What is advanced-level mathematics used for?

I barely understand the bare basics of algebra, my math skills are abysmal. But what applications do advanced mathematics such as stochastic calculus and linear algebra have?

Other than in physics, science, and engineering, what other things can advanced-level mathematics be used for? How about in daily life?

It can enhance your abstract thinking ability.

Not directly useful for anything in daily life.

It can enhance your abstract thinking ability.

Not directly useful for anything in daily life.
I fully disagree, how do you think barcodes were invented?

A few uses of Linear Algebra:

Codabar system
Digital image compression
Calculating life expectancy
Modelling population growth
Profit maximization
Universal Product Code
Lots more

If you want a thorough discussion of exactly how they are used, then just open up some linear algebra books, or do a Google search.

Higher math isn't just solving puzzles (In fact, that's not really what math is). People don't just do mathematics to improve their thinking abilities; it certainly helps, but it has many applications.

Keep in mind that mathematics need not be applied to anything. Just because you can't use a result of mathematics (at first) for anything practical does not make it useless.

Demystifier
There is great deal of uses in physics (also era involves some Chemistry) and engineering. In general relativity a lot of linear algebra and calculus is required. In engineering, mostly calculating some basic mechanics problem.

Other than these, Economics uses great deal of calculus to model the market which is very important. You can search more on financial mathematics (not accounting~~boring).

Also, I've heard that matrices can be used to balance out chemical reactions in chemistry. I haven't actually done that myself, but I was happy to know that there was an easier way than what I did in my first year chemistry class!

A few uses of Linear Algebra:
Oh sure it's useful in all sorts of professions. But not daily life, and many well paid jobs don't need it either.

But the trouble is, when you're 16 you don't quite know what you'll be doing in 10 years time, and by then it's too late to learn so easily.

Everything has its applications. Of course, applications of some fields are more obvious than others.

What about the use of high-level math in areas other than physics, science, and engineering?

Mathematics models the natural world.
So your question is nearly identical to ......
What use is it to learn English ?

Furthermore, Logic, one of the foundations of Mathematics, is the link between The Arts & The Sciences.
All artforms (nearly) seek to communicate.
How better to make your case than with clear precise easy to understand logic ?
Be it painting, screenplay, poem, courtroom summation or a novel.

Some of the very the best lawyers were good at Math.
That is one of the reasons they excel at the Law.

Mathematics underlies nearly everything you see around you.

But it will not guarantee a good life.
That is the province of religion and moral philosophy.

Also, I've heard that matrices can be used to balance out chemical reactions in chemistry. I haven't actually done that myself, but I was happy to know that there was an easier way than what I did in my first year chemistry class!
I think balancing equations is simply simultaneous equations, I mean for rather complicated equations. Matrices are just simple forms of simultaneous equations, they just save your paper and ink. Of course there are many ways of balancing equations, but many of them might not work for all cases.

Also, matrices are very useful in doing statistics, though I haven't learn much of statistics, I heard of something called covariant matrix that is used for complicated systems. And statistics can be applied to many areas. May be you can look more on that.

This article on mathematics education (and so-called applications of math in real life) is a good read:
http://www.maa.org/devlin/LockhartsLament.pdf [Broken]

Somewhat long, but well worth the time.

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Oh sure it's useful in all sorts of professions. But not daily life, and many well paid jobs don't need it either.

But the trouble is, when you're 16 you don't quite know what you'll be doing in 10 years time, and by then it's too late to learn so easily.
How does that even matter? Just because some random CEO doesn't use his knowledge of basket-weaving doesn't make basket-weaving useless. That's a really poor argument. Why does everything have to be immediately useful in daily life, and by daily life, I assume you mean eating, breathing, sleeping, and no more.

It seems to me that you think that if you don't use something every day, or can't use it to make lots of money, then it's useless. As said many times in this thread, mathematics is all about logical and abstract thinking; it's basically a form of creativity. Now tell me, how useless are the former?

When people ask me what the use is for mathematics, I always respond with the following poem by Morris Bishop:

There's a tiresome young man in Bay Shore.
When his fiancee cried, "I adore
the beautiful sea".
He replied, "I agree,
it's pretty, but what is it for?"

Math_QED
How does that even matter? Just because some random CEO doesn't use his knowledge of basket-weaving doesn't make basket-weaving useless. That's a really poor argument. Why does everything have to be immediately useful in daily life, and by daily life, I assume you mean eating, breathing, sleeping, and no more.

It seems to me that you think that if you don't use something every day, or can't use it to make lots of money, then it's useless. As said many times in this thread, mathematics is all about logical and abstract thinking; it's basically a form of creativity. Now tell me, how useless are the former?
He never said higher math was useless in the general context, simply useless in daily life. There's nothing wrong with the validity of his statement since we take the meaning of "useless" in every day conversation as "generally useless" rather than "completely useless". However, there are few professions that are useful in daily life, such as cooking, etc. so the statement, although basically true, is misleading.

gb7nash
Homework Helper
Cryptography is a pretty big one.

When people ask me what the use is for mathematics, I always respond with the following poem by Morris Bishop:

There's a tiresome young man in Bay Shore.
When his fiancee cried, "I adore
the beautiful sea".
He replied, "I agree,
it's pretty, but what is it for?"
I prefer this:

A math professor, a native Texan, was asked by one of his students: "What is mathematics good for?"
He replied: "This question makes me sick! If you show someone the Grand Canyon for the first time, and he asks you `What's it good for?' What would you do? Well, you kick that guy off the cliff!"

As said many times in this thread, mathematics is all about logical and abstract thinking; it's basically a form of creativity. Now tell me, how useless are the former?
Yes, I was one of those people who said that. But I think the OP was concerned about direct applications. Like when you would want to sit down with a pen and paper to write an integral or perform a matrix operation. For most people the answer would be never in their life.

Us mathy types would think about it all the time when we hear news stories or write on internet forums, but that's not normal people. If you aren't inclined to analyze things for fun, then knowing how to integrate won't make you do it.

Yes, I was one of those people who said that. But I think the OP was concerned about direct applications. Like when you would want to sit down with a pen and paper to write an integral or perform a matrix operation. For most people the answer would be never in their life.

Us mathy types would think about it all the time when we hear news stories or write on internet forums, but that's not normal people. If you aren't inclined to analyze things for fun, then knowing how to integrate won't make you do it.
*Science
*Physics
*Engineering
*Computer programming
*Genetics and other fields of biology
*Chemistry

But people other than physicists, scientists, and engineers wouldn't have any real use for any advanced maths.

I believe that advanced-level mathematics (especially pure maths) is for fun and for appreciating the beauty.

I am currently at high school and love learning math (college-level math), but find the maths at high school very dull and boring. The current education system just turns maths into a very systematic work. For example, when we learn Pythagoras Theorem, after teaching the theorem itself, we are told how to
(1) Find the length of the hypotenuse if the sides are given
(2) Find the length of one side when the hypotenuse and one of the sides are given
while the teacher can just let us find the way of doing it ourselves with the original theorem. Even with the exercises provided, the questions are divided into parts about the first type of problem and second type of problem. It is just plain stupid (sorry for being a bit too rude).

What about the use of high-level math in areas other than physics, science, and engineering?
Finance, cryptography...

I believe that advanced-level mathematics (especially pure maths) is for fun and for appreciating the beauty.

I am currently at high school and love learning math (college-level math), but find the maths at high school very dull and boring. The current education system just turns maths into a very systematic work. For example, when we learn Pythagoras Theorem, after teaching the theorem itself, we are told how to
(1) Find the length of the hypotenuse if the sides are given
(2) Find the length of one side when the hypotenuse and one of the sides are given
while the teacher can just let us find the way of doing it ourselves with the original theorem. Even with the exercises provided, the questions are divided into parts about the first type of problem and second type of problem. It is just plain stupid (sorry for being a bit too rude).
There is a method to this madness. True you can derive these different formula's from the original theorems each and every time you need to use them. But, you will need to apply these things from time to time as you move into higher level work and it's helps if you have a lot of these very basic things like trig formulas memorized (at least somewhat memorized) such that you don]t have to go back and derive them each and every time you need them. Of course there is nothing wrong with learning how to use the theorems and understand their meanings to derive the formulas or, given a formula prove it's validity based on the theorem(s). When i was in high school (and freshman college) many of the more fundamental courses omitted the proofs or simply glossed over them. But I never felt comfortable , I always preferred working through the proofs and, thinking of other approaches I could take to them.

Stephen Tashi
FishmanGeertz said:
But people other than physicists, scientists, and engineers wouldn't have any real use for any advanced maths.
You must distinguish between these two questions: "What do people often use advanced mathematics for" and "What can advanced mathematics be used for". People who have training in advanced mathematics, and a certain knack for applying it, can apply it to almost any subject, even art and literature. Statistically, the people who know advanced mathematics tend to be engineers, physicists etc. so that's where you most often see advanced mathematics applied. If an artist or literary historian happened to be an expert in differential equations, they might well be able to apply it to their field of study. However, they might not find many of their peers able to understand or appreciate their work.

You must distinguish between these two questions: "What do people often use advanced mathematics for" and "What can advanced mathematics be used for". People who have training in advanced mathematics, and a certain knack for applying it, can apply it to almost any subject, even art and literature. Statistically, the people who know advanced mathematics tend to be engineers, physicists etc. so that's where you most often see advanced mathematics applied. If an artist or literary historian happened to be an expert in differential equations, they might well be able to apply it to their field of study. However, they might not find many of their peers able to understand or appreciate their work.
Because of it's sometimes mind-boggling complexity and difficulty, it is difficult to wrap your mind around that level of math without having to have an IQ of 140+

Math is despised by most high school and college students. Only the people with high IQ's (a tiny percentage of the population) tend to excel in, and take further interest in it.

I do not think IQ = math talent.