What you can learn from this centuries-old math mystery

What you can learn from this centuries-old math mysteryWhat you can learn from this centuries-old math mysteryIn 1637, Pierre de Fermat scribbled a note on a textbook margin that would baffle mathematicians for more than three centuries.Fermat had a theory. He proposed that theres no solution to the formulaan+bn=cnfor any n greater than 2. I have a truly marvelous demonstration of this proposition, he wrote, which this margin is too narrow to contain.And thats all he wrote.Fermat died before supplying the missing proof for what came to be known as Fermats Last Theorem. The teaser he left behind continued to tantalize mathematicians for centuries (and made them wish Fermat had a bigger book to write on). Generations of mathematicians tried- and failed- to prove Fermats Last Theorem.Until Andrew Wiles came along.For fruchtwein 10-year-olds, the definition of a good time doesnt include reading math books for fun. But Wiles welches no ordinary 10-year-old. He would hang out at his local library in Cambridge, England, and surf the shelves for math books.One day, he spotted a book devoted entirely to Fermats Last Theorem. He welches tantalized by the mystery of a theorem that was so easy to state, yet so difficult to prove. Lacking the mathematical chops to tackle the proof, he set it aside for over two decades.He returned to the theorem later in life as a math professor and devoted seven years to working on it in almost total secrecy. In an ambiguously-titled 1993 lecture in Cambridge, Wiles publicly revealed that he had solved the centuries-old mystery of Fermats Last Theorem. The announcement sent mathematicians in attendance, and around the globe, into a tizzy Its the most exciting thing thats happened in - geez - maybe ever, in mathematics, said Dr. Leonard Adelman. EvenThe New York Timesran a front-page story on the discovery, exclaiming At Last Shout of Eureka in Age-Old Math Mystery.But the celebrations proved premature. Wiles had made a mistake in a critic al part of his proof. The mistake emerged during the peer-review process after Wiles submitted his proof for publication.It would take another year, and collaboration with another mathematician, to repair the proof. Describing the day he found the missing piece, Wiles said, I walked around the department, and Id keep coming back to my desk looking to see if it was still there. It was still there. I couldnt contain myself. At the end, the proof was 150 pages long - far longer than any book margin would have allowed Fermat to write on.Reflecting on how he managed to prove the theorem, Wiles compared the process of discovery to navigating a dark mansion. You start in the first room, he said, and spend months groping, poking, and bumping into things in a hit-or-miss process. After tremendous disorientation and confusion, you might eventually find the light switch. You then move on to the next dark room and begin the process all over again.These breakthroughs, Wiles explains, are the cu lmination of - and couldnt exist without - the many months of stumbling around in the dark that proceed them.In school, were given the false impression that scientists took a straight path to the light switch. Textbooks with lofty titles - The Principles of Physics- magically reveal the principles in three hundred digestible pages. An authority figure then steps up to the lectern to feed us the truth. We learn about Newtons laws - as if they arrived by a grand divine visitation or a stroke of genius - but not the years he spent exploring, revising, and tweaking them. The laws that Newton failed to establish - most notably his experiments in alchemy, which attempted, and spectacularly failed, to turn lead into gold - dont make the cut.The path to the light switch is not a straight one. There are fits and starts, mistakes and corrections, failures and successes.Be careful if the paths youre taking to the light switches in your life are straight. If the drugs youre developing we re certain to work, if your client were certain to be acquitted in court, if your roter planet rover were certain to get to its destination, your jobs wouldnt exist.Its the ability to make the most out of uncertainty that creates the most potential value.Where certainty ends, progress begins.Ozan Varol is a rocket scientist turned law professor and bestselling author.Click hereto download a free copy of his e-book, The Contrarian Handbook 8 Principles for Innovating Your Thinking. Along with your free e-book, youll get the Weekly Contrarian - a newsletter that challenges conventional wisdom and changes the way we look at the world (plus access to exclusive content for subscribers only).Thisarticlefirst appeared onOzanVarol.com.Sources usedStuart Firestein, Ignorance How It Drives Science, 2012.Simon Singh, Fermats Last Theorem, 1997.Solving Fermat Andrew Wiles,https//www.pbs.org/wgbh/nova/proof/wiles.html.At Last, Shout of Eureka In Age-Old Math Mystery,https//www.nytimes.com/1993/ 06/24/us/at-last-shout-of-eureka-in-age-old-math-mystery.htmlA Year Later, Snag Persists In Math Proof,https//www.nytimes.com/1994/06/28/science/a-year-later-snag-persists-in-math-proof.html.

Universities With Great Open-Courseware Tech Programs

Universities With Great Open-Courseware Tech ProgramsUniversities With Great Open-Courseware Tech ProgramsIf youre looking for educational advancement and new skills but dont have the money or the time to enroll in a college program, online education may be a good option. Open-Coursewareor OCW is a form of learning that involves taking free online courses over the internet.Students can learn at their own pace, and there are a wide variety of courses. However, the courses typically do not count as college credit. More and more colleges are offering free courses online, including many prestigious institutions.The courses outlined in the programs are available to anyone for free and feature some of the worlds foremost authorities on subjects. Finding them isnt always easy, so start with this list of some of the best resources available online today. Many of these websites include video recordings of lectures however, lecture notes, interactive activities, tests, and even free certificat es are now being made available as well. MIT The Massachusetts Institute of Technology (MIT) Open Courseware (OCW) website has 2,400 free courses online using a combination of lecture notes, audio, and video resources. Engineering courses cover just about every discipline, from aeronautics and astronautics to mechanical engineering and nuclear science. If youre looking for computer science courses, you can find them in the Electrical Engineering and Computer Science section. There are dozens of undergraduate and graduate courses in this section alone, ranging from Introduction to Computer Science and Programming to specific programming languages like Java and C. Advanced courses range from quantum electronics to nonlinear programming and organic optoelectronics. Other courses include microeconomics, linear algebra, health sciences, technology, energy courses, hard science courses in chemistry, and physics. UC Berkeley UC Berkeley offers free online courses in a variety of su bjects including english, writing, blockchain technology, marketing analytics, and statistics. UC Berkeley has also partnered with edX, where many of their new free courses are featured.Edx is an online website portal for those looking to learn from many colleges including Harvard, MIT, and UC Berkeley to anthroponym a few. The courses include engineering, chemistry, biology, economics, business, medicine, social sciences, and many more. Carnegie Mellon Carnegie Mellons Open Learning Initiative (OLI) offers courses in a wide range of disciplines. Technical courses include engineering statistics, data science, business, media programming, principles of computing, and coding. Carnegie Mellons OLI has a student program where the courses are $25 each. However, the Independent Learner courses are free and open to the public. In addition to lectures, the website offers resources like learning activities, quizzes, and itemized lists of objectives. Like with most of these websites, the courses are free but there is no interaction with instructors, nor are course credits or certificates offered. Harvard University Similar to other universities, Harvard offers a wide variety of free courses online through their Open Learning courses. Some are free others charge tuition fees at reduced rates. Course topics range from programming to data science to security and more. They also have a few offbeat ones, like Bits The Computer Science of Digital Information, which you probably wont find at other universities Stanford University Stanford Online offers a variety of free online courses to interested learners. Check their course list for the latest offerings, which some have a fee, but many are free to the public. Available courses currently cover topics like software security, big data, computer science, statistics, quantum mechanics, computer networking, and more. Open.Michigan Created by the University of Michigan, Open.Michigan features a huge collection of c ourses, complete with syllabi and lectures. Under the Educational Resources section, youll find many free courses that include chemistry, engineering, nursing, statistics, and education. The school also allows the public access to data, which includes research as well as publications and scholarly journals published in years past. Conclusion Open courseware has been hailed as the future of education around the world. Its affordable, accessible, and (in most cases) as good a quality as youd get attending the school. Theres no better time to start learning new skills.

How to Handle Extended Unemployment Tips from a Marathon

How to Handle Extended Unemployment Tips from a MarathonHow to Handle Extended Unemployment Tips from a MarathonWhat to remember when a job search goes from weeks to months, or longer.Before you can deliver a great performance, you need an opportunity to perform.With at least 15 million Americans out of work, the length of the job search has stretched from a sprint to a marathon.To endure and succeed, you need to be in shape. Here are a few tips to get you through the long haul1. Warm up and cool downBe ready for an employer before the employer is ready for you.Being without a paycheck for months on end can be a very difficult blow to your self-esteem. After a while, it can be hard to remember the qualifications that make you a contender in the first place. Consequently, its very important for you to take exceptionally good care of yourself.So my very first suggestion when youre looking for a job for an extended time is physically exercise. Ge t in the best condition you can. This is something you are in control of.Rather than working eight hours a day searching for a job, I suggest you carve out 90 minutes a day to warm up properly, exercise and warm down properly. Even if this means walking around the flgel one time to get started, do it. As you begin to get into better physical shape, you will strengthen your self-esteem and remind yourself that you are to a large degree in charge of your destiny.This physical workout will prepare you mentally for your search.2. Count your calories.Before you start searching for a job, know what youre getting into. Research the industry and any targeted companies you would like to work for. Learn everything you can.Before I speak to an audience I always interview at least a dozen people, study as much information as I can get my hands on about the organization, and usually volunteer to go on site and observe people in their normal workday activities.Go on the Internet, and be creative. Put in search words for the type of ind ustry, organization or job that you want. See what you come up with. Keep searching online to binnensee if you can find a key person to contact. Intelligently use Facebook and Twitter to reach out to people to see if you can uncover opportunities for the type of job you want and the type of company you want to work for.When the actual job opportunity opens up, you will be infinitely better prepared if youve been doing your research all along.3. Block out time.Businesses sell products and services. You are selling yourself. Your product comprises yourValuesStrengthsPassionsKnowledgeSkillsExperience.Take out a sheet of paper.Under each of those headlines describe what you bring to a befhigung employer. Then think of an example that supports why you feel you bring that characteristic.Invest 60 minutes in this exercise. Pretty soon, youll see that some employer is going to be very fortunate to hire you.4. Dont train alone.Take out several sheets of paper. Start writing down every single person you know.Really challenge yourself to think of people who might know you. Write their names down, and then start to contact them systematically. Let these individuals know specifically what type of job you want and what type of organization you want to work for. Remember Clarity is powerful, vagueness is not.You are trying to stir up a wide range of people who can recommend you to a potential employer. If they dont specifically know what you want, what are the odds they are going to be successful in recommending you?When I speak to entrepreneurs and salespeople, I often explain how some of my biggest business opportunities came from people I never would have expected to help me. I just didnt know who was going to open a door for me or how big the room was going to be. And neither do you. Never write off the possibility that an unlikely source might turn out to be the most important person in your career.I used to be a high-school teacher. I wanted to be a management consulta nt and business speaker. That was 13 years ago. I taught freshmen algebra. The father of a sophomore, whom I had taught the year before, worked for McDonalds Corp. I gave one speech to his group, which led to more than 500 presentations in the end.You dont need to groe nachfrage this race alone.5. Make it a lifestyle.Searching for a job is not a job. A job is when you receive an opportunity to create and deliver value for other people for which you are financially compensated. You dont have a job until you close the deal.Instead of thinking of a job search as a once-a-decade activity, think of it as part of your professional life.Not having a job right now isnt the point. Whatever your current employment situation, you should always sharpen your ability to search for a job. Its really like running a marathon. Get yourself ready and go after the finish line.Its an exciting and challenging adventure, and it will bring out the best in you.