I was just reading about the mathematician Tom Zhang and his fascination with "twin primes."
Please read this interview with this brilliant mathematician and consider at least one of the many things he's saying. Choose something about his views of mathematics and write about it.
To get your creative juices flowing, a couple thoughts I had about the interview include (but are not restricted to):
1. The idea that mathematicians are born, not made.
2. He views math as beautiful and interesting not at all for the application. He loves math for itself and for the way mathematics helps him use his mind.
3. I remembered something I read, written by Harold Jacobs in his Geometry text book from 1974:
Pythagoras was a Greek geometer who lived about 2500 years ago. He wondered whether he could teach geometry even to a reluctant student. After finding such a student, Pythagoras agreed to pay him an obel for each theorem he learned. Because the student was very poor, he worked diligently. After a time, however, the student realized that he had become more interested in geometry than in the money he was accumulating. In fact, he became so intrigued with his studies that he begged Pythagoras to go faster, now offering to pay him back an obel for each new theorem. Eventually, Pythagoras got all of his money back.
Now ok, a bunch of you admitted that you do some math in secret or in ways and times that you didn't think you were actually doing math. A bunch of you claimed that over use of technology contributes to math illiteracy. Will any of you to admit that there's something in math --anywhere -- that you've found lovely, beautiful, cool, interesting, intriguing, puzzling, worth thinking about, or simply fun? Oh, do share!
I have always enjoyed doing simple algebra, like finding x in an equation. The first time I did algebra like this, the problem was like this: 5 + x = 8. Find x. I loved doing these problems. I’m not sure what was so fun about them, but they just were. I continued to enjoy finding x in simple problems like this. When they got harder though, like
ReplyDelete2x2 + 2x + 40 = x2 + 8, they didn’t become as much fun. But if there were any basic math problems with x in them, I’ve liked them.
And like I said in Fractions in the Fast Lane, I love to use math with geeky stuff, like measuring how strong Superman is, or what scale all my dinosaurs are compared to the real ones, or that a Lego minifigure’s head is scaled down to being one and a half feet tall. I’ve always loved doing math when it contributes to doing something else that I love. I think that’s a reason why I love doing math in science. Science and math coencide so much that the only difference in my mind between the two is that science uses math in a physical way, instead of just numbers, which I find math is sometimes. But when math is applied to something physical, especially something I like, it is more fun.
In his interview he keeps mentioning to never give up and keep going no matter what and not to let any obstacle stop you from doing what you love. When I was reading this interview I kept thinking of sports and how when your in practice or a game you need to push yourself to achieve the best you can be. If you give up when you come across a tough situation you will never achieve what you want to achieve. In this case he never gave up. Although it took him a long time to find the solution after hard work he did find it. Also he's motivated to do math, any math. In sports the only way to be able to push through the pain is to be motivated in what you're doing and Tom Zhang had this motivation to push through all the hours of work that led to his success.
ReplyDeleteWhile I was reading the interview, I noticed that Tom Zhang isn't very talkative but he is a very focused person. He is so quiet because he is thinking. During the questions of the interview, he doesn't ramble on about the questions, he gives a concise answer; a simple yes or no if he can. I thought it was interesting how he didn't show his work to his colleagues because they hardly understood the problem and he wanted to wait until he was done and had finalized a result. This also leads onto where when he finally found an answer he showed no emotion. I found this interesting because I think he just felt relief sweep over him, not being excited or anything; just closure to what he has been working on for so long.
ReplyDeleteBecause Tom Zhang is so quiet and shy, he becomes really focused about his problem. I found this to be a reason to why he would never give up, and just keep trying.It was also interesting that his breaks he had between the solving the problem were listening to classical music and reading novels.He didn't like to watch TV. It felt like Tom Zhang just kept calm during his whole experience and had his ways to stay calm. That is what helped him push through. I like how he says he is famous, but he seems so down-to-earth about it. His personality of being quiet, shy, focused, and calm routed him to success.
Overall, I got the feeling from this interview of Tom Zhang that if you stay focused, determined, and calm you can solve any problem.
I think that it is amazing that Tom Zhang had enough patience to solve this problem. He keeps repeating that if you are focused and work hard enough for long enough that you can solve any problem. He keeps repeating that his quiet peaceful personality is what allowed him to work for so long. I think that it takes a certain person to be able to be this focused on math. The person must love math, and must love doing math just to do math. The person must be somebody that is happy to work alone for years. I agree that a person like this is born, not made.
ReplyDeleteThis article made me think that math can be not only a school subject, but a lifestyle. Tom Zhang spent hours a day doing math, and even when he wasn't doing math, he was doing math. He would think about math while doing other things, and when taking a break from his math by taking a walk, he often got new ideas. The peace he found in doing math transferred into his everyday life, and he seemed like a very clam man in the interview.
I think that the main message to take away from this is to find something that you love and emerse yourself in it and to not give up.
What struck me the most about Tom Zhang's interview was what he said about perseverance. " If we count the time I spent thinking about the problem, then it was more than 10 hours a day," he said. 10 hours a day, seven days a week, fifty-two weeks in one year...for four years. In total, Zhang spent about 14,500 hours thinking about one problem. Earlier this summer I read a book that talked about why some people succeeded (Outliers by Malcolm Gladwell). Gladwell talked about how the most successful people all have worked at their goals for about ten thousand hours. Now, I can't be the one to suggest that Zhang reached a solution because he worked for more than ten thousand hours; the point is that he worked for a very long time and was persistent. Math is a very fair system- you get out of it what you put into it. Math is all about hard work and perseverance. Math is somewhat of a safe haven for people who appreciate certainty. There is always a solution in math, and the process is more important than the answer. Zhang's process took time and dedication and in the end he prevailed. There is beauty in math because hard work pays off.
ReplyDeleteWhat I find to be the astonishing answer he gave was when he was asked “why did you solve this problem and not somebody else” he answered “I think the important reason is that I persisted for several years. I didn’t give up”. Tom Zhang’s personality, an unusual one for someone in this day and age, gives an explanation for why he answered this way. He is very different from the majority of our culture. He describes himself to be a quiet, shy and patient person. Just that is enough to set him apart from many people. Although, he mentions his compassion for the problem and I was taught that with enough dedication and compassion for a subject, others can have a mind set like Zhang.
ReplyDeleteMy mind repeatedly came back to this quote because I am easily intimidated by difficult looking problems. I immediately assume I could never understand or solve something so complicated. When I do try to comprehend them, I find that with enough patience and sometimes a little guidance the problem will make sense and become easily solvable. His answer inspired me to always attempt every problem, no matter how intimidating. On a larger scale, his words reminded me that with consistency and perseverance I can accomplish my goals.
Haha! That interview was quite short! It's obvious to me that Zhang was never in any of this for the fame or fortune he would receive by solving this problem, but instead he was in it for the pure joy of simply knowing the answer. I don't know if anybody else is like this, but when I get the right answer on a test question that I worked so hard to find the answer to... it's such a great feeling. That's the same way I think Zhang felt. He didn't want to become famous, he didn't want to be interviewed, he simply was in it for his great love of math.
ReplyDeleteMath is a beautiful thing indeed. It's all around us. I don't really think of it that way very often, but it is. In nature, we see patterns in all sorts of plants and perfect shapes and angles everywhere around us. Take the simple example of when you cut an apple down the middle, a perfect little star is formed. Simple, yet beautiful. Everything can be tied back to math!
The thing that surprises me the most about Tom Zhang, besides his overall brilliance and love of math, is how persistent he was for the whole four years he worked (10 hours a day for a seven day week). That just blows my mind! I can't even spend more than fifteen minutes on a problem that has been solved countless times prior and yet here's Zhang, pushing through his moments of weakness and thoughts of giving up, to solve one of the hardest unsolved problems. It's amazing!!
ReplyDeleteWhen I was reading Zhang's interview, I couldn't help but think how this relates to any sport/audition/competition where you have to put yourself out there to achieve the things that you want. Because I'm into preforming arts and singing, I can relate this to auditions. To be the best, and get the part you want, you can't let fear of failing turn you away from being the best you can be! You must use that fear to motivate you even more and let it keep pushing you to be even better. I'm sure Zhang failed countless times during his four year discovery, but because he kept pushing and let that drive him for greatness, he was able to succeed! In everything we do, there is a risk. But that risk is what makes our victories all the more rewarding!
Tom Zhang had a drive to solve the "problem" of prime numbers that I could not imagine! He worked on it for so many years, and in his interview he states that he solved it because he did not give up. It is very hard to comprehend the idea of prime numbers for me. I can comprehend the idea that there are infinite prime numbers, because there are infinite numbers, I could not think of how to figure out all of the different numbers.
ReplyDeleteAt the beginning of the interview, he implies that mathematicians are not given enough credit for their work. It is very easy for humans to do this because we do not use complicated math problems in our daily lives, we just take them for granted. For example with Zhang, I could picture some people saying "oh, there is a way to find prime numbers, so what?" This idea won't gain any of us profit or anything entertaining, so we don't care about the fact.
Something i find beautiful in math is a problem that takes years to solve. Pages filled with with numbers from top to bottom all to try and solve one problem. Mathematicians work diligently every day to try and solve one problem and to create new ones. I'm not sure i would ever be motivated enough to spend multiple years of my life to try and solve a problem but Tom Zhang feels differently. I find it extraordinary that he would be motivated enough to spend 4 years on one problem and I enjoyed hearing that the only reason he did it was because it's what he loves to do. I can't imagine the amount of though that is put into a problem that takes years to solve and the frustrations that go along with it. One would think that after solving a problem that took 4 years you would be so excited. But for Tom Zhang it's not just about solving the problem, its the fun he has doing it. Doing something because you love it is a beautiful thing to me.
ReplyDeleteWhen I was in 3rd grade, my class took a trip to the planetarium at the Natural History Museum to see a presentation about fractals. I didn’t know what in the world a fractal was, so I was expecting a view of the stars in our galaxy, a short discussion, and an early dismissal. We all sat down in the large round room, craning our heads up to look at the domed screen on the ceiling when the presentation began. I was astounded by the intricately beautiful designs that swirled above me. It amazed me that these incredible patterns were made from a single, simple mathematical equation; not only were they stunningly detailed, they continued on forever. Even more astounding to me was the fact that these were imitations of characteristics found in nature, such as leaves or ice crystals. I learned that mathematical equations could describe things that were wild and unpredictable as the sight of tree branches growing in natural splendor. So just like Tom Zhang, who found his fascination and comfort in his work on the twin primes, I can find solace in the labyrinthine depths of fractals.
ReplyDeleteI think that math like everything in the world has its own beauty. I think when a a hard problem finally works and it the most perfect of numbers is when math is beautiful. On the other hand Tom Zhang found an even deeper and more meaning full connection with math. He loves math so much it drove him to work for several years on this one problem, where he dedicated his life. I think this is really important to all of us because he showed us that if you love to do something enough, that you should just put your head down and work until you achieve it. This work for anything; sports, school, music, art.
ReplyDeleteI tend to enjoy doing some high digits multiplication from time to time. By that I mean, if someone asks me answer a problem right off the top of my head, I'll do it without thinking to say no or ask why. I always enjoyed doing it because it gives a chance to see how fast my mind can work. When asked, I tend to break the numbers down into simpler ones, multiply THEM, and then add all the products together to get my answer. For example, if I'm asked 18 x 32, my thought process would be this:
ReplyDelete20*32=320*2=640.
2*32=64
640-64=576 <--- Answer
I enjoy doing problems like these quickly in my head because I always find a sense of pride when I finish them.
I just got to read the article on Tom Zhang and his adventures with the Twin prime conjecture. I found the article a little bit tough to get through, but it was interesting once you got through it. I found it refreshing to read what he was saying, for he seemed to be a very humble person. This it me as a very cool thing, because I expected a very shy mathematical wizard who wouldn't enjoy sharing his thoughts. Though he was a bit shy at points in the interview, giving short almost unexplained answers, he didn't seems tense. Now, one of the questions made him tell us that as time has gone on after he solved the conjecture, he has grown accustomed to public speaking. It told us that he was the way i thought he would be. I admire this quality mainly because I don't feel to strongly about speaking in public. I also am glad to know that he was, and still is, very humble. After he was asked if he shared his work with his colleagues, he told us that he didn't share it with them. He said he might have mentioned it a few times, but didn't say anything about the problem. I feel that he is the kind of person that takes his time to make sure he is right before answering, which requires patience. Without patience, math would be way harder than it needs to be. I think he is a great advocate for patience and thoroughness. We could learn from him that there are many ways to deal with problems and that if we just work at our issues, we can find a way to solve them. I mean, honestly, he worked on a single math problem for FOUR YEARS. If that doesn't require patience and thoroughness, I don't know what does.
ReplyDeleteNow to answer the second half of the prompt. I have always loved geometry. I don't know why but I like shapes and lengths. I guess that it could relates to sports. in swimming or golf, there are all sorts of shapes that are involved. Golf- concentric circles: your hands create part of the inner circle, while your club head creates a portion of the outer circle. Both circles are on a center point, your spine. In swimming, you can look at the water as a horizontal line and when swimming at the ideal positions, you are either parallel with the line or at a slight angle with your head above the water and your legs below. I guess Geometry just relates to my life pretty well, making me like it more than other subjects, as long as I don's have to prove triangles similar ever again. :)
After reading Tom Zhang's interview, I was immediately struck by his humility. Even though he was world famous and had his face on magazines and news shows, he thought no higher of himself. I also admired him for his patience. It took him four years worth of 10 hour days to finish a proof deemed improvable by countless mathematicians. Not only did he work long hours on the problem, he worked at subway and the university. This would have also required a lot of humility because he had completed his phd in mathematics. Another interesting fact that he brought up was that mathematicians are not credited with enough. While people with major scientific discoveries are common names, mathematicians, who work behind the scenes on things that may not directly effect our lives are forgotten. Just look at all of the technology. Often we don't think of the math or programming behind such things. Instead we focus on the engineering and how such a small device was crafted.
ReplyDeleteOne thing that I find incredibly beautiful is math in nature. I can still remember last summer when I was canoeing in the Boundry Waters when I found an island in some of the large lakes. The island was big but when we got on it I found it very pristine. We explored the island and one of our discoveries was a small cedar sapling. This was the most perfect plant I had ever seen. Its limbs were perfect fractals, each branching in the same places the same number of times, even down to the pine needle. Not only the shape, but the last inch of every limb was a yellow green, much brighter than the darker, older leaves.This was very beautiful.
The most beautiful thing about math in my opinion is the fact that people and places involve math in their lives without them even realizing it. For example, in sports, athletes train to pass the ball just right in order to get it to a teammate. While they never think of math while they play, when they throw, kick or toss the ball, they unwillingly use their senses to calculate distance, power, toss height and etc. to be as efficient as possible transferring the ball. Another example is that when people know that it is getting dark in the night, or getting light in the morning, they are involuntarily judging the angle that is created by the sun's point in the sky. Flowers, mollusks, and plants use symmetry, - another aspect affected by math. In music, the lines and bars of music that are played all add up to the time signature, whether it is a simple 3/4, 4/4, or complex 5/4 time.
ReplyDeleteAs you can clearly see, there are many common places around you everyday, where you can look at something and not even know that it involves math. This is much like the approach that I thought Mr. Zhang had in his research - being that he conducted his research mostly in private. Then, when everyone realized what he had discovered, it was like they all had an epiphany. Everyone took a step back, and said, "Wow this is really interesting, it was here all along and we didn't even notice!"
First I’d like to talk about how I’ve found certain topics puzzling. Currently I can’t think of a specific instance, but this has happened to me. This tends to happen whenever I’m learning a more difficult subject. Sometimes it takes me days and days to figure out how it works. Then, when I finally put the pieces together, it makes me so bubbly about the topic. It also makes me become very interested in the subject, and maybe even figure out why I didn’t understand it for so long. It amazes me how some things can be so incredibly complicated to one person and so simple to the next.
ReplyDeleteI’m sure everyone can find at least one thing that they have enjoyed in math, or even enjoyed at one point and now hate. I’d have to say this happened to me with factoring, or foil. When we first learned it I had to go through the steps in my head: first, outer, inner, last; first, outer, inner, last… Then I moved on to liking it (probably even more when the factoring program was installed on my calculator). Now I’m at the point where I don’t think about it. It means the same as a simple algebra problem. It’s interesting how our brains process the information we learn in class. To some it might be really confusing and to some it might be very fascinating.
Math is beautiful, but you can only see this beauty when you stop doing math just to find the answer to a problem or finish your last bit of homework. You have to slow down, and love math for what it is, much like Tom Zhang did. He worked seven days a week, 10 hours a day on a single problem that no one in the world had yet to solve, not once thinking that by solving this problem he would become famous worldwide. He did this problem because he loved the satisfaction of math, being able to work incredibly hard on something that you thought was impossible. Whenever I finish a problem, a really lengthy, ambiguous problem, I feel so good about my accomplishment. The problem, once solved, becomes a beautiful masterpiece.
ReplyDeleteAnother beautiful aspect of math that really speaks to me is how math can provide the answers for phenomena that happen in our daily lives. Take a computer for example. Every program that we run on our laptops and tablets are all made up of math, a lengthy chain of zeros and ones. Whenever I turn on my computer its seems like magic that all the programs I'm running are using numbers to function. When math provides insight into something unexplainable, like the twin-prime conjecture, there is just an explainable beauty present.
This interview seems to highlight the collective personality of Tom Zhang as he was constantly thinking throughout the interview. Math is definitely not a subject that everyone is focused or interested in but we still use it constantly like how it was mentioned in your other blog. Tom had taken an interest in twin prime conjecture when he was a child, and while this is the first time I have even heard of this, it is apparent that he had a love for math that reached out to learn new material.
ReplyDeleteEveryone does find something they love in math even if they don't realize it at the time and I believe that is the beauty of math as it represents the way your mind processes information and facts that it gets. We process a problem and eliminate uncertain and wrong answers as we center in on a correct answer. I personally love finding a fitting answer that just completes all of my questions and that is what I like about math even if it doesn't relate directly to the subject itself. Tom Zhang simply points out that if you love something and have an interest in it, you will find a way to love it and embrace it.
I would like to think as myself as having more of an "English Brain" as opposed to a "Math Brain," but of course, there are times I find myself, late at night in my room having a ball while doing math homework. Usually this only happens when I completely understand what I'm doing and have the confidence to express these feelings towards math without the risk that I'm doing everything wrong.
ReplyDeleteThe most monumental moment I have spend with mathematics was in 8th grade when I learned how to solve equations with two variables. The fact that you could find what Y was equal to X by and then substituting it in was brilliant to me. This was mostly because when I first heard about solving for two variables I thought it was impossible. It left me feeling accomplished and (for lack of a better word) very smart.
I think math will end up teaching me a lot in life, not just mathematical related things but life lessons. One thing math teaches a lot of is not giving up, just trying and that it's ok to fail. Sure, volleyball has taught me that too, but I never have struggled with volleyball like I do with math. I have also learned a lot about myself in the process as well. I learned that I CAN do it. It just takes a good relationship with someone that can help you, you have to be able to admit you need help and a whole lot of will-power!
Dispite my love-hate relationsip with math, it really is a beautiful thing!
For me, I think that the most beautiful and interesting part of math is by far fractals. The fact that a simple mathematical equation can create an infinite pattern of colors and shapes is truly amazing. I've known about fractals ever since I was a kid, but never really understood the concept of them until recently, and I'm not even sure I fully understand them now. I just think it's so amazing that a small pattern can go on forever and ever, and its even more amazing that that pattern is written in the form of math. The concept of infinity is really difficult for me to understand on its own, but when put into a visual form, its much easier. Thats the beauty of math; for those who don't understand it, it can be put into other forms. There are so many ways to view math that if you don't understand it one way, like as a formula, you can put it into a program that will display it a different way. I've never been good at math; in fact, Ive always been pretty bad at math, but the concept of visual learning really helps me which is why I think that the idea of fractals is so amazing and beautiful.
ReplyDeleteGA2 Beauty and Geometry
ReplyDeleteThe interview with Tom Zhang is not only inspiring but encouraging; he states that with focus, hard work, and patience one can solve a difficult problem. When the interviewer asked why Tom was the one to solve the problem not someone else, Tom Zhang responded, "I didn't give up." He had determination. His main reason for solving this mathematics problem was not for money but for his love of math. Math has always been fascinating to me. It is astonishing that with focus and hard work one can find the answer to x, find a certain angle, or find the length of a side of a figure. As I mentioned in my last blog response, every since I was in elementary school, I would always try to find the relationship between numbers on the clock. With focus and determination, I would look for the relationship between the numbers even if the answer was not always apparent right away. Though at times the problem was puzzling, I found it intriguing that the numbers somehow related through addition, subtraction, multiplication, division, etc. Another type of math that intrigues me is geometry. During the first semester of geometry, we learned about proofs and how to prove theorems such as a^2 + b^2= c^2. Through a series of steps, we would be able to prove that in a right triangle the square of the legs of a triangle would be equal to the square of the hypotenuse of the same triangle. To me, math is interesting and intriguing in a unique way. I agree with Tom Zhang's encouraging words that focus, hard work, patience, and determination will help you overcome an obstacle. When I am stuck on a math problem on homework or a test, I focus on the problem and, though it is hard, develop patience to solve the difficult problem. With hard work and determination to not give up, sooner or later I will solve the problem, and when the problem is solved, a sense of accomplishment overcomes me. Tom Zhang's words have reminded and encouraged me that with these factors a difficult problem can be solved as long as one does not give up.