Is there a hierarchy between pure and applied mathematics?

[pivoxa15]

I always get the impression that pure maths is more superior meaning harder, grander than applied maths and that the smart people on average go into pure maths. Is this a misconception?

Also rarely is it that applied mathematicians switch into pure maths but the vice versa is plentiful.

I do find pure maths harder then applied maths.

 

[Gib Z]

The distinction between the two is becoming blurred, and not to mention many people are considering themselves to be both at the same time. I believe it is a misconception, because applied maths can be extremely difficult, on par with pure maths. Just ask the teams of physicists trying to fix up the infinities involved in string theory.

 

[morphism]

gaaaah not this nonsense again

 

[pivoxa15]

gaaaah not this nonsense again

I share your concern but we have hope of being honest and just say it.

I believe that not everything is created equal, speaking on average off course.

 

[MrJB]

gaaaah not this nonsense again

Agreed.

Questions like this makes less sense than asking: Which weighs more, a plant or an animal?
Pure and Applied Math are both rather complicated which makes them impossible to compare as a whole.

The notion that one is more difficult implies that the other is easy, and this is certainly not the case. Mathematics would be better off if the notion of superiority was dropped. Perhaps then, people would be more likely to share ideas from those different camps and more discoveries could be made.

 

[pivoxa15]

Agreed.

Questions like this makes less sense than asking: Which weighs more, a plant or an animal?
Pure and Applied Math are both rather complicated which makes them impossible to compare as a whole.

The notion that one is more difficult implies that the other is easy, and this is certainly not the case. Mathematics would be better off if the notion of superiority was dropped. Perhaps then, people would be more likely to share ideas from those different camps and more discoveries could be made.

It just means one is more difficult then the other. Easy is not implied at all. Though again it doesn't mean both words are specific but just that one is more specific then the other.

I am perhaps more concerned with undergraduate pure and applied maths. Research is always tough as there are 'impossible' problems in both fields. Just look at the mellinium problems. 4 pure, 3 applied.

As for superiority, it's a vague word. A more specific word is 'harder'.

It is definitely the case that the living standard in Africa is lower then it is in America. We shouldn't turn away from that and say it's nonsense because happiness is unmeasureable or something. We should just be honest, accept and declare it.

 

[MrJB]

How would you define a measure of the difficulty of pure or applied math?
Is there also a subjective element, as some people may be better at one than the other?

 

[Office_Shredder]

Considering more superior is meaningless, it's difficult to answer the question :p

Grammar nazi-ing aside, would you want someone to say the easier or harder subject while doing an undergraduate degree is superior?

It should be noted that research in any field is always difficult... if it was easy, someone else would have thought it up already. I think this has a kind of balancing effect, where if one subject blows past another in sophistication, people in the other start finding results easier as a result of it being a less mature subject, meaning more people start focusing on that area. I could be completely wrong, but it's a nice theory and I'm going to stick with it :)

 

[wysard]

I always get the impression that pure maths is more superior meaning harder, grander than applied maths and that the smart people on average go into pure maths. Is this a misconception?

Also rarely is it that applied mathematicians switch into pure maths but the vice versa is plentiful.

I do find pure maths harder then applied maths.

Can't speak for anyone else, but growing up in a house where Dad had switched from applied maths (Physicist for GE) to pure maths (Combnitorics Prof.) just made the math jokes more obscure. That and conversations in the car went from "Given a frictionless bearing supporting..." to "You are trapped in a dungeon by an evil magician with N choices before you.." kind of problems I think it's more about what your mind has a bent for, some of which may be more common than others, but not necessarily "harder" unless you are trying to force a square brain into a round degree.

 

[pivoxa15]

Can't speak for anyone else, but growing up in a house where Dad had switched from applied maths (Physicist for GE) to pure maths (Combnitorics Prof.) just made the math jokes more obscure. That and conversations in the car went from "Given a frictionless bearing supporting..." to "You are trapped in a dungeon by an evil magician with N choices before you.." kind of problems I think it's more about what your mind has a bent for, some of which may be more common than others, but not necessarily "harder" unless you are trying to force a square brain into a round degree.

Combinatorics is not the center stage of pure maths, it's kind of applied to me. In my department, combinatorics is definitely considered applied reserach. When I refer to pure maths, I think about the deep or abstract areas where students can even find the definitions diffcult, let alone do problems.

 

[pivoxa15]

Considering more superior is meaningless, it's difficult to answer the question :p

Grammar nazi-ing aside, would you want someone to say the easier or harder subject while doing an undergraduate degree is superior?

It should be noted that research in any field is always difficult... if it was easy, someone else would have thought it up already. I think this has a kind of balancing effect, where if one subject blows past another in sophistication, people in the other start finding results easier as a result of it being a less mature subject, meaning more people start focusing on that area. I could be completely wrong, but it's a nice theory and I'm going to stick with it :)

Fair point. But it may be the case that on average the smart grad students go into pure maths. They could have gone into applied maths with high success as well but on average the applied student may really struggle in any pure maths research.

 

[pivoxa15]

How would you define a measure of the difficulty of pure or applied math?
Is there also a subjective element, as some people may be better at one than the other?

True but I was always talking about on average.

Another genearlisation is that applied maths is about concrete examples.

Pure maths is about generalising concrete examples so more abstract. On average people find the abstract harder.

It's often the case that the pure mathematicians start with concrete examples then generalises them so they also do concrete stuff which also occurs in doing counter examples. In that way the pure mathematicians do both concrete and abstract stuff so more work for them compared to the applied mathematicians.

 

[Integral]

Fair point. But it may be the case that on average the smart grad students go into pure maths. They could have gone into applied maths with high success as well but on average the applied student may really struggle in any pure maths research.

Grad students choose their field of study out of personal preference not because it is hard or easy. I studied applied math because I wanted to pursue mathmatical modeling. My interests were differential equations and numerical methods. I have little interest in fields of pure theory, but wanted a knowledge base that would help me understand the world I live in.
Others have other goals. Intellegence at this level is common to all, and simply not a factor in these decisions.

Your generalizations and made up for argument situations are flaky at best.

 

[Gib Z]

Combinatorics is not the center stage of pure maths, it's kind of applied to me. In my department, combinatorics is definitely considered applied reserach. When I refer to pure maths, I think about the deep or abstract areas where students can even find the definitions diffcult, let alone do problems.

If you characterize all pure maths to be the deep or abstract areas when even definitions are difficult, and applied maths the rest, of course you are going to think that pure maths is harder...you sound like a pure math supremest to me.

 

[pivoxa15]

If you characterize all pure maths to be the deep or abstract areas when even definitions are difficult, and applied maths the rest, of course you are going to think that pure maths is harder...you sound like a pure math supremest to me.

My comments are general. Too general to be worthy of anything serious as most of you think but that's okay. I have my opinions because I have struggled at pure maths. In fact I am actually thinking of a more applied area to do research in because I find pure maths to be boring at times. Maybe it's because I don't get it.

 

[Gib Z]

I find pure maths to be boring at times. Maybe it's because I don't get it.

The main thing you are not getting through your head is that the two distinctions are very blurred these days. Don't think of maths as pure and applied, think of it as its different fields, which links between the fields. Some fields are purely for application, some fields have none at the current time, and some fields are a good mix. When you say "Maybe it's because I don't get it.", you are referring to 'pure' maths. Instead think you are just struggling a bit with a certain aspect of one field.

 

[JeffN]

..don't you find it a bit childish to worry about something like this? you can't possibly think that applied math is some sort of a second rate field that failed mathematicians head off into after they fail their exams..

 

[Count Iblis]

Applied math is superior, because most results were originally found using vague intuitive methods. In most cases pure maths is about proving results that are pretty much known to be true anyway.

Newton invented Calculus, pure mathematicians made it rigorous centuries later. And only in the 20th century did pure mathematicians invent infinitesimal numbers to do computations in the same way Newton did (i.e. without limits)

Dirac invented the Dirac function, pure mathematicians invented the theory of distributions to make it rigorous.

 

[pivoxa15]

Applied math is superior, because most results were originally found using vague intuitive methods. In most cases pure maths is about proving results that are pretty much known to be true anyway.

Newton invented Calculus, pure mathematicians made it rigorous centuries later. And only in the 20th century did pure mathematicians invent infinitesimal numbers to do computations in the same way Newton did (i.e. without limits)

Dirac invented the Dirac function, pure mathematicians invented the theory of distributions to make it rigorous.

It just shows that pure maths is harder as it comes after concrete examples.

 

[JasonRox]

I find Applied Mathematics way harder than Pure Mathematics!

 

[pivoxa15]

I find Applied Mathematics way harder than Pure Mathematics!

Because you spend much more time in pure maths.

Also why is it that the greatest mathematicians did pure and applied but not many only applied. Some only pure though.

 

[JasonRox]

Because you spend much more time in pure maths.

Also why is it that the greatest mathematicians did pure and applied but not many only applied. Some only pure though.

My degree is geared towards applied mathematics, so I've done enough of both.

Are you really a senior student thinking like this about mathematics?

 

[morphism]

Are you really a senior student thinking like this about mathematics?

My thoughts exactly. It's disheartening!

pivoxa15, why do you keep asking these questions and making these threads? Are you learning math only to feel superior to other people? I get the impression from most of your posts that you use math as a device to disconnect yourself from everyone and everything. In my humble opinion, this is very unhealthy.

 

[cristo]

Also why is it that the greatest mathematicians did pure and applied but not many only applied. Some only pure though.

You're talking of "great mathematicians" of many years ago, when it was a lot harder to draw a line between the two disciplines.

Some of your points are pretty bad. I agree with Integral's post (which you seem to have ignored) that grad students do not select what to study on "what is hardest," they generally pick what they enjoy the most.

Finally, I agree with the other posters above: why do you keep asking questions like this. You don't appear to be a student who is about to enter grad school, to me.

 

[pivoxa15]

My degree is geared towards applied mathematics, so I've done enough of both.

Are you really a senior student thinking like this about mathematics?

Yes. I am only trying to be honest with things.

I do realize that I should so to speak 'shut up and calculate/mathematise.'

 

[pivoxa15]

My thoughts exactly. It's disheartening!

pivoxa15, why do you keep asking these questions and making these threads? Are you learning math only to feel superior to other people? I get the impression from most of your posts that you use math as a device to disconnect yourself from everyone and everything. In my humble opinion, this is very unhealthy.

I am trying to be honest. I do feel inferior to the top pure maths students but don't generally feel superior to anyone because I know my limitations and intelligence which is average at best. I only rely on hard work to climb up.

 

[JasonRox]

Yes. I am only trying to be honest with things.

I do realize that I should so to speak 'shut up and calculate/mathematise.'

It's fine to speak up, but not about these silly things.

Like I'm not afraid to say that school is just retarded now. School is no longer about the opportunity to learn, it's now about future job security. Sure you still get the "opportunity" to learn, but that's mainly an illusion because you only have the opportunity to learn AFTER you go through all the ****ing loops they make you go through. It's pathetic.

 

[Gib Z]

The OP is ignoring everything we are saying. Cristo, I've told him the barrier between pure and applied is very vague these days at least 3 times in this thread. morphism, "very unhealthy" is a lot kinder than what I'm thinking.

 

[pivoxa15]

The OP is ignoring everything we are saying. Cristo, I've told him the barrier between pure and applied is very vague these days at least 3 times in this thread. morphism, "very unhealthy" is a lot kinder than what I'm thinking.

I am not ignoring them but that their reasons aren't good enough to convert me or is irrelevant. What is pure and applied is indeeded blurred but I have already mentioned that by pure maths I was always thinking of the pure maths that is not part of applied. By applied I am thinking of the more traditional applied subjects not for example QG.

THe thread was always about the average and in general.

 

[Gib Z]

And this whole discussion would have been settled much quicker if you looked at maths like I said in Post 16. Then you would realize there are many fields that are both pure and applied, so it makes little sense to say which in harder in those situations. And I would not have placed Quantum Gravity as a mathematics topic, unless theoretical physics and maths is all the same to you.