Is there a hierarchy between pure and applied mathematics?

[morphism]

This thread should be locked.

 

[J77]

This thread should be locked.

Yeah -- these pure vs applied discussions can get messy...

 

[mathwonk]

to paraphrase a teacher friend of mine at the start of school year, the problem is letting all these people post their opinions on here.

 

[animalcroc]

People should not be bashed for asking certain things even if one finds them silly. The last thing we need is enforced uniformity and if that was the case there would have never been progress in world. There are ways to disagree without unprovoked insults or rudeness.

 

[pivoxa15]

One clear reason for me why I think pure maths is superior (to put it succinently and bluntely) to applied maths is the concentration one must exert when doing pure maths sometimes to the extent of headache. However with applied maths, it's sometimes just a 'trick' one needs to use or just trying different things. So there is much more an element of deep thinking in pure maths. A lot of it is obviously to do with the fact that pure maths is much more abstract.

Thinking things from the barest of fundamentals is also attractive and gives the feeling of superiority to me.

However that said, there are plenty of long standing unsolved applied problems. What does it take to solve them?

 

[Gib Z]

animalcroc, pivoxa15 asked us if we think "pure" is superior to "applied". If we voted no/equal, he asked why. We told him why, then he ignores that and continues as if we didnt make a decent point. look through the entire thread and just see how he does this. His last post just gave us an example of how he still thinks pure vs applied. We've told him its hard to differentiate between them anymore, a lot of pure mathematics can be applied in some way. Both complex analysists and computer scientists would like to see the Riemann hypothesis dis/proven, is the Riemann Hypothesis now in "applied maths"? To date no 'trick' has solved it.

pivoxa15 is a mathematical supremist, who a) thinks mathematicians are superior to any other scientists and b) "pure" mathematicians are better than the rest.

Considering this forum has many people who are primarily interested in biology, chemistry, etc etc, I recommend he finds a "pure" mathematics only forum, I'm sure he would like that.

 

[yasiru89]

Can't say I'm entirely free of sin either then Gib Z, I for one am positive on both counts, though with regard to other scientists I shall exclude psychologists and, if so categorised, philosophers;
just as well though, since the distinction I've forwarded has been largely ignored as well. Perhaps I need to apologise for not being politically correct but honesty has had its moments!

 

[ice109]

animalcroc, pivoxa15 asked us if we think "pure" is superior to "applied". If we voted no/equal, he asked why. We told him why, then he ignores that and continues as if we didnt make a decent point. look through the entire thread and just see how he does this. His last post just gave us an example of how he still thinks pure vs applied. We've told him its hard to differentiate between them anymore, a lot of pure mathematics can be applied in some way. Both complex analysists and computer scientists would like to see the Riemann hypothesis dis/proven, is the Riemann Hypothesis now in "applied maths"? To date no 'trick' has solved it.

pivoxa15 is a mathematical supremist, who a) thinks mathematicians are superior to any other scientists and b) "pure" mathematicians are better than the rest.

Considering this forum has many people who are primarily interested in biology, chemistry, etc etc, I recommend he finds a "pure" mathematics only forum, I'm sure he would like that.

pivoxa is a ______ . many things go there. i choose dummy.

 

[Holocene]

Okay, I am a total newbie here, just finishing up a study of algebra 1.

I have a question:

What exactly is the primary difference between pure math and applied math?

I take it that "applied" math means using mathematics as a means to define or understand aspects of the physical world, while pure math is strictly a study of mathematics in and of itself?

...if that makes any sense?

 

[HallsofIvy]

In recent years, it has become fashionable to divide mathematics into three general areas- "pure" mathematics, "applied" mathematics, and "applicable" mathematics.
"Pure" mathematics is mathematics that is done for the sake of the mathematics itself- it does not depend upon whether or not that mathematics can, at some later time, be applied to a non-mathematical problem. "Applied" mathematics refers to applying mathematics to some non-mathematical problem. "Applicable mathematics" refers to mathematics that does involve non-mathematical applications but is being done specifically to give techniques that can, immediately, be applied to non-mathematcal applications.

Notice that I am saying that whether or not a mathematical theory can, at some future day, can be applied to some non-mathematical problem does not affect it being "pure" mathematics. Also, notice my reference to "non-mathematical" applications. In Norbert Wiener's classic "The Fourier Transform and Certain of its Applications" the "applications" are only to mathematics.

Finally, I must say that pivoxa15's statement,

One clear reason for me why I think pure maths is superior (to put it succinently and bluntely) to applied maths is the concentration one must exert when doing pure maths sometimes to the extent of headache. However with applied maths, it's sometimes just a 'trick' one needs to use or just trying different things. So there is much more an element of deep thinking in pure maths.

is just silly. That is not a "clear reason", it is a meaningless reason. It says that "pure" mathematics is superior to "applied" mathematics because some problems in pure mathematics are hard and some problems in applied mathematics are easy! Some problems in pure mathematics are very easy and some problems in applied mathematics are very difficult. I rather suspect that the "multi-body" problem requires as deep thinking as any "pure" mathematics problem.

 

[lfallo1]

LOL @ saying it doesn't matter... I wasn't ALLOWED to take "Applied Math" with a COSC minor at Towson. So i ended up taking a tougher workload, and graduating with a Pure Mathematics degree + the COSC minor. The Pure Math major was identical (aside from 3 classes... my 3 extra classes being monsters). Either way, it really isn't paying off after a few months of applying for jobs b/c most places have a fetish for the word "applied."

Alot of places also seem to think the "pure" guys are too abstract.

It sucks for me, but IMHO i'd say applied is the better way to go, unless you plan on getting your MS or PHD.

 

[lfallo1]

I find Applied Mathematics way harder than Pure Mathematics!

Hilarious. At most colleges, the difference is but 2 or 3 classes at most... And the Pure classe at THE VERY LEAST cancel themselves out.

In my experience, the classes at my college (that Applied didn't have take) were Real Analysis, Algebreic Structures, and Applied Combinatorics... If someone finds proving the backbone of math easier than taking Stat II & Math Models, then more power to 'em. But FWIW, NO ONE wanted to take Pure Math over Applied (frankly, neither did i but i got screwed due to Towson).

But like i said, companies love the word "Applied." So take the easy route, and go "Applied."

 

[Diffy]

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.

Maybe this is just me, but, your post almost has an elitist tone to it.