TED Conversations

Tomas Fernandez Nuñez

Student System Engineering, TEDxUTN

TEDCRED 500+

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Do Mathematics really help us to think and open our minds?

Well, i put that TED talk because was the only one that i found kinda related to this topic.
So a year ago I was in secondary school where teach about many subjects but very little mathematical content. I saw this as a problem, since my intention after leaving school was to pursue a engineering carrier, which obviously has a lot of math. So i studied and practiced hard to pass the entrance examination. After weeks of study, i noticed that was starting to think like in a more clear and analytical way.
I'm sure that most advanced mathematics might can help us when time to think.
Maybe was a growth phenomenon? or caused by mathematics?

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    Nov 17 2011: Mathematics at its earlier levels is one of the fields that helps cultivate an eye for patterns.
    Mathematics at its higher levels centers on proof, which creates a model of precise deductive reasoning- the examination of what conclusions can be drawn definitively from premises.
    Both aspects of exposure to mathematics have widespread application in situations that require logical thinking.
    Mathematics also, for many students, offers an excellent opportunity to struggle with challenge and then, with adequate perseverance, to succeed. This practice and feeling of perseverance and ultimate success may create a disposition to tackle other challenges across domains.
  • Nov 23 2011: Tomas, look at the math not as a big formula which organizes everything and anything but rather as a way to abstract. This view has more power than devoting of Great Constitution. I believe the abstraction makes the mathematics mathematics.
  • Nov 21 2011: Having an axe does not make you a lumberjack!
    But if you don't have an axe you can't be a lumberjack.
  • Nov 17 2011: Hi Tomas ~
    Excellent observation and question.
    Mathematics can be an "exercise" (and a very good one) for the brain.
    My Mom, who loves Math, and was a math teacher - actually does Suduko everyday - she feels its wakes up her mind and sharpens her thought processes. I think that's what you're saying about the changes you observe in yourself.
    From a personal perspective, it's not something that comes easily to me - so I tend to get very distracted when engaging in most math related tasks, which means I have real difficulty focusing. I did discover though, that when I can relate the math problems to be solved to something I am very interested in or understand, suddenly I feel as though a "light goes on" and I have a much easier time with math.
    My children are both lucky enough to have really gifted mathematics teachers - they teach in a manner that the kids relate to, and it makes a ton of difference regarding how quickly and completely the grasp the concepts, and are able to put them into practice. A critical component of this is how they teach and that they really love kids and want t0o see them learn - so they are happy to work with them until they understand. My older daughters teacher even taught me a few things recently - and did so enthusiastically, without an ounce of criticism - I have to say, it made a huge difference in the way I understood concepts I hadn't reviewed in over 20 years! (and made me wish I had a teacher like her when I was in school - methods have changed so very much! For the better I think :)
    I think a key part to it IS practice - like any exercise, the more you do - the better you get. Having a goal behind the repetition is also motivating - you are a great example of that!
    Good luck to you! It sounds like you are well on your way to a wonderful career!
  • Nov 16 2011: A very nice question, Tomas!

    I've been experiencing the same during the past 3 years! I started my maths undergrad 3 years ago.

    In my mind, every thought structure has to have some physical representation inside of my skull.
    Thought structures develop over time and studying like any learning process alters the mind and the
    connections within.

    It is less maths than logic you have to use in order to understand the mathematical formulas.
    Therefore I would say as long you try to understand the maths and the motivations and structural considerations
    for the construction of formulas and proofs, you improve thinking logically.

    However! I realized for myself, after reaching a decent logical level, it is hard for some people to follow some of my considerations. I have to learn now how to formulate my thoughts so that others understand what I tell them.

    Finally: I think it is important to not forget to grow the heart for logic does not help you anything with your personal relationship to fellow humans (and with women in particular).

    Cheers, mate! Good luck for your studies!

    PS: To the ladies: No offense! To me men are as capable of logic as women are ;)
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    Nov 23 2011: No subject helps anyone to be anything until s/he wants to be. It is first one's own intension to have an open mind then only subject can help.
    My college math teacher who was considered to be an expert , was a person of extreme blind belief. I know some more such.
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    Nov 23 2011: Humans are networked beings and creativity is a network function not a single discipline. I'm not sure we do ourselves a service by preferring one discipline over another. Mathematics is just one of our languages. It is no more or less creative than other languages. Each of us have talents toward one or more languages and creativity comes from how well we use these languages to collaborate and bring multiple disciplines to bear on any given problem.

    Consider that the most creative artist has nothing without a cultural context of collaboration among other artists and with potential audiences of said art.
  • Nov 22 2011: The problem with mathematics is the way it is taught. Just because there is a linear way of answering a question doesn't mean there has to be a linear question. For example: If sally has five apples and you eat two how many are left. This is a dumb down version of a dumb question. By making it more creative allows people options and relevance. Same question changed to be relevant: There are five questions on this test and you are on question 3 how many questions are left? This is relevant to the task at hand. it allows them to see the problem and then actually make it a reality, which is creative in it's own right. let make this even harder and relevant.

    If a ball is rolling a long a table at 50 inches per second how long would it take to get to the end of a 50 foot table . . .

    That was boring just writing it.

    The change: You are late for work and driving 50 miles per hour to get to work which is 50 miles away. how much gas does it take to get there if you car uses 10 miles per gallon? What speed would you have to go to get there 10 minutes earlier?

    By changing the equation allows people to put themselves into the problem. by making it relevant makes it creative and then the answer can be answered in a creative way even though there is a clear logical way of answering it you still feel like you are in control of how to get to the answer, which is the goal of creativity.


    Math can help us open our mind if it is applied to a real world personal situation and allows us the opportunity to engage with it.
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    Arul V

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    Nov 22 2011: Life is all about applied mathematics.

    When you buy a car, follow a recipe, or decorate your home, you're using math principles. People have been using these same principles for thousands of years, across countries and continents. Whether you're sailing a boat off the coast of Japan or building a house in Peru, you're using math to get things done.

    How can math be so universal? First, human beings didn't invent math concepts; we discovered them. Also, the language of math is numbers, not English or German or Russian. If we are well versed in this language of numbers, it can help us make important decisions and perform everyday tasks. Math can help us to shop wisely, buy the right insurance, remodel a home within a budget, understand population growth, or even bet on the horse with the best chance of winning the race.

    In this exhibit, you'll look at the language of numbers through common situations, such as playing games or cooking. Put your decision-making skills to the test by deciding whether buying or leasing a new car is right for you, and predict how much money you can save for your retirement by using an interest calculator.

    Reference: http://www.learner.org/interactives/dailymath/
  • Nov 22 2011: Without the perception of a 'problem' there is no call for 'mind tools' such as logic or maths.

    But, if a problem IS perceived, maths is the 'tool of choice' that humans use to solve them rationally.

    'Problems' are things or situations that appear to threaten our safety, stability or future success.

    Things that threaten our safety, stability or future success cause us to experience fear emotions and upset.

    So maths is merely a tool used to avoid feeling upset and irrational should we NOT solve perceived problems.

    So the human obsession with the rationality of maths is generated by the (adult) human fear of upset, or better put, 'aversion to irrationality'.

    When we engage the courage necessary to 'not solve' through letting go of our rationale and instead face our fear of irrationality and upset, problems dissolve. So failing to let go of our rationale or 'judgments', is failing to face fear.

    Accepting our fundamental irrationality ought be easy, it re-unites us with 'home', since 'fundamentally irrational', is the 'birth state' from which we each emerged.

    So maths cannot open the mind. When there is a percieved 'problem', the mind is already closed. Maths cannot open it, it merely moves the mind away.
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    Nov 22 2011: Mathematics gives the real way , the right procedure to solve the problem
  • Nov 21 2011: algerbra is super fun, just sayin
  • Nov 21 2011: who cares math is beautiful and fun! does any art expand or mind? can you really prove it? math is about understanding not just solving a problem. sometimes you do math and you aren't looking to solve anything, as you learn to play with an equation you learn all kinds of things even things about your self. math is amazing for many reasons including that there are so many ways to do anything, and it truly is simple.
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    Nov 21 2011: I can't speak for others but it really gives me more headaches than imaginations.

    It did help me organize my thoughts and logic
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    Nov 21 2011: Mathematics is logic, and skill in using mathematics means skill in approaching a problem in an organized, logical way. That is clearly an advantage in planning and resolving issues. I see that some commenters seem to equate mathematics with the simple rules learned in elementary and intermediate school. Those simple tools are of course essential, but the tools of more advanced mathematics allow you to solve problems that those unskilled in math can't even begin to approach. Every addition of skills in higher mathematics gives access to new solutions and allows you to see more possibilities. It may or may not make you more creative, but it will give wings to the creativity you have. At the highest levels, pure mathematical research is of course highly creative, and has nothing to do with the tools we've all learned.
    I'd like to beat the drum for a branch of mathematics that is not among the esoteric and theoretical, namely statistics. I think everyone should have at least a basic course in statistics, because it corrects the way one thinks about truth. Statistics gives you the understanding to grasp that "truths" you hear or read in the media are often at best likelihoods.
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    Nov 21 2011: It probably depends on the person more than the method.

    Howard Gardner talks about multiple intelligences, which is really just grouping the ways like-minded people think in general ways. There is probably some merit in this.

    Personally, mathematics was like a foreign, dead language to me and still is.
  • Nov 21 2011: In fact, mathematics is the language of physics. And is no doubt about the "open mind" of many physicists. Is almost impossible to imagine the ideas they have had. And the only way to transmit those ideas was through mathematics. In the other hand, the "pure" mathematics also tries to explain abstract concepts, and to imagine those concepts you need a lot of imagination and open mind.
    In the art, perhaps in a hidden way, is always a kind of logic (normally named "style"). That means that the subjacent concept is totally logic, even if it doesn´t look like. Is the general relativity "logic" or intuitive? Not at all.
    I think that the main way to get an open mind is to think as much as possible, and mathematics is one good way for that.
  • Nov 21 2011: Tomas,
    As others have said, mathematics basically uses a specific algorithm to resolve different exercises (of course, there are lots of algorithms, formulae and theorems because there is a large spectrum of domains and areas of mathematics). In other words, you learn to apply a pattern to various problems, which leads to convergent thinking. This is useful because there are so many problems that you can't solve each one of them in a different way. So in this way, it does develop your analytical process of thinking, it helps you make rational connections and optimize the path to a solution.

    However, creativity in its main meaning is about divergent thinking, which is the opposite of what maths help you improve. Here, you find multiple solutions to a single problem (all kinds of problems, not necessarily involving numbers and calculations), and you choose the one that represents the best compromise.

    So in my opinion, the fact that you become more open-minded and creative is indirectly related to better understanding and knowing mathematics (for example, your passion can drive you to research a specific mathematician, you find about more about his life and work and you can make a better connection between the rational side and how he did it).

    I'm studying engineering like you, so I'm more interested in mathematics and physics more than the other subjects and this has indeed helped me rationalize most of the things in my life. I can advise you though to not become hung up on it because it might block/lead to a slower development of your interpersonal abilities (because you can't find reason in feelings, emotions and so on).

    All the best!
  • Nov 21 2011: Great comments, most comments touched the part where we seem to look at Math as a sense of formulaic process. IMHO, the joy of math lies in it's application in daily life. Example: I am big fan of geometry and when I drive I use it the most, like approximating turning radius, braking length etc. It is like math which I learnt while in college and Engineering is in play with a reflex, a recreated formula set to analyze things out of habit in the head.

    That is sort of a kick when you are able to apply the understanding of math in our daily life.

    Maths making us open minded? I am still not sure how a 'clinical sense of being analytical' is related to 'being open minded' about things around. Maybe an extra degree of awareness is available (from proof of Math fundamentals)to take an open minded decision.

    Me & my wife have a small interest in Machine Learning, patterns etc things. While working on these subjects we particularly found the aspect of math being fun with application and less fun on paper. :)

    Please correct me if this idea seems skewed.

    Thanks
    Cheers
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    Nov 21 2011: Speaking for myself, probability theory (and statistics) really opened my mind quite a lot: it allows you to think inductively (in a right, non-intuitive way... the intuitive one is too often wrong), and how to express everything between any dichotomy (instead of 1 and 0, you have all values in between, and can compare uncertainties)

    Mathematics is a great way to learn thinking abstract. And it has beauty and elegance

    Jake: http://comment.rsablogs.org.uk/2011/10/24/rsa-animate-divided-brain/
    => please revise your ideas around lateralization of the brains
  • Nov 21 2011: I studied maths at high school and at the first year in my college.I both did it well ,but my logical thinking ability is still bad.I do not know why?
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    Nov 19 2011: Mathematics uses the right side of your brain which is not creative. Math is not creative. However, I believe that learning math will allow you to think through a more realistic and rational approach to problems in everyday life. However, if you want to open your mind to new ideas and inovations you need to use your left side of your brain which involves music, art, science, literature, etc. Together, both sides of your brain keep your mind in check and provide you with a perfect amount of both creativity as well as rationality.
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      Nov 20 2011: I'm not entirely agree with what you propose. Mathematics actually uses creativity. The mathematicians´s theorems were created based on their creativity and imagination. They are fundamental. When someone tries to solve a complex Geometry problem must inevitably resort to the imagination and the ideas. Then comes the "technical "process. Thanks for your reply.
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        Nov 20 2011: When you solve a mathematics problem, you use a set of formulas/theorems that have already been discovered. Geometry is no different. When you want to solve a geometry problem, depending on the problem, you graph it or you solve it using a set of formulas/theorems. Now, the people who created those theorems and formulas needed to think creatively, but most people do not find formulas/theorems.
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          Nov 20 2011: It is not just a matter of raising a formula or follow a particular theorem. That would not be efficient. What you propose is a prelude to the ideas. The problems of calculus, and geometry agebra need ideas. think that is irrefutable. If you ever had an opportunity of solving a geometry problem you'll notice what I mean. Also you said that "left side of your brain which involves music, art, science, literature, etc.".Is important to clarify that Math is the one most important science for not say the most important.

          I recommend you a nice book:

          http://en.wikipedia.org/wiki/Mathematics_and_the_Imagination_(book)
        • Nov 21 2011: You don't need creativity to read a Shakespeare but you need lots of it to create one!

          Even past PhD in Mathematics it's extremely difficult to be creative.

          But that doesn't mean that maths is not creative is it?
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        Nov 22 2011: I am taking Geometry right now. I have/done many geometry problems some of which I did today. Solving math, whatever type it may be, involves logical thinking and formulas to solve a problem. The person who thinks of formulas or who comes up with math problems is creative, the person who solves them is not.
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          Nov 23 2011: Isn't geometry fun? It was one of my favorite subjects in school (in the 1950s). No other subject illustrates logic so clearly, and when you really understand geometry you'll find thousands of times throughout life that a problem, especially (but not only) in the physical sciences, engineering and mathematics, can be reduced to geometric relationships, which improves insight into the problem and helps solutions to spring forth. Having the tools of geometry, trigonometry, and analysis at hand allows you to be creative in problem solving in ways that you can't be without that knowledge. Enjoy your study of geometry, which is a study of space itself. Nothing is more fundamental.
    • Nov 21 2011: thats sad i love art and math! to me they go together, sometimes i see a math problem and think, DAMN THATS PRETTY, it happens.
  • Nov 19 2011: Human beings are natural born problem solvers. We constantly are solving problems whether its to get to an appointment on time (time management problem) or a place (traversing from one point to another) or placing a football in the hands of a receiver 30 yeards down the field (physics problem). Underneath this natural problem solving ability is process our brains perform of combining realltime information to adapt to the environment around us. Mathematics is a vehicle (or means to an end as Debra says) that opens up our mind to understanding how we are solving these problems. As we gain insight into how we solve simple problem, we can combine approaches and techniques to solve larger more complex problems and turn iideas into reality. If we focus just on the how such as equations, algebra, calculus , math is perceived as hard and unintelligible. If we look at math as our portal to understanding of the what we as natural born problem solvers are accomplishing we gain understanding as to why it helps us adapt to the world around us.
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    Nov 19 2011: For me mathematics is a means to an end. I am not sure that it is the math itself but the things that it illustrates and makes apparent that opens my mind. For example: learning to do statistics helped me to understand a lot about the world of people by showing me what was true or solid and what had no basis in fact.
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    Nov 19 2011: Mathematics is the most important part of life. It teaches you not only calculations but also the lesson of life.
    Mathematics can teach you the real meaning of practice actually i feel that Mathematics is a alternative of practice.
    Mathematics can tech you a lesson on patience.
    Mathematics is life and it is everywhere. mathematics gives you the different way of thinking.
    I LOVE MATHEMATICS...
    • Nov 19 2011: To the smart man, math is simply the whistle that always blows the loudest.
  • Nov 17 2011: I see others have given you references, so here is one i found useful and fun when i started the journey:

    Courant and Robbins book What is mathematics?
  • Nov 17 2011: Mathematics is a language as well as a means to develop creative ideas in a precise and understandable way. It can be an aid in understanding at least some aspects of any subject, from psychology to physics, but it has some limitations. For instance, every logical system is either inconsistent or incomplete (Kurt Goedel). Yet compared to most other languages it has the major advantages of precision and conciseness. It is the languge of science. Why? because science is about measuring things, and Math is a big help in getting that right. Wittgenstein believed that math was tautologous, and it may be, but so are most languages when one concerns oneself with definitions and tries to be accurate. It has been my lifelong comapnion, and i hope will continue to be as long as i can continue to pursue truth.
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    Nov 16 2011: Las Matemáticas ayudan en todo mi amigo.-
    Maths help at all my friend...