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Thread: How important is mathematics

  1. #1 How important is mathematics 
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    Ok well this is one of d biggest questions i have.Do u really have to be a math genius to be good at or understand all sciences?Or is that what the school system just wants us to be because honestly i don't think you do need to be.Science was born out of philosophy not math like everyone keeps thinking.Thinks I'm talking nonsense?Ok fine,lets look at this another way.If you can do math excellently but you don't really understand science then your math skills are basically useless if you want to really do science.Because if you don't understand what you're calculating then it's just going to be a big waste.I admit math is very important i can't deny that fact but if you don't understand let's say physics but you can calculate a lot of the equations used in it how would you know where to apply these calculations?See my point?But honestly i just want an answer do u think a person who understands and loves science a lot shouldn't be allowed to do them just because they can't understand math all that well?


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    Many sciences are largely independent of mathematics, so no, one does not have to be a "mathematical genius" to be a good scientist. As for the rest of the OP.... er... I'm not on the same page.


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  4. #3  
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    Quote Originally Posted by gregg kurbanali View Post
    Ok well this is one of d biggest questions i have.Do u really have to be a math genius to be good at or understand all sciences?Or is that what the school system just wants us to be because honestly i don't think you do need to be.Science was born out of philosophy not math like everyone keeps thinking.Thinks I'm talking nonsense?Ok fine,lets look at this another way.If you can do math excellently but you don't really understand science then your math skills are basically useless if you want to really do science.Because if you don't understand what you're calculating then it's just going to be a big waste.I admit math is very important i can't deny that fact but if you don't understand let's say physics but you can calculate a lot of the equations used in it how would you know where to apply these calculations?See my point?But honestly i just want an answer do u think a person who understands and loves science a lot shouldn't be allowed to do them just because they can't understand math all that well?
    PhDemon is spot-on regarding physics and chemistry, certainly. And you will need to be comfortable with simple algebraic equations and perhaps a bit of simple calculus to do just about any form of science these days.

    What you say about maths being the servant rather than the master is quite right, because scientific insights relate to the physical world itself. But I think you are setting up a bit of a false antithesis by talking about needing to be a mathematical "genius". Nobody would suggest that is necessary. On the other hand, someone who is a mathematical "moron" should be advised to try his or her hand elsewhere.
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    Brassica oleracea Strange's Avatar
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    The whole point of science is that it deals in objective and quantitative data (unlike the philosophy it was, arguably, born out of).

    Certainly physics and chemistry are impossible to study to any significant level without a reasonable grounding in mathematics. I have never been great at math but I did some physical chemistry at degree level (but had to drop out of physics). I have just about been able to keep up with the math in my engineering career.

    For example, you can understand the basic ideas of Newtonian gravity without math but you can't apply it unless you are happy with the (relatively simple) math of .

    And you cannot really understand General Relativity if you cannot do the (pretty advanced) math involved. You can read popular articles and analogies but that is not studying or doing science.

    I guess the requirements for math in the "softer" sciences such as biology are lower, but you still need to be able to count and do basic statistical analysis (otherwise it is just "admiring" plants and animals, rather than "studying" them).
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    Quote Originally Posted by Strange View Post
    I guess the requirements for math in the "softer" sciences such as biology are lower, but you still need to be able to count and do basic statistical analysis (otherwise it is just "admiring" plants and animals, rather than "studying" them).
    Depends on the area you are in Strange - DNA sequence alignment is quite mathematically advanced and the only place I have ever had to use delayed differential equations (which are a bugger) was when I was doing some modelling for the NICD here in South Africa.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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    Quote Originally Posted by river_rat View Post
    Depends on the area you are in Strange - DNA sequence alignment is quite mathematically advanced and the only place I have ever had to use delayed differential equations (which are a bugger) was when I was doing some modelling for the NICD here in South Africa.
    Good point. After I wrote that, I also thought of some of the modelling done in areas such as population genetics, which can be pretty sophisticated as well.
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    I dont have a particularly good grasp of mathematics - I am numerically literate but equations/principles etc.. are over my head. I do think however that a better grasp of mathematics would have helped even my mathematically light degree (psychology). Without a good grasp of seeing the picture the numbers are telling you its very hard to see what the statistics/results are telling you. Its also very hard to question them in any meaningful way.

    Do you not like maths then or do you think its not your thing?
    "And we should consider every day lost on which we have not danced at least once. And we should call every truth false which was not accompanied by at least one laugh" Nietzsche.
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    I was thinking of applying mathematics to psychology and behaviourism.
    I'm still currently in year 11, moving to 12 (A-Levels), so I have lots of time.

    In applying formulas and algorithms for the human behaviour, it would be possible to predict behavior with 100% accuracy, as I'm sure we all know, that mathematics is an abstract means in predicting reality.

    Basic emotions must first be deduced of course, which can cause some outrage, if it is discovered that fear (as J.B Watson suggests) is one of the basic emotion of humans. I'm still afraid that I would fall into the category of probablity, as this would mean that the 100% accuracy will not be achived, however, it's nice to think that perhaps humans are not so easily predictable.

    A ridiculously simple basic example, is to give a value to certain psychopathies, postive numbers can stimulate certain syptoms, whereby negative numbers does not. The formula could go anywhere, such as 'x=y/z', y and z being the condition of the patient deduced in certain tests, to get the value of x, which then will predict the likelihood (don't like probability,'perhaps someone else will think of something vastly superior) of the actions of the individual, which will then be set in the algorithm.

    I believe psychology have many potential with mathematics, my knowledge is still tiny however, neurology will probably be quite important.
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    Mathematics is amazing, a true tool of the human mind.

    If you can apply it, you should, subjects such as psychology lack mathematics, if no one reach it before I reach university, that will probably be my main focus.
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    Mathematics, logic, rationality and human behaviour don't sit very well together. Although things like psychometrics try to quantify intelligence, personality etc.. you don't have to scratch the surface too deep to see how flawed it is. But companies and governments like them because they feel they provide some sort of predictability of behaviour. Humans are not predictable in that sense, the way a person behaves depends very much on the social situation they are in - so there are a lot of variables you would need to consider in your calculations. I am sceptical that human behaviour per se can be expressed in any meaningful way in a mathematical formulae.
    "And we should consider every day lost on which we have not danced at least once. And we should call every truth false which was not accompanied by at least one laugh" Nietzsche.
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  12. #11  
    Forum Masters Degree LuciDreaming's Avatar
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    Having said that don't let me discourage you from trying
    "And we should consider every day lost on which we have not danced at least once. And we should call every truth false which was not accompanied by at least one laugh" Nietzsche.
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    Quote Originally Posted by LuciDreaming View Post
    I am sceptical that human behaviour per se can be expressed in any meaningful way in a mathematical formulae.
    To the contrary, human behavior in aggregate is quite open to modelling and mathematics - see the areas of crowd dynamics to the use of continuum mechanics to model queuing behavior to general game theory for how we make decisions.
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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    Science (at least, advanced science) depends on mathematics, but mathematics does not depend on science. Mathematics is very important for scientists, engineers, and technologists. Without mathematics, we would be in the stone age, and it requires to know everything up to advanced calculus to get to the present day with technology. The rest is called "pure mathematics" which can be very interesting, but isn't currently useful. I said currently, because we do use mathematics today which was considered "pure mathematics" hundreds of years ago, and it is a big possibility that what is pure mathematics today, might be essential in the far future. Thus, to continue advancing, we may need to invent more and more mathematics. If mathematical progress stays ahead of scientific process, we will never have to invent new maths (with a few exceptions) to do new things in science.
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    Quote Originally Posted by anticorncob28 View Post
    Science (at least, advanced science) depends on mathematics, but mathematics does not depend on science. Mathematics is very important for scientists, engineers, and technologists. Without mathematics, we would be in the stone age, and it requires to know everything up to advanced calculus to get to the present day with technology. The rest is called "pure mathematics" which can be very interesting, but isn't currently useful. I said currently, because we do use mathematics today which was considered "pure mathematics" hundreds of years ago, and it is a big possibility that what is pure mathematics today, might be essential in the far future. Thus, to continue advancing, we may need to invent more and more mathematics. If mathematical progress stays ahead of scientific process, we will never have to invent new maths (with a few exceptions) to do new things in science.
    But this is contradicted by actual history. Newton did not sit around and say, "I think I'll invent calculus in case anyone needs it later." Rather, Newton was doing physics -- trying to work out the theory of gravity -- and invented calculus for that purpose. Newton's formulation of calculus was not logically rigorous. He had no proper, logical definition of the fluxion. It took 200 more years for mathematicians to work out the logical details and come up with a proper definition of the limit and the derivative.

    Likewise, in the 20th century, three physicists won the Nobel prize for their theory of renormalization; a mathematically bogus procedure that happens to predict (to a reasonably large number of decimal places) the results of physical experiments. I'm not even sure if renormalization has been made legit yet or not.

    Likewise again we have string theory; which, even if it turns out to be a blind alley in terms of physics, has already generated a lot of beautiful and original math.

    What's actually true is that physical science tends to drive certain areas of mathematics; not the other way 'round.

    Of course it's true that very often a piece of pure math turns out to be useful years later. The most striking example I can think of is the theory of factoring large numbers. For 2000 years, number theory was totally useless but supremely beautiful. And since the mid 1990's, suddenly the mathematics of factoring is the theory underlying public key cryptography, the heart of modern e-commerce and computer security. This is a very striking example: a branch of math totally useless for two millennia, suddenly supremely useful.

    But I just wanted to point out that physical science turns out to drive math quite often, more often than people realize. Physical application often leads mathematical rigor by centuries, as in the case of the definition of the derivative.
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    Quote Originally Posted by someguy1 View Post

    But this is contradicted by actual history. Newton did not sit around and say, "I think I'll invent calculus in case anyone needs it later." Rather, Newton was doing physics -- trying to work out the theory of gravity -- and invented calculus for that purpose. Newton's formulation of calculus was not logically rigorous. He had no proper, logical definition of the fluxion. It took 200 more years for mathematicians to work out the logical details and come up with a proper definition of the limit and the derivative.

    Likewise, in the 20th century, three physicists won the Nobel prize for their theory of renormalization; a mathematically bogus procedure that happens to predict (to a reasonably large number of decimal places) the results of physical experiments. I'm not even sure if renormalization has been made legit yet or not.

    Likewise again we have string theory; which, even if it turns out to be a blind alley in terms of physics, has already generated a lot of beautiful and original math.

    What's actually true is that physical science tends to drive certain areas of mathematics; not the other way 'round.

    Of course it's true that very often a piece of pure math turns out to be useful years later. The most striking example I can think of is the theory of factoring large numbers. For 2000 years, number theory was totally useless but supremely beautiful. And since the mid 1990's, suddenly the mathematics of factoring is the theory underlying public key cryptography, the heart of modern e-commerce and computer security. This is a very striking example: a branch of math totally useless for two millennia, suddenly supremely useful.

    But I just wanted to point out that physical science turns out to drive math quite often, more often than people realize. Physical application often leads mathematical rigor by centuries, as in the case of the definition of the derivative.
    Interesting post!
    I have a vague understanding of renormalization and I have heard it being referred to as "a mathematical sleight of hand".
    Perhaps someone, with sound knowledge of maths, might give an accurate description of the process of renormalization?
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    How important is mathematics?
    WV2 = kd3(t/d)n.

    Hope that answers your question.
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  18. #17  
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    Quote Originally Posted by Halliday View Post
    Interesting post!
    I have a vague understanding of renormalization and I have heard it being referred to as "a mathematical sleight of hand".
    Perhaps someone, with sound knowledge of maths, might give an accurate description of the process of renormalization?
    It isn't very difficult to outline what renormalization is and how it is used. I'll start a new thread under physics with a summary, and we'll see what the response is. Personally, I think that there are interesting philosophical aspects that are seldom mentioned.
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    Anyone interested in the "non-physical" sciences, psychology, sociology, epidemiology and the like, has to have a firm grasp on statistics. Not just the simple stuff, but a good mathematically based understanding of statistical procedures and techniques. It is not enough to rely on the statistical computer packages you can get for most purposes, you have to understand what the various techniques mean both for the results and what they imply for the data you're using.

    I remember a friend of my husband's 30+ years ago kept a heap of medical and similar journals in his bottom drawer. Whenever he felt he needed to top up his publication score but didn't have much original mathematical work ready to go, he'd flip through and find an article with dodgy analysis. He'd re-do it, and publish a criticism most often, or a rebuttal where they'd got the significance reversed as well as miscalculated, then settle back to work on his own projects without breaking stride.
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    I think most of you have misunderstood me.I wasn't saying that math isn't important.I do know how important math is an that math doesn't need science but science needs math.The point i was just trying to make is that if a person(who isn't a mathematical moron) isn't good at math but has a very good understanding of science should be denied d opportunity to make a future for himself/herself in the world of science.
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    Short answer, as a scientist do you need to understand mathematics as a tool in your area of expertise? Yes

    Do you need to be a mathematician? No
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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    Quote Originally Posted by gregg kurbanali View Post
    The point i was just trying to make is that if a person(who isn't a mathematical moron) isn't good at math but has a very good understanding of science should be denied d opportunity to make a future for himself/herself in the world of science.
    You can have a very correct grasp of the basis of science with basic of mathematics (especially logic), and minor encyclopedic knowledge.

    You can fake(sometime honestly) good understanding in science with extensive encyclopedic knowledge and no math.

    You cannot understand the depth of any theory, without the corresponding depth of the mathematics it is expressed into.

    But science is fun/useful even on the first level. Like any sport, you don't have to be a professional hyper gifted fellow to play a good game with your friends.
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