Sunday, November 29, 2009
Wednesday, November 11, 2009
A FALLEN GIANT
One of the giants of twentieth century mathematics fell last month at the age of 96. He was called "one of the last of the greatest who worked in nearly every field of mathematics." He was called by one student, "very unpredictable and very wise," and a colleague considered him the most interesting person he had ever known.
Gefland never finished high school and never attended college as an undergraduate student. He went to Moscow at age 16 or 17 and worked odd jobs but was always interested in mathematics, attended seminars, and at the age of 19 was admitted directly to graduate school of Moscow State University. He worked in extremely abstract areas of mathematics, which most people do not even know exist, but much of his work has profound application as well, and some medical imaging tests that most of us benefit from at some time in our lives (such as 3D images created by MRIs and CAT scans) are possible due to his work. It is said that he sought not just to teach the rules of math but also the beauty and exactness of his field (my kind of guy!). He also had a sense of humor and was quoted in a 2003 interview with the New York times as saying:
“Mathematics is a way of thinking in everyday life. It is important not to separate mathematics from life. You can explain fractions even to heavy drinkers. If you ask them, ‘Which is larger, 2/3 or 3/5?’ it is likely they will not know. But if you ask, ‘Which is better, two bottles of vodka for three people, or three bottles of vodka for five people?’ they will answer you immediately. They will say two for three, of course.”His obituary (from which I took the information above) can be found at
Wednesday, August 5, 2009
"The top 15 highest-earning college degrees all have one thing in common -- math skills. That's according to a recent survey from the National Association of Colleges and Employers, which tracks college graduates' job offers.This quote is from the article Most Lucrative College Degrees at CNNMoney.com. For the full article, click here.
'Math is at the crux of who gets paid,' said Ed Koc, director of research at NACE. 'If you have those skills, you are an extremely valuable asset. We don't generate enough people like that in this country.'"
Friday, July 10, 2009
Wednesday, June 10, 2009
Amaze your friends!
Be the first to tell them: "At five minutes and six seconds after 4 AM on the 8th of July this year, the time and date will be 04:05:06 07/08/09. This will never happen again."
Hmm . . . I'm not so sure about that last sentence. What do you think?
Friday, May 22, 2009
Thursday, May 21, 2009
Wednesday, May 20, 2009
Tuesday, May 19, 2009
Usually my posts on this site are MUCH shorter - and just kind of curiousities, jokes, comics, etc. - pretty light stuff. I am so often asked, though, "Why do we have to learn math?" that I feel I need to address it in writing. What follows is a written response I am formulating for my students - though I hope to work with it a bit and make it more concise!
"At some point during the semester – usually more than once, actually – the question comes up, “Why do I have to learn math?” Usually this question doesn’t come up right away when things are review, when the topics are easier. So there seems to be something about learning that makes it such that people don’t mind doing it as long as it’s easy or fun – whether there is a use for what they are learning or not, but as soon as it becomes harder and frustrating people want a reason for all the stress they are under.
It seems the sort of answer people are looking for when they ask this question is how they will use, in their everyday lives, the specific mathematical formulas they are currently learning – such as for figuring out how to save money on their taxes or how to do home repair or what it will do for them in their career. Math IS used in all of these places, of course, and there are lots of answers I could give that are very specific, but they would depend on individual life-style and career.
Math is used in everything from balancing your checkbook to determining your mortgage payments to designing buildings that will not fall down to figuring out the gas mileage your car is getting to how your credit card number is kept private when you make a purchase on the internet to making financial decisions such as how to invest your money and whether to buy or rent your home to the way in which your cell phone works and how medical imaging procedures help doctors diagnose health problems you have to how airplanes fly – the list goes on and on. What other subject is this applicable to "everyday life?" At almost every moment either you are using math or you are using something someone else created using math.
Math is probably the most readily applied of all the subjects you will take in school (though there might be a tie with reading). But, honestly, the things that frustrate students about math and cause them to ask this question are probably not the things they will use directly in everyday life. I'll be very honest and tell you that I’ve never used the quadratic formula in MY everyday life - never ever ever ever. So let’s be honest about it. Yes, there are many specific items in math that you will use in your everyday life, but there are many things you will learn in math that you will not use specifically (like the quadratic formula or partial fractions decomposition) unless you have a job that requires it.
However, what is most important about learning math is not how you will apply an equation or formula on a day-to-day basis. What is important in learning math is learning how to use logical reasoning to solve problems, and the harder and more frustrating math gets the better you are becoming at solving genuine problems. Learning math teaches you to think.
It is this more general nature of mathematics rather than the specifics of it that is the most valuable piece of learning mathematics for most people. Life is filled with problems – scheduling problems, relationship problems, home repair problems, health-care problems, vacation-planning problems, time-use problems, financial-planning problems, and on and on and on. Whenever you are faced with a problem, whether it is how to work out a disagreement with another person and try to find a fair compromise (or to logically convince them that you are right!) or planning a vacation with a certain time frame and within a certain budget or deciding which path of treatment to follow if you have been diagnosed with cancer, you are using logical reasoning and problem solving. This IS Math. Problem solving and logic are the heart of mathematics. Wrestling with difficult mathematical problems prepares you in general to deal with many types of problems in life that have nothing to do with numbers or shapes or formulas but that have everything to do with clear thinking, logic and finding solutions.
So the next time you face a frustrating math problem that seems impossible, don't look at it as some crazy school requirement you just have to suffer through; look at it as an opportunity to practice (in a safer environment than real life sometimes is!) logic, creativity, and problem-solving skills. You will be faced with many situations in your life that you need to solve, whether they be conflicts with other people, decisions about finances, planning your time, making home repairs, determining the wisest course of medical treatment to follow, deciding how to vote on important political issues, whether or not to believe a politician or salesperson, etc.
Lessons you learn in mathematics about logical reasoning and problem solving can give you the underlying skills to excel at problem solving in real life. Mathematician John von Neumann once said, “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”
You may not agree that math is simple, but, if you are lucky enough to live long enough, you are guaranteed to run into some big complications in life that make mathematics seem like a piece of cake by comparison. And chances are that the logic and problem solving skills you learn in mathematics can help you reason your way to the best solutions to those problems. That is one of the many reasons we learn math, and it is probably the most important reason for most students in a math class."