What is math?
Asked by
ftp901 (
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September 12th, 2010
Why does it exist, who invented it, and how do you know it’s correct?
Of course I’ve done math all my life in school but I never understood what it was for. I just had all these teachers telling me that it was important to learn all these crazy symbols but they never explained the big picture of why we were doing it.
I can understand why ancient people would invent a basic system for measuring things so that they could build houses or draw a map or count/add things…but the more complicated math, like huge formulas, I don’t get.
When you watch a movie like A Beautiful Mind or Good Will Hunting and Will is able to come up with some genius mathematical formula that no one else in the world has been able to answer, how does his teacher know that the answer is correct if the teacher couldn’t answer it himself? and what are they solving? are they solving something related to the real world that is actually useful to humans?
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14 Answers
Please explain in layman’s terms
Math is the language of nature and science. It is elegant.
10 + 10 = 20, no matter where you are.
in math, we use a 10 digit system, we call base 10. 0,1,2,3,4,5,6,7,8,9. We do this because we have 10 fingers.
God has 8 fingers, and uses base 8. To see that, you need to study chemistry and astrophysics, but it’s true. This is truly amazing stuff when you get it.
The huge formulas are often complicated because of what they are trying to determine. If you are trying to study where a planet will appear in the sky on a certain date, you need that.
@filmfann We do not use a ten base system because we have ten fingers.
Math is a language of humans. And like all other languages, we use it to describe observable and theoretical phenomenon.
Math is used as a precise language for description. The descriptions and meanings are meant for exactness. We may use it to describe how and when the sun rises, but Math will never be used to describe how we feel about that sunrise. Only poetry will suffice for that.
Math is a language tool. It has a specific purpose, just as all language tools do. Best to use the proper tool for any given task at hand.
Math is also the language of music! yes, music. And as we will one day see, music is the language of string theory, one of the bases of all life. All life is based on the harmonies of the Strings, and the harmonies are mathematical in nature.
Also, math is the language of physics.
”When you watch a movie like A Beautiful Mind or Good Will Hunting and Will is able to come up with some genius mathematical formula that no one else in the world has been able to answer, how does his teacher know that the answer is correct if the teacher couldn’t answer it himself? and what are they solving? are they solving something related to the real world that is actually useful to humans?”
These were only movies, and so they weren’t really solving anything.
But if something like this were to happen, the teacher might see that the student is correct, because once you see the solution to a problem you couldn’t answer, it is sometimes obvious to you that this solution is in fact correct.
Math is used for describing natural phenomena.
As for the genius mathematical formulas, I believe there is a difference between establish math principles and math theory. Theories are correct according to logic but whether or not they actually describe natural phenomena remains to be seen (sometimes). Like people have measured the vastness of the universe, but the truth is that no one will really be able to fathom how big the universe actually is. We can only make somewhat educated guesses.
Maths is a set of self-consistent rules that can describe every physical phenomenon. It has many varied uses, because it can be applied to anything. For example the Fourier Transform is used in image processing for most medical images, and it is vital to reconstruct the data acquired by an MRI scanner. Our equations to describe the universe are extremely complicated, but as far as I know the most complex maths is used in computer animation. Fluid dynamics (which describes the motion of liquids) is used to make the movements realistic and believable. Computer games also have versions of the n-body problem to simulate the effects of a collision or ricochet.
Maths teachers should make this more clear, because maths only starts to get exciting when you see it applied to real situations. Once you can calculate the path of a projectile taking air resistance and the Earth’s curvature into account, maths is both elegant and beautiful. I wish I could still do that.
In Good Will Hunting, the teacher had spent four years (I think) on the formula with a colleague and had solved it. Will just managed to solve it overnight.
There is an ongoing debate over whether mathematics has an independent existence, whether it is discovered or invented. In either case, math is reducible to laws of logic. A math system is based on a set of axioms that define the objects in the system by telling how they relate to one another. These axioms are neither true nor false, so it is not possible to say whether math, in its pure form, is correct or incorrect. The only necessary criterion for a set of axioms is that they not contradict one another.
Although mathematics beyond arithmetic is not used by most people, our technology is strongly dependent on it. Equations are used in all engineering applications, for building bridges or electric plants or launching satellites.
The reason that something whose correctness can not be determined can be so useful is that mathematics can be used to model the world and the correctness of the models has been tested by making measurements.
@Whitsoxdude From Wiki: Ten is the number which is the count of fingers and thumbs on both hands (or toes on the feet). The English word digit as well as its translation in many languages is also the anatomical term for fingers and toes. In English, decimal (decimus < Lat.) means tenth, decimate means reduce by a tenth, and denary (denarius < Lat.) means the unit of ten.
Why do you think we use base 10?
As several have already told you, math is a language.
Some say it is a precise and elegant language, but I say that’s irrelevant if people can’t or don’t understand it.
Anything you can say in math, you can also say in natural language. It might take longer, and it might be a little more confusing since terms are not defined as clearly, but it can be done.
Why is math complex? Because it is trying to model complex situations. You may not see it this way, but you walk through life with a model of how the world works in your head. You see things move or behave in one way, and you predict their future behavior. If you see a yo-yo on a string, you can predict its future behavior based on what you are looking at now.
You make an approximation. Math can help you get make much more precise predictions because it allows you to measure current behavior more precisely.
Math formalizes all the rules you have in your head that allow you to predict the future behavior of your environment. It forces you to formalize that thinking. If you are trying to predict complicated behavior, such as how time changes when you are traveling at the speed of light, or what you need to do to teachers and schools in order to give poor kids the best chance, you can do it in your head and you can do it with words, but it is done much more easily if you use math—a language designed specifically to formalize models about how the world works.
“When you watch a movie like A Beautiful Mind or Good Will Hunting and Will is able to come up with some genius mathematical formula that no one else in the world has been able to answer, how does his teacher know that the answer is correct if the teacher couldn’t answer it himself?”
It is usually easier to recognize that a solution is correct than it is to find a solution. That’s one reason that math textbooks often have solutions to exercises in the back.
One Good Will Hunting problem.
Some pictures.
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