Math professors thoughts on pure vs applied

[1MileCrash]

Paraphrased something like (this is an early proof based class)

"I hear engineering majors and physics majors say that they like math as long as it can applied to something. So these folks won't take any upper level pure mathematics courses. It's useless.

Is it? Did you know that (something about matricies) was once pure mathematics? Then one day, wow this does work nicely for (something in physics.)

Mathematicians working on pure mathematics that 'can't be applied' are really just finding new things that are true, and if they are true, why can't they be applied? We just haven't found out how yet!

How many times in history do you think physicists have looked for a mathematical way to explain some phenomenon, only to find that a perfect description was already there, tucked away in the land of pure mathematics?

I'm not saying any inconcievable math can be applied to physics or whathaveyou. I'm saying that for an engineer to disregard pure mathematics because it cannot be applied is foolish. Studying pure mathematics is just staying ahead of the game."

 

[DoggerDan]

If you have the time and money... Or room in your electives bin.

Getting through engineering in four years is tough enough. As it's an engineer's job to apply mathematics to solve real-world problems, it doesn't make much sense to pile on theoretical courses.

I knew some engineers who really liked math and took a few extra courses as electives.

 

[Pythagorean]

Much advanced science and requires significant programming skills. Abstract mathematics can contribute a lot to program design when handling all the ways you gather, calculate, store, and visualize data.

 

[Ivan92]

That is why I want to learn pure math. When I had my advising session, I told her about minoring in math and I was hoping I would take pure math classes, but no she's like "Yea, that would help if you did some applied math courses." bleh

 

[micromass]

That is why I want to learn pure math. When I had my advising session, I told her about minoring in math and I was hoping I would take pure math classes, but no she's like "Yea, that would help if you did some applied math courses." bleh

Aand uuuh, why do you listen to your "advisor"? Just take those pure math classes, you'll enjoy them!


To the OP: many people say that pure math is useless and non-applied, but it's far from the truth. I would even dare to say that all undergraduate math classes are applicable to the real world in some way.

Some math topics (Galois theory,number theory,...) were invented for pure mathematics sake. But most topics (functional analysis, linear algebra, differential geometry,...) were invented because applied people needed it.

 

[phoenix:\\]

I like abstract mathematics, even though they don't necessarily apply to my field of study right now, the topics help me think in a number of different ways. Who knows, the abstract has a high likely-hood of becoming applied with the advancement of society like people have mentioned previously.

 

[DoggerDan]

...undergraduate math classes are applicable to the real world in some way.

I like abstract mathematics, even though they don't necessarily apply to my field of study right now, the topics help me think in a number of different ways. Who knows, the abstract has a high likely-hood of becoming applied with the advancement of society like people have mentioned previously.

I've used very little of higher mathematics in my career. That's not to say it was all bad. It's just that as an engineer, we get a broad spectrum, and wind up specializing in whatever mathematics, if any, are needed for our particular fields.

The problem is, we don't know what we'll need. Hindsight says I should have had a better idea of my eventual career field, and that should have determined what I studied.

I wish I'd studied a lot more of what I needed on the job. Much of what I studied was useless.

 

[Jack21222]

For me, it's not that pure math can't have any application to the real world. It's just that it is often taught with no connection to the real world, and that makes it FAR more difficult for me to learn. The endless march of of "Axiom, definition, lemma, lemma, proof, corollary" makes me lose interest rapidly. I am a visual thinker, and if I can't visualize something in my head, I struggle more than I otherwise would.

That's why I like learning math from physics professors. I love to read "a rigorous proof of this is outside the scope of this book." I see math as a tool. I really don't care how my tools are made, just teach me how to use them.

 

[1MileCrash]

For me, it's not that pure math can't have any application to the real world. It's just that it is often taught with no connection to the real world, and that makes it FAR more difficult for me to learn. The endless march of of "Axiom, definition, lemma, lemma, proof, corollary" makes me lose interest rapidly. I am a visual thinker, and if I can't visualize something in my head, I struggle more than I otherwise would.

That's why I like learning math from physics professors. I love to read "a rigorous proof of this is outside the scope of this book." I see math as a tool. I really don't care how my tools are made, just teach me how to use them.

The fact that mathematics is so fitting to describe the physics world doesn't make you the least bit curious about how and why it works?

 

[Jack21222]

The fact that mathematics is so fitting to describe the physics world doesn't make you the least bit curious about how and why it works?

Nope.

 

[Pythagorean]

The fact that mathematics is so fitting to describe the physics world doesn't make you the least bit curious about how and why it works?

That's kind of a misnomer. The only reason it's so "fitting" is because math is logical clay; you can shape any function from mathematics to match the behavior you're observing. It's not inherently descriptive, humans append meaning to mathematics just like they do with other natural languages.

 

[DrummingAtom]

For me, it's not that pure math can't have any application to the real world. It's just that it is often taught with no connection to the real world, and that makes it FAR more difficult for me to learn. The endless march of of "Axiom, definition, lemma, lemma, proof, corollary" makes me lose interest rapidly. I am a visual thinker, and if I can't visualize something in my head, I struggle more than I otherwise would.

This is exactly how I feel.

I was blown away by calculus the first time I learned it because I felt like I finally found visual, dynamic math. Some math professors kind of annoy me in how they teach because it's not how I would approach it. For instance, I'm currently taking linear algebra and it drives me nuts that the professor literally never relates anything to a visual representation. I know we can't draw in R⁴ but we can easily draw things in R² to grab an intuition about what is going on. Most math professors seem to have endless stream of abstract thought that I just can't keep up with. I definitely learn math easier from a physics professor but that's just because it's more of my style.

 

[mathsciguy]

Maybe it's just me, but I don't think I'd start studying physics if I classify mathematics as applied or pure, I like both, actually I lean more towards pure. My view towards mathematics is just the same as every sciences, if it's interesting, it's worth learning weather it's pure or applied. I'm not a professor though.

 

[LaurieAG]

Maybe it's just me, but I don't think I'd start studying physics if I classify mathematics as applied or pure, I like both, actually I lean more towards pure. My view towards mathematics is just the same as every sciences, if it's interesting, it's worth learning weather it's pure or applied.

I'd have to agree as I've studied both pure calculus and (applied) technical calculus.

It's financial maths that gives me a headache though mainly because finance and financial systems are man made not natural systems.

Whenever I come across anything that smacks of financial maths in any maths/physics I wonder if something is wrong in the application of the pure maths itself.

 

[deRham]

That's why I like learning math from physics professors. I love to read "a rigorous proof of this is outside the scope of this book." I see math as a tool. I really don't care how my tools are made, just teach me how to use them.

I'm not sure this will always work, though. If you want to really understand physics, I'm pretty sure you'll find yourself poking a bit deeper into how the mathematics behind what you're studying works, because ultimately, the mathematicians who developed it were probably not completely unaware of physics when they sought out the proofs. In practice, this doesn't mean you have to know every last proof of course.

The only reason it's so "fitting" is because math is logical clay; you can shape any function from mathematics to match the behavior you're observing.

This means that how it was shaped to achieve such an end can have deep meaning.

 

[deRham]

humans append meaning to mathematics just like they do with other natural languages.

There are varying perspectives on this - I think the mathematics actually includes the meaning, and that mathematics is not quite just a language together with logical syntax.

 

[Jack21222]

If you want to really understand physics...

NOBODY really understands physics at the levels you're talking about, especially not those that use the more abstract math.

 

[ych22]

As an engineering major, I prefer the mathematics of applied topics such as algorithms, mathematical optimization and statistics to analysis, probability and algebra.

That said...the latter group was pretty helpful to my learning as much as they were damaging to my GPA (B- to B+ usually)

 

[Tosh5457]

Knowing mathematics is staying ahead of the game, totally agree...

Only knowing the "necessary" mathematics for physics is comparable to, for example, only knowing specific cases of electromagnetism theory to make a circuit. You'll be able to make it, but you'll never be able to make more complex circuits and you'll never know exactly how and why it works. That's superficial knowledge.

I regret going to physics instead of mathematics, I'm tired of physics professors putting those ambiguous integrals (whether it's indefinite, definite, line integral, surface integral, it's just like it means the same to them) and those deductions in thermodynamics that a mathematician would consider completely wrong...

 

[quantum13]

As an engineering major, I prefer the mathematics of applied topics such as algorithms, mathematical optimization and statistics to analysis, probability and algebra.

That said...the latter group was pretty helpful to my learning as much as they were damaging to my GPA (B- to B+ usually)

these are all interesting topics and i would personally like to learn about all of them. unfortunately if ur not a genius then it will take you a lot of time to study these topics and if you think you can just pile them on top of a typical engineering workload... try it for a semester and you will realize you never want to do it again

 

[DrummingAtom]

I regret going to physics instead of mathematics, I'm tired of physics professors putting those ambiguous integrals (whether it's indefinite, definite, line integral, surface integral, it's just like it means the same to them) and those deductions in thermodynamics that a mathematician would consider completely wrong...

Can you expand on this? I've heard things like this and still haven't completely figured out what the heck it means. Just today my physics professor was going through an integral and said something like "I know I would be upsetting the math professors by using the differentials like this but it still works." All he did was separate the variables and integrate..

 

[Jack21222]

Only knowing the "necessary" mathematics for physics is comparable to, for example, only knowing specific cases of electromagnetism theory to make a circuit. You'll be able to make it, but you'll never be able to make more complex circuits and you'll never know exactly how and why it works. That's superficial knowledge.

Your analogy is nonsensical. Electrical engineering and E&M are two different subjects. One can know how to make as complex of a circuit as is made without knowing the finer details of E&M.

Next think you'll tell me is that without knowing the finer points of thermodynamics, mechanics only have a "superficial knowledge" of the internal combustion engine.

 

[Bourbaki1123]

The fact that mathematics is so fitting to describe the physics world doesn't make you the least bit curious about how and why it works?

I'm not certain that learning pure mathematics answers the question of why it works. You'll understand how the conclusions are drawn and develop a feel for the logic and art of deriving proofs and constructing theoretical frameworks, but this doesn't really touch on the http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html"

I think that there is quite a bit to be said about the role of evolution, neurobiology and cognitive science (plus the logic of statistical inference) in really understanding why mathematics allows us to organize all of the data in meaningful ways that gives us the nice predictive frameworks we expect from the sciences.

That said, I'm a bit of a logic junkie and I really enjoy thinking about mathematical logic as well as the less formal reasoning/intuition that goes into coming up with deep and beautiful proofs. I just don't know if that side of things is really sufficient for getting at the why of mathematics' effectiveness.

 

[clope023]

Only knowing the "necessary" mathematics for physics is comparable to, for example, only knowing specific cases of electromagnetism theory to make a circuit. You'll be able to make it, but you'll never be able to make more complex circuits and you'll never know exactly how and why it works. That's superficial knowledge.

Not true, many electrical engineers don't know that much about E&M but are masters at building circuits. I can build pretty complex circuits and filters and the stuff I do goes over the head of most of my physics/math double major friends who know more E&M than I do.

Knowledge of magnetostatics and magnetodynamics are very useful in building transformers, motors, and generators,but even then the finer details of actually building the damn thing is quite separate from the theory.
Also can you use your knowledge of electrodynamics to build analog digital converters, digital analog converters, schmitt triggers, high/low/bandpass/allpass filters, and weinbridge oscillators? I doubt it.

 

[deRham]

NOBODY really understands physics at the levels you're talking about, especially not those that use the more abstract math.

I didn't realize we still all have to preface these things with "as much as we can" ... of course nobody understands anything really in some sense of the word, but my point was there are pretty clear reasons to also understand some of the math.

I didn't say you have to use super abstract math, either - just not ignore the workings behind the math entirely.