effective mode of earning money without sacrificing the luxury of flexible timing and the comfort of home.

2 – Social media marketing: The dynamics of the internet has changed due to the growing popularity of social media among people of all age groups. Contrary to popular belief, social media is not about teenagers and pastime anymore. You can offer social media marketing solutions to both the local businesses and offshore businesses. However, you need to be well versed with in the dynamics of the popular networking sites before you start the same. Facebook Ads, tweeting, blogging and participating in online forums can help you immensely in making money online from the comfort of home.

3- Affiliate marketing: It offers you the opportunity to earn without any limit if you have your own blog or web page. Here, you can add affiliate advertisements and for every sale through your website, you get a reasonable part of the profit. It is a symbiotic business model for the affiliates. To start affiliate marketing, all you need to have is a web page or a blog. Blogs can be created free of cost. However, you need to be very cautious while choosing an affiliate. Credibility, pay out pattern and popularity of the affiliate should be considered before you commence the association.

4 – Online advertisement:  If you are best in publicizing, organizing and managing events, you can provide your services online. You can earn money though writing about client’s activities. The pay per click model can also help you in the direction of making money. If you are having an idea regarding pay per click online advertisement, you can help businesses by organizing and developing their online visibility. You can approach conferences and offer them the online version of that event. Through this, you can reach the entire audience, who can’t keep track with the offline happenings. Through blogging, you can make cash from the advertising banners which are placed along your logs and can also get benefited by the sponsored blogging.

5- Multi level marketing: On the internet you will find several opportunities to start or become associated with the multilevel marketing business ventures. Here, every referral is capable of giving you a handsome reward. In case of online multi level marketing, two things are pivotal. One is the credibility of the company and second is the product/service. It is a fact that success rate in case of online multi level marketing is drastically lower as compared to the other online money making ways. But, if you are determined and put your sincere efforts, success shall touch your feet.

6 – Online marketing: You can sell your own products/services or of others online. Websites like eBay are the perfect platform to start your online selling career. You can also go for your own website and sell goods from there. To achieve success in online marketing, you need to pay attention to several factors. The most significant of them is making your online store a specialty one. Demand for online specialty stores is now at an all time high. Providing a secured gateway for online money and data transaction is another such factor relating to online marketing success. If you are unable to provide a secured gateway for your customers, it will hamper your business significantly. Along with this, you will also have to make prompt arrangements for faster shipping of the ordered product/service.

7 – Forex trading: Though there is a fringe of risk attached with the foreign exchange trading, yet it is one of the most lucrative business ideas. With internet’s assistance, you can start this business from home itself. To excel in Forex trading, you need to have a clear idea regarding the fluctuations prevailing in the Forex market. These fluctuations are going to pay you the profit. For this, you need to have the required patience to bear the initial losses and the required risk taking capability to venture into a highly volatile market. There are several software packages and online tools available which can help you in starting your career as a Forex trader.

8 – Website redesigning: A new website doesn’t give an expected result. Recently, the New York Times mentioned that, one can make a reasonably good life through flipping the web sites without launching any brand new web site. You can find the niche site which has good potential with poor execution. You can purchase the website, redesign it and search for the engine optimization. Then you can sell it to anybody who is in need of the same. You have to invest your sweat in all these things to reach at a desirable level.

9 – Microstock Photography:  You should cover the market of microstock photography. Microstock videos are also available in the market. As a video fanatic, you have to carry the video footage such as the Pixelflow, Pond5 and istockphoto video through the sites of stock imaging. Fix your price, terms and conditions and then you can add a new source of income.

10- Online Consulting: If you possess good command and expertise over a professional field, you can share your knowledge online and can make money out of it. Lawyers, doctors, financial advisors and tutors are of high demand at web space.

One can start his/her own online business with low investments. By using one or two of the ideas listed above ideas above you can increase your income potential significantly

How to Become As Rich As Bill Gates

As a graduate student in computer science at MIT earning a $1600/month research stipend, I feel amply qualified to instruct the entire Internet on the art of becoming as rich as Bill Gates (check the Wealth Clock to see how much he has right now). I get my confidence from Dr. Leo Buscaglia, author of Love, Born for Love : Reflections on Loving, Living, Loving and Learning, and Bus 9 to Paradise. Dr. Buscaglia, our nation's most prominent lecturer on the subject of love, turns out to be divorced ("it was a very loving divorce").

Lesson 1: Choose Your Grandparents Carefully

"There are three ways to make money. You can inherit it. You can marry it. You can steal it."
-- conventional wisdom in Italy

William Henry Gates III made his best decision on October 28, 1955, the night he was born. He chose J.W. Maxwell as his great-grandfather. Maxwell founded Seattle's National City Bank in 1906. His son, James Willard Maxwell was also a banker and established a million-dollar trust fund for William (Bill) Henry Gates III.In some of the later lessons, you will be encouraged to take entrepreneurial risks. You may find it comforting to remember that at any time you can fall back on a trust fund worth many millions of 1998 dollars.

Lesson 2: Choose Your Parents Carefully

"A young man asked an old rich man how he made his money. The old guy fingered his worsted wool vest and said, "Well, son, it was 1932. The depth of the Great Depression. I was down to my last nickel. I invested that nickel in an apple. I spent the entire day polishing the apple and, at the end of the day, I sold the apple for ten cents. The next morning, I invested those ten cents in two apples. I spent the entire day polishing them and sold them at 5 pm for 20 cents. I continued this system for a month, by the end of which I'd accumulated a fortune of $1.37. Then my wife's father died and left us two million dollars."

William Henry Gates, Jr. and Mary Maxwell were among Seattle's social and financial elite. Bill Gates, Jr. was a prominent corporate lawyer while Mary Maxwell was a board member of First Interstate Bank and Pacific Northwest Bell. She was also on the national board of United Way, along with John Opel, the chief executive officer of IBM who approved the inclusion of MS/DOS with the original IBM PC.Remind your parents not to send you to public school. Bill Gates went to Lakeside, Seattle's most exclusive prep school where tuition in 1967 was $5,000 (Harvard tuition that year was $1760). Typical classmates included the McCaw brothers, who sold the cellular phone licenses they obtained from the U.S. Government to AT&T for $11.5 billion in 1994. When the kids there wanted to use a computer, they got their moms to hold a rummage sale and raise $3,000 to buy time on a DEC PDP-10, the same machine used by computer science researchers at Stanford and MIT.
Note: Recall that in the 1980s we venerated Donald Trump and studied his "art of the deal". If Donald Trump had taken the millions he inherited from his father and put it all into mutual funds, you'd never have had to suffer through one of his books. But he'd be just about as rich today.

Lesson 3: Acquire Research Results by Hiring and Buying

Conventional (loser) economic wisdom holds that monopolies should spend heavily on research because they are in a position to capture the fruits of the research. But if you want to become as rich as Bill Gates, you have to remember that it is cheaper to wait for a small company to come up with something good and then buy them. In the old days, antitrust laws kept monopolies from buying potential competitors. But not anymore. When Microsoft products were threatened by network computers and Web-based applications, they simply bought WebTV and Hotmail.Another good strategy is to hire the right people. Some of the guys who wrote Microsoft Windows had previous worked on window systems at Xerox PARC. So Xerox paid for the research; Microsoft paid only for development.
In the long run a tech company without research probably can't sustain its market leadership. So you'll eventually need to build something like research.microsoft.com (check outnetscan.research.microsoft.com to see some interesting online community research).

Lesson 4: Let Other People Do the Programming

If you're a great engineer, it can be frustrating to rely on other people to translate your ideas into reality. However, keep in mind that the entire Indian subcontinent is learning Java. And that if Microsoft, Oracle, SAP, and Sun products simply worked and worked simply, half of the world's current IT workers would be out of a job. You're not going to get rich being "just a coder." Especially working in painful low-level imperative languages such as C or Java. It might be worth writing your own SQL queries and HTML pages since these tend to be compact and easier than precisely specifying the work for another person to do. But basically you need to get good at thinking about whether a piece of software is doing something useful for the adopting organization and end-user. Bill Gates does code reviews, not coding.[If you aren't sure that you need to be filthy rich and like to do some coding, see this old misguided article for more about what it might mean to be a great software engineer.]

Lesson 5: Train your new CEO

If you're an intelligent curious person it can be painful to run a company of more than 50 people. You spend more time than you'd like repeating yourself, sitting in boring meetings, skimming over long legal documents in which you know there are errors but aren't sure how serious, etc. The temptation is to hand over the reins to the first "professional manager" who comes along. And that's what the standard venture capitalist formula dictates. But Bill Gates didn't do that. He hired Steve Ballmer in 1980 and gave him the CEO job 20 years later. Making money in the software products business requires domain expertise and a commitment to solving problems within that domain. Great tech companies are seldom built by non-technical management or professional managers who aren't committed to anything more than their paycheck. Adobe is another good example. The two founders were PhD computer science researchers from Xerox PARC who were passionate about solving problems in the publishing and graphics world. They are still guiding operations at Adobe.Note that this is a principle that Old Economy companies have long understood. Jack Welch joined GE in 1961 and became CEO 20 years later. Sometimes an Old Economy company may pull in a few outsiders to senior positions but, because they have such stable bureaucracies underneath, they can more easily afford this than startups.
See Charles Ferguson's High Stakes, No Prisoners (1999) for a longer explanation of how hired-gun CEOs manage to kill software products companies.

Lesson 6: Focus on Profit

"At Hewlett-Packard, people, materials, facilities, money, and time are the resources available to us for conducting our business. By applying our skills, we turn these resources into useful products and services. If we do a good job, customers pay us more for our products than the sum of our costs in producing and distributing them. This difference, our profit, represents the value we add to the resources we utilize."
-- David Packard in The HP Way

Remembering to make a profit was tough in the dotcom 1990s but it turns out that Hewlett and Packard's ideas were right. Most of the management teams at dotcom businesses, by being disorganized, unintelligent, and ignorant, were subtracting value from the resources that they controlled.How does one make money in the software products business? Simple. The necessary step is to build something that becomes part of information systems that generate value for organizations and end-users. Once you've created value you can extract a portion in lots of ways. You can be closed-source and charge a license fee. You can be open-source and charge for training, service, support, and extensions. But if you aren't getting your software product into important information systems, you don't have a prayer, no matter how slick your marketing materials.
If you're creative and diligent the software products business is extremely lucrative. If you're losing money, ask yourself what you're doing wrong. The answer is probably "plenty".

Lesson 7: Let the Venture Capitalists Schmooze Wall Street ...

... but don't let them run your company. A profitable Microsoft Corporation brought in venture capitalists (VCs) at the last minute. They didn't need or spend the money but used the VCs to boost their valuation at the initial public offering, thus getting more money for the shares that they sold. Venture capitalists are dangerous because even the most successful might not know anything about business. Remember that there are tens of thousands of venture capitalists in this world. Assuming that they make random choices of companies in which to invest there will be a Gaussian curve of performance. Some firms will do consistently better than average even if everyone is guessing. Imagine that thousands of monkeys are flipping coins; some of the monkeys will get 10 heads in a row. These are the monkeys that will be celebrated for their insight. These are the monkeys whose track records will lead to uncritical cheerleading by underwriters and public investors. In bull markets such as we had in the 1990s nearly all the monkeys will be fairly consistent winners. But remember your next-door neighbor who made money in the stock market in 1985. He convinced himself that he had special insight and ability when actually he was only holding high-beta stocks in a rising market. So his foray into the commodities futures market wiped him out in the crash of '87.Bottom line: successful software products companies spend most of their time listening to their customers and users rather than to venture capitalists.
[See "Money, Money, Money (and Investing)" for how the Gaussian curve works for mutual fund managers and also read Princeton Professor Burton Malkiel's A Random Walk Down Wall Street.]

Lesson 8: Self-Esteem is Not Job 1

Gentility, politesse, decorum, and high self-esteem are wonderful. You can achieve all of these things within your organization. And then watch it be destroyed by competitors where frank and, if necessary, harsh criticism is encouraged. Technical people, even (and especially) those fresh out of school are always convinced that whatever they've developed, no matter how hare-brained, is perfect. It takes a technical person with good judgement to notice the flaws and it may require repeated and increasingly harsh delivery for the, uh, pinhead to realize his or her mistake.Example: I once encountered a group of 6 people who called themselves "engineers." To solve what they thought was a new problem, they were going to build their own little database management system with their own query language that was SQL-like without being SQL. I pointed them to some published research by a gang of PhD computer scientists from IBM Almaden, the same lab that developed the RDBMS and SQL to begin with in the 1970s. The research had been done over a five-year period and yet they hadn't become aware of it during several months of planning. I pointed them to the SQL-99 standard wherein this IBM research approach of augmenting a standard RDBMS to solve the problem they were attacking was becoming an ISO standard. They ignored it and spent another few months trying to build their enormously complex architecture. Exasperated, I got a kid fresh out of school to code up some Java stored procedures to run inside Oracle. After a week he had his system working and ready for open-source release, something that the team of 6 "engineers" hadn't been able to accomplish in 6 months of full-time work. Yet they never accepted that they were going about things in the wrong way though eventually they did give up on the project.
An 1994 New Yorker article about Microsoft relates "If he strongly disagrees with what you're saying, [Gates] is in the habit of blurting out, 'That's the stupidest fucking thing I've ever heard!'". Jennifer New, a former Microsoft contractor, writes "Meetings with Bill or one of his top people are often replete with a barrage of expletives and other disdainful comments." (Salon, September 1997) My friends who work or have worked at Microsoft tell similar tales. But how different is this from other elite organizations?
When I arrived at MIT as a first-year graduate student in electrical engineering and computer science, I asked a professor for help with a research problem. He said "The reason that you've having trouble is that you don't know anything and you're not working very hard." A friend of mine was a surgery resident at Johns Hopkins. He complained to one of his teachers that he was having trouble concentrating because he'd been up all night for several nights in a row. The professor replied "Oh... does your pussy hurt?" According to Business Week, Jack Welch "encouraged near-brutal candor in the meetings he held [at GE]".
The bottom line: self-esteem is great but beware of creating a cozy home for unproductive people with bad ideas.

More

Plato addresses some of these issues in the first book of The Republic (available online from www.gutenberg.net). Socrates asserts that people who've inherited fortunes tend to be light with their money but that people who've made their fortunes "have a second love of money as a creation of their own, resembling the affection of authors for their own poems, or of parents for their children, besides that natural love of it for the sake of use and profit which is common to them and all men. And hence they are very bad company, for they can talk about nothing but the praises of wealth."Socrates asks Cephalus, a wealthy old man, "What do you consider to be the greatest blessing which you have reaped from your wealth?" Cephalus replies that "The great blessing of riches, I do not say to every man, but to a good man, is, that he has had no occasion to deceive or to defraud others, either intentionally or unintentionally."
In the Decameron, Boccaccio writes "If you really want to make the big bucks, what you really need is a monopoly on the desktop operating system. But the Sherman Antitrust Act, 15 U.S.C. § 1 and 2, and Clayton Antitrust Act, 15 U.S.C. § 25, are real bitches."

Sources

Good sources of facts about Bill Gates and Microsoft are the following books:

• Hard Drive (James Wallace and Jim Erickson; 1992)
• Overdrive (James Wallace; 1992)
• Gates : How Microsoft's Mogul Reinvented an Industry-And Made Himself the Richest Man in America (Stephen Manes, Paul Andrews 1994)
• How the Web Was Won : How Bill Gates and His Internet Idealists Transformed the Microsoft Empire (Paul Andrews 1999)
• High Stakes, No Prisoners (Charles Ferguson 1999) explains how Microsoft crushed Netscape
• if you don't feel like reading Project Gutenberg's version on-line, you can pick up a paperback copy of Robin Waterfield's translation of The Republic.                   
  
  
  
  

  The easiest way to get rich

  Judging by their behavior, most people have an obsession with wealth. Politicians promise to create it, most popular magazines are filled with gossip about those who have it, and the average person spends much of their adult life trying to obtain it. We are creatures obsessed with money, partly for what it can buy, but also as a thing of value in itself.
  
  But most people misunderstand money. They don't really know how to obtain it, or how to hold onto it once they have it.
  
  If you're interested in getting rich, 
  I'm going to give you the simplest formula for doing so. In fact, if you follow it you're virtually guaranteed to build enough wealth to get you into the top 5% of society. As the shampoo advertisement says: "It won't happen overnight, but it will happen".The hardest way to get rich
  Before I go into my formula, let me tell you about hard ways to get rich.
  
  One of the hardest is to be born into it. Of course, if you happen to enter this world as a Hilton, a Gates or a Windsor, then life is sweet. But since 99.9999% of the population aren't that lucky, I'm assuming you didn't win that particular lottery.
  
  And speaking of lotteries, gambling is another very difficult way to get rich. Sure, some people buy a lottery ticket and win big, but most don't. You can gamble your entire life and you'll most likely end up broke rather than wealthy.
  
  When I was younger, I thought the easiest way to get rich was to become famous through some kind of creative act. Stephen King got rich writing horror novels, so why not me?
  
  I'm now much wiser and realize that the vast majority of novelists never even get published. Of those who do, most wallow in obscurity. Only very few make it anywhere near the best-seller list, and only one in a million will achieve any kind of serious wealth.
  
  The same fate awaits the majority of musicians, software company founders, sportspeople and website creator. For every Google that makes its owners billions, there are a million websites that lose money. Creativity is the most fun and rewarding way to get rich, but it's also a very difficult way.
  
  The reason the media raves about and idolizes those who've built wealth through creativity is because they're so rare. You don't hear about the vast majority who wallow in obscurity and poor pay, because they're not interesting. "Young genius makes $1 billion from website" is a great headline "Ten thousand young geniuses make nothing from their hard work" isn't.
  
  I'm not saying you shouldn't keep your dreams alive. It's one of the best parts of life. But this article isn't about the most fun way to try and get rich - it's about the easiest way.
  
  Okay, here's the system. Step 1: Get a well-paid job
  This is a reasonable amount of work, and takes a few years, but it's a virtually guaranteed way to make a good income. If they're willing to put in the work, almost any intelligent person can get a job paying $100,000 or more within the space of a few years. While it's not easy, it is by far the easiest and most likely way to secure a good income. In fact, I've already written an entire article on how to get a job paying more than $100,000 a year for those who wish to pursue this avenue.Step 2: Get good tax advice
  However you make your money, your number one expense is likely to be funding the government. In most developed countries, the average worker pays around 30% of everything they earn straight into the taxman's pocket. If you've taken my job advice, you'll most likely pay even more than that.
  
  While taxation is necessary to fund the good things governments provide, you don't do yourself any favors by paying more than your fair share. If you're serious about building wealth, get a good accountant who understands how to legally minimize your tax bill. Step 3: Save 20% of everything you ever earn
  As soon as you get paid, arrange to have 20% of your income removed into a savings account. Many banks can do this automatically for you. Keep your savings account separate from your spending account, and you'll barely miss this money.
  
  There's a saying in economics "expenses rise to meet income". This means money that's easily available to you is certain to be spent. That's why most people's paychecks disappear before their next payday. They get used to having a certain amount to spend, and habitually run down their bank account.
  
  Have your savings moved somewhere it's a hassle to get them out of to avoid this risk. Many high interest accounts require you to give them a few days notice, which is ideal for this purpose. Step 4: Conservatively invest the funds that build up in your savings account
  Once a month, go into your savings account and divide the money by investing it into the three core conservative assets: shares, property and cash. Open a mutual fund account for shares, a property fund for property, and a money market fund for cash. Look for share and property funds that invest in a broad range of assets and most importantly charge very low fees. An index fund is ideal for the shares. An index of property funds is ideal for property.
  
  Put an equal amount into each account. This will diversify you against risk in any one particular asset. If you're younger, this rule is a little bit flexible, allowing you to take a little more risk and put more into shares and property if you like. Step 5: Reinvest any income you get from your assets straight back into buying more assets
  Mutual funds and property funds pay dividends. Money market accounts pay interest. Don't take this income into your spending account. Instead, select the option to have it reinvested into the fund that generated it.Step 6: Never touch these funds and do your best to ignore them
  The business press, like the mainstream press, loves a crisis. "Shares to skyrocket" or "Property to plummet" headlines will sell many more copies than "Things to continue steadily". All markets go up and down. Every day, some speculation will be published about some crisis or opportunity.
  
  Ignore it all.
  
  Just keep putting the 20% into your assets. Sometimes they'll go up and sometimes they'll go down in value. But over the long term, they'll almost certainly go up. Step 7: Wait a decade
  Do what I've outlined above and in a decade you'll be rich. Sure, you won't be Bill Gates, but you'll almost certainly be in the top 20% of wealth holders. Wait another decade and you'll be in the top 5% or higher.
  
  That's the plan. It's not the most exciting or glamourous way to build wealth, but it's the easiest. Quite simply, this is how most rich people got there.
  
  You too can join them, if you follow it.
  
  
  
  
  
  
  

  How maths can make you rich and famous

  here are many good reasons for doing mathematics. There is the sheer joy of mathematical discovery, the beautiful interplay between mathematical structures and patterns, the fascinating way that mathematics helps to reveal the mysteries of the physical world and the excitement of solving age-old puzzles. Becoming rich and famous is not usually a motivation for doing maths, and is an endeavour more usually linked to film stars and sports personalities. However, in this article I will tell you how you can become rich and famous by doing maths - but be warned, this is not an short cut to riches, and becoming a film star may be easier.
  

  How maths can't make you rich and famous

  
  

  Sometimes maths is no use at all...!
  Image DHD Photo Gallery

  There are various ways that mathematics has been claimed to be able to make you rich and famous and I thought that it would be good to dispose of some of these as quickly as possible. One of the questions that I am frequently asked when people find out that I'm a professional mathematician (apart from "when will you leave?") is "how can I choose my numbers for the National Lottery to maximise my chances of winning?". Unfortunately mathematics is of no great use here as all combinations of numbers are equally likely (or unlikely) to win (a fact not well appreciated by the general public).

  The same conclusion, by and large, applies to any form of gambling. The invention of the branch of mathematics now called probability was motivated, in part, by attempts to understand gambling. However, in the long term, all gambling will lead to a loss of hard-earned cash (as the people who own casinos understand probability as well and can adjust the various games so that the odds are in their favour).

  A final way not to become rich and famous with mathematics is to win a Nobel prize.There is no Nobel prize in mathematics. The reason for this is that Alfred Nobel, when setting up the prizes (for physics, chemistry, economics, peace, etc.) did not include mathematics because he, quite misguidedly, thought that mathematics had no practical use.

  How mathematics could make you rich and famous

  Faced with the depressing conclusions of the previous section we have to ask ourselves whether mathematics can ever make us rich and famous. Fortunately (for the reader) the answer to this question is yes. One way is to work for a bank. There is a new branch of mathematics called financial mathematics which looks at questions like the right price to set for an option (a right to buy shares on the stock market). Mathematicians able to work in this field are in high demand, but have to understand the complexities of tricky subjects such as stochastic differential equations.

  
  

  Maths is the key...
  Image www.freeimages.co.uk

  Another way to become rich and famous is to devise, or break a code. Nearly all modern codes are based upon ideas from pure mathematics (number theory to be precise). Codes are incredibly important to nearly all aspects of modern life, including transactions between you and your bank (if you have a bank account) and any time that you send "secret" information (such as a credit card number) over the Internet. Most of them rely for their security on the current belief that it is very hard to find the prime factors of a large number. (Later on we shall find out exactly how hard this is.) If you can find a quick way to factorise a large number quickly, then fame and fortune (possibly obtained illegally) are yours for the taking. (It may however be easier to rob a bank direct, although there is a possibility that a quantum computer will do it for us.)

  The final way that maths could make you rich and famous is the main subject of this article. You can attempt to solve one of the prize problems put together by the Clay Institute. A prize of $1,000,000 is out there for any one of you who can solve one of these problems.

  $1,000,000 to be won!!!!!!!

  Be warned, however, the problems are hard and it may be easier to rob a bank after all.

  The Clay Institute

  As you will probably have noticed, we are now not only at the start of a new century, but also at the start of a new millennium. It was felt appropriate by many mathematicians the 21st century should start off with a series of unsolved problems in mathematics. There were several groups that proposed different lists of problems ranging from the very applied to the very pure. It is not difficult to pose a problem in mathematics which is hard to solve. Indeed most nonlinear differential equations have no known exact solution, nor can we see how any such equation ever could have an exact solution. Similar technical problems arise in all fields of mathematics.

  However, these are not in a sense good problems. A good problem is one which is not just hard in its own right, but the solution of which, or even the attempts at a solution of which, will generate a lot of new mathematics in the process and which will lead to the solution of problems in areas of mathematics far distant from those in which the problem was originally posed. This is a much harder test of a good problem.

  In the end, out of the vast range of possible problems, a list of seven Millennium Prize Problems problems emerged. These were posed by an organisation called the Clay Institute which is based in Cambridge, Massachusetts. As I said in the introduction $1,000,000 is out there to be won. To win this prize you must either solve a problem or produce a counterexample and (here's the catch) your solution must stand the rigours of inspection by all of the world's mathematicians for at least two years!

  The full list of problems is as follows:

  1. P versus NP;
  2. The Hodge Conjecture;
  3. The Poincarë Conjecture.
  4. The Riemann Hypothesis;
  5. Yang-Mills existence and Mass gap;
  6. The well-posedness of the Navier-Stokes equations;
  7. The Birch and Swinnerton-Dyer Conjecture.

  

  There - do you feel challenged? If you want more information about any individual problem, full details are given on the Clay institute website, where you will also find the rules of the competition. There is also an excellent book by Keith Devlin, "The Millennium Problems", which goes into detail not only on each problem but also on the various teams of mathematicians around the world who are trying to solve them.

  Roughly speaking, problems 4 and 7 are in number theory, 2 and 3 are in topology, 1 is in optimisation and 5 and 6 are problems about differential equations. It is dangerous to say that any one mathematical problem is more applied than any other (and even more dangerous to say which is more important), however I think it is fair to say that the solution of problems 1 and 7 will have immediate practical importance, whilst the application of the others lies further in the future.

  We will now look in more detail at Problem 1.

  Problem 1: P versus NP

  Please forgive the rather dry title to this section as the problems that it lead to are fascinating, relevant, important and (in keeping with the title of this article) potentially the source of great riches. The P versus NP problem is all about how easy it is to solve problems, so it is a problem about problems. Put another way, this problem relates to the question of whether a computer can ever replace a mathematician, ie. will I (and perhaps you!) have a job in a few years time.

  The party problem

  To motivate this question we will look a little ahead, into the future of those readers who are still at school, and endeavour to give a bit of advice to those going up to university. When you go to university certain rather unimportant things will occupy your time, such as the need to study, feed yourself and look for a job. These are all distractions in the pursuit of the most important student activity, namely that of going to parties. Imagine now that you are in your first week at university, and to celebrate having survived for a whole week you decide to throw a (wild) party. In this first week you have made a grand total of five friends, named (conveniently for a mathematician) Angela, Brian, Colin, Daphne and Edward. Sadly you live in rather cramped university accommodation, and your room can only hold a (fun-filled) party of three. The first week at university has already been quite eventful. A and B have gone out, have split up and B is now going out with D. As a consequence A and will not come to the party if B or D are there. C used to be going out with D and will not go to the party if she is there. D beat E in the first week test, and E will also not go if D is there.

  So, the question that you are faced with is which three friends can you invite to the party so that all are compatible with each other? In this case it doesn't take very long to see that you can safely invite Angela, Colin and Edward to have an ACE party.

  
  

  Party time - but who is coming?

  Now let's move a few years on to the end of your final year at university. You plan now to have a (mega) party to celebrate your departure (complete with refreshments and a band). You have been very socially active during your university career and now have 200 friends (who said that maths wasn't fun?). You are also a bit more organised and decide to hire the Student Union building to hold your party in. This metropolis will hold 100 people. Sadly, however, the love lives of your friends have been varied and complex and you have a long list which tells you which of your friends cannot possibly come to the party together (at least if the union building is to survive the experience).

  
  

  The party planner
  Image freeimages.co.uk

  The question is who do you invite? Fortunately your university mathematics course has included a module on computing and you decide to try to solve this problem on a computer. At this stage I invite (educated) guesses from the gentle reader as to how long it will take your computer to come up with the party list. Did I hear a minute from the reader on the right? Who was that who said 10 seconds? Would anyone be prepared to wait for an hour?

  Solving the party problem

  Let's now look at a simple strategy with two parts for solving this problem.
  

  Part A: Get the computer to select a random set of 100 people from your list of 200 friends.

  Part B: Check this selection against your list to see if there are any incompatible friends. If the selection is OK then you have a party. If not, go back to Part A.

  We now have to ask how long it will take our computer to implement this strategy. Suppose that we have a possible party chosen in Part A. To check this party we need to go through the list in Part B. This operation takes a time proportional to the number of possible pairings of friends at the party. You go through each possible pair and see whether it is on the list.Your possible party has 100 people and there are a possible  items to check. Thus Part B will take 4950 times the time it takes the computer to do one operation. On a fast computer each operation might be around 1ns (a nanosecond is  seconds), so Part B takes 4590ns=4.59s (a microsecond is  seconds); ie. it is almost instantaneous.

  Now let’s look at the time it takes to do Part A. To implement the algorithm, the computer has to check out every possible party. Given that there are 200 possible people and 100 need to be chosen, the number of possible parties is given by , where

  Using this formula with  and  we find that the total number of possible parties is

  This is the total number of parties, and each takes 4.5s to check out. So, in total the computer will take

  to find a possible party. To put you in the picture, the estimated life time of the universe is about 15 billion (15  ) years.

  So what are we to do? Well, one solution is to deep-freeze the computer programmer until the computer comes up with the answer. Of course by this time your friends may have got a bit bored with waiting. The alternative strategy is to find a better way of programming the computer (or, in maths speak, to find a better algorithm). However, it is very far from obvious what sort of algorithm this should be.

  Let's have a closer look at the difficulty of this problem. Suppose that we have  friends and we want to invite half of them to the party, so that  or . The number of possible pairs of enemies among your friends cannot be more than the total possible number of pairs which is  This is the maximum total length of the list of pairs of enemies. Also, in your list of  attendees at the party there are  different pairs. To check your party you must check each one of these pairs against the master list, which takes  operations. Thus the time it takes to check a party is (at worst) proportional to .

  We say that the time of this checking process is polynomial in n, or takes polynomial time. Polynomial time means that the checking time is always bounded by some power of n.

  Anything which can be done in polynomial time is (essentially) doable on a computer. If a problem can be solved in polynomial time then we say it is of type P, and is in a sense easy. An example of an easy problem is that of sorting a list of  numbers into increasing order. Although the total number of different ways of arranging  numbers is , you can put them into order in a time proportional to (which is even smaller than ). Rapid algorithms for sorting lists lie at the heart of data-bases.

  Is the party problem an easy problem?

  Let's look at how many different parties there are which half of your friends can attend. A good approximation to  can be found by using Stirling’s formula for  and is given by
  This formula allows us to quickly estimate the size of task A. For even moderate values of  this number is huge. It is far, far bigger than . For comparison, suppose that we want to host a moderately sized party. Here is a comparison of  with .
  

  r	r2	2rCr
  1	1	2
  2	4	6
  3	9	20
  4	16	70
  5	25	252
  6	36	924

  The number of parties grows faster than any polynomial function of r. Indeed it is an exponential function of r. The time that it takes to check out this number of parties that we need to check is not polynomial in r, but grows exponentially with r. We call such problems N. Nproblems are hard to solve.

  The party problem is a bit special. Although it takes N-time to generate all of the parties, it only takes P-time to check each one. This type of problem is called NP (hence the name of the problem in this section).

  The procedure that we have identified for solving the party problem takes far more than polynomial time. Thus the problem appears to behard. Of course, we may not have come up with an especially efficient algorithm for solving the party problem. For example, one way to sort a list of length n is to try every one of the n! possible lists and to see which one is in order. This method is very slow indeed, much slower than the nln(n ) operations that the quick-sort algorithm takes.

  
  

  How long will it take to decide?

  The million dollar question (quite literally) is whether we are forced to always use a slow algorithm for the party problem, or whether we can find a perfect party using a computer algorithm which takes polynomial time. If this is the case then we could say (for the party problem) that

  P = NP.

  The problem is that noone has ever found such an algorithm nor has it has even been proven for certain that such an algorithm cannot exist.

  The immensity of our task is this. To show that a problem is of type P you must find a polynomial time algorithm, however, to show that it is not-P you must check all possible algorithms and show that none of them work in polynomial time.
  

  Why do we care about P versus NP?

  If this were just a question about parties, it wouldn't have made it into anyone's list of top problems for the new millennium. However, there are many, many problems which are very like the party problem, in that they take P operations to check, but there are N possibilities to go through. We call all such problems NP problems. The remarkable thing is that it has been proven that there is a large set of NPproblems which have the property that if you can solve one in polynomial time then you can solve all such problems in polynomial time. This is called the set of NP complete problems. Crack one and you crack them all. It is the all-encompassing nature of this result which makes the P versus NP question such an important problem.
  

  Here are some of the variety of problems which are NP:

  • The knapsack problem: fitting a set of oddly shaped items into a knapsack (closely related to the question of placing components on a circuit board).
  • The time-tabling problem : constructing a working timetable for a school so that teachers and students are never in two places at once (a similar problem arises in placing pilots in an airline).
  • Solving the minesweeper game that you have on your computer.
  • Colouring a map with four colours, so that no two adjacent regions have the same colour.
  • Factorising large numbers.

  

  As we hinted earlier, the last of these problems lies at the heart of modern cryptography for which the security of a code relies on the difficulty of finding the factors of a number. You can find out why in The code book by Simon Singh, and there is more about cryptography in Safety in numbers from Issue 21 of Plus.

  Briefly, modern codes (based on the RSA cipher) start with a pair of large prime numbers p₁ and p₂ and multiply them together to give a product m=p₁p₂. The number m is released to the public, but p₁ and p₂ are kept secret. To crack the code you have to find p₁ and p₂, given the value of m. Now m is usually a very large number, maybe m has ndecimal digits where n may be around 100. To find the factors of m one simple technique would be to check each of the numbers less than the square root of m to see whether it divides into m. Given any number, checking that it divides into m is easy and takes a number of operations proportional to at most n² (you can check this for yourself). So seeing if a number is a factor can be determined in a time which is a polynomial function of N.

  It is also easy to see that the square root of m must have a value somewhere between 10^(n-1)/2 and 10^n/2. However, this means that we must check about 10^n/2 different numbers to find the factors of m. As in the party problem, this number does not grow polynomially withn. For example, if n=100 we must check about 10⁵⁰ different possible factors. Like our party problem, this is an enormous number and no computer can check all of these numbers within the lifetime of the computer programmer. It is this fact which makes modern codes so secure.

  It should be said at this stage - especially if this article is read several years into the future when all of these issues may resolved - that there is a chance that quantum computers might be able to perform this feat, however a working quantum computer has yet to be built! Thus, at this stage the P versus NP problem is wide open, although most mathematicians suspect that (when using a conventional computer) P is not equal to NP.

  If this is so, our party organiser will simply have to wait!

  In conclusion

  
  

  Rich - and who cares about famous?
  Image freeimages.co.uk

  I hope that this brief overview has given you some insight into the sort of problems that mathematicians are interested in and why some of them are important. In the next issue of Plus I will look in more detail at another of the Millennium Prize Problems - the well-posedness of the Navier-Stokes equations. It is certainly true that solving one of these problems would give you a form of mathematical immortality and maybe even fame and fortune. My advice to any of you who think that you might have a crack at one of the problems is go for it!

  However, it is also worth saying that maths can make you rich and famous in many other ways as it unlocks the doors to a huge number of interesting and varied careers. But, I still wouldn't advise you to rob a bank.

  ---

  About the author

  

  Chris Budd is Professor of Applied Mathematics at the University of Bath, and Chair of Mathematics for the Royal Institution. He is particularly interested in applying mathematics to the real world and promoting the public understanding of mathematics.

  He has recently co-written the popular mathematics bookMathematics Galore!, published by Oxford University Press, with C. Sangwin.

  
  

  
  
  
  

  
  
  
  
  
  
  

  Warren Buffett's 10 Ways To Get Rich

  With an estimated fortune of $62 billion, Warren Buffett is the richest man in the entire world. In 1962, when he began buying stock in Berkshire Hathaway, a share cost $7.50. Today, Warren Buffett, 78, is Berkshire's chairman and CEO, and one share of the company's class A stock worth close to $119,000. He credits his astonishing success to several key strategies, which he has shared with writer Alice Schroeder. She spend hundreds of hours interviewing the Sage of Omaha for the new authorized biography The Snowball. Here are some of Warren Buffett's money-making secrets -- and how they could work for you.
  
  1. Reinvest Your Profits: When you first make money, you may be tempted to spend it. Don't. Instead, reinvest the profits. Warren Buffett learned this early on. In high school, he and a pal bought a pinball machine to pun in a barbershop. With the money they earned, they bought more machines until they had eight in different shops. When the friends sold the venture, Warren Buffett used the proceeds to buy stocks and to start another small business. By age 26, he'd amassed $174,000 -- or $1.4 million in today's money. Even a small sum can turn into great wealth.
  

  

  
  
  

  
  2. Be Willing To Be Different: Don't base your decisions upon what everyone is saying or doing. When Warren Buffett began managing money in 1956 with $100,000 cobbled together from a handful of investors, he was dubbed an oddball. He worked in Omaha, not Wall Street, and he refused to tell his parents where he was putting their money. People predicted that he'd fail, but when he closed his partnership 14 years later, it was worth more than $100 million. Instead of following the crowd, he looked for undervalued investments and ended up vastly beating the market average every single year. To Warren Buffett, the average is just that -- what everybody else is doing. to be above average, you need to measure yourself by what he calls the Inner Scorecard, judging yourself by your own standards and not the world's.
  3. Never Suck Your Thumb: Gather in advance any information you need to make a decision, and ask a friend or relative to make sure that you stick to a deadline. Warren Buffett prides himself on swiftly making up his mind and acting on it. He calls any unnecessary sitting and thinking "thumb sucking." When people offer him a business or an investment, he says, "I won't talk unless they bring me a price." He gives them an answer on the spot.
  4. Spell Out The Deal Before You Start: Your bargaining leverage is always greatest before you begin a job -- that's when you have something to offer that the other party wants. Warren Buffett learned this lesson the hard way as a kid, when his grandfather Ernest hired him and a friend to dig out the family grocery store after a blizzard. The boys spent five hours shoveling until they could barely straighten their frozen hands. Afterward, his grandfather gave the pair less than 90 cents to split. Warren Buffett was horrified that he performed such backbreaking work only to earn pennies an hour. Always nail down the specifics of a deal in advance -- even with your friends and relatives.
  5. Watch Small Expenses: Warren Buffett invests in businesses run by managers who obsess over the tiniest costs. He one acquired a company whose owner counted the sheets in rolls of 500-sheet toilet paper to see if he was being cheated (he was). He also admired a friend who painted only on the side of his office building that faced the road. Exercising vigilance over every expense can make your profits -- and your paycheck -- go much further.
  6. Limit What You Borrow: Living on credit cards and loans won't make you rich. Warren Buffett has never borrowed a significant amount -- not to invest, not for a mortgage. He has gotten many heart-rendering letters from people who thought their borrowing was manageable but became overwhelmed by debt. His advice: Negotiate with creditors to pay what you can. Then, when you're debt-free, work on saving some money that you can use to invest.
  7. Be Persistent: With tenacity and ingenuity, you can win against a more established competitor. Warren Buffett acquired the Nebraska Furniture Mart in 1983 because he liked the way its founder, Rose Blumkin, did business. A Russian immigrant, she built the mart from a pawnshop into the largest furniture store in North America. Her strategy was to undersell the big shots, and she was a merciless negotiator. To Warren Buffett, Rose embodied the unwavering courage that makes a winner out of an underdog.
  8. Know When To Quit: Once, when Warren Buffett was a teen, he went to the racetrack. He bet on a race and lost. To recoup his funds, he bet on another race. He lost again, leaving him with close to nothing. He felt sick -- he had squandered nearly a week's earnings. Warren Buffett never repeated that mistake. Know when to walk away from a loss, and don't let anxiety fool you into trying again.
  9. Assess The Risk: In 1995, the employer of Warren Buffett's son, Howie, was accused by the FBI of price-fixing. Warren Buffett advised Howie to imagine the worst-and-bast-case scenarios if he stayed with the company. His son quickly realized that the risks of staying far outweighed any potential gains, and he quit the next day. Asking yourself "and then what?" can help you see all of the possible consequences when you're struggling to make a decision -- and can guide you to the smartest choice.
  10. Know What Success Really Means: Despite his wealth, Warren Buffett does not measure success by dollars. In 2006, he pledged to give away almost his entire fortune to charities, primarily the Bill and Melinda Gates Foundation. He's adamant about not funding monuments to himself -- no Warren Buffett buildings or halls. "I know people who have a lot of money," he says, "and they get testimonial dinners and hospital wings named after them. But the truth is that nobody in the world loves them. When you get to my age, you'll measure your success in life by how many of the people you want to have love you actually do love you. That's the ultimate test of how you've lived your life."