Math Elitists: A Controversial Opinion

[xdrgnh]

So what do you guys think about those math elitist that think that all math that is taught should be very rigorous and contains a lot of proofs in them. They usually I notice look down a lot on those who don't use math rigorous and use proofs like engineering and sometimes physicist. Personally I can't stand them at all they give math a bad name to whoever they encounter. Just to clarify most mathematicians I've met were wonderful people and were very humble and respectful of all uses of math. I'm just talking about a small amount of them.

 

[berkeman]

So what do you guys think about those math elitist that think that all math that is taught should be very rigorous and contains a lot of proofs in them. They usually I notice look down a lot on those who don't use math rigorous and use proofs like engineering and sometimes physicist. Personally I can't stand them at all they give math a bad name to whoever they encounter. Just to clarify most mathematicians I've met were wonderful people and were very humble and respectful of all uses of math. I'm just talking about a small amount of them.

You seem to be painting with a broad and sloppy brush. Can you give a few concrete examples with associated contexts so that we can try to comment appropriately?

 

[xdrgnh]

Yes just look in the "Should Calculus be taught in High School" thread, a lot of the people there are in favor of it not being taught in high school because it's not rigourous enough. Even AP calculus isn't good enough for them and should not be given college credit. Other examples is this time when I was talking to someone trying to get there PHD in math. I told him about the math I took which is calc, multi and linear algebra and that I wanted to be a physicist. He then asked me if we did a lot of proofs in my classes and he said that I don't really know math and that physics plus engineering butcher math by making it less proof based. Even more extreme examples I see is that some believe that all math from high school should be taught using mostly proofs, sort of how the way new math worked in the 60s.

 

[DrummingAtom]

I try to learn what I can from a different outlook than my own. I think that's the best part of anything in life. Trying to view something through someone else's eyes is a wonderful process and usually very rewarding, at least for me. Honestly, I think it's odd that you feel so angered over a different viewpoint. Aren't you being just as guilty as them, in the elitist sense, of your own point of view?

 

[MissSilvy]

Who cares? Someone will always try to look down on you, no matter what the issue at hand is. Smile and keep kicking their butt at whatever it is they're trying to judge you for. I never got why some people would just try to pick fights out of thin air with an ideology of all things.

 

[xdrgnh]

I try to learn what I can from a different outlook than my own. I think that's the best part of anything in life. Trying to view something through someone else's eyes is a wonderful process and usually very rewarding, at least for me. Honestly, I think it's odd that you feel so angered over a different viewpoint. Aren't you being just as guilty as them, in the elitist sense, of your own point of view?

They are entitled to there view point, the problem is that they try to force there view point on people that don't want it or need it. It's sort of like how in small town communities they aren't allowed to teach the big bang because small churches get there noses into the science education. There's nothing wrong with rigorous math and I'd like if it was taught more often but forcing everyone to take it and thinking that calculus shouldn't be taught in high school is very radical.

 

[berkeman]

They are entitled to there view point, the problem is that they try to force there view point on people that don't want it or need it. It's sort of like how in small town communities they aren't allowed to teach the big bang because small churches get there noses into the science education. There's nothing wrong with rigorous math and I'd like if it was taught more often but forcing everyone to take it and thinking that calculus shouldn't be taught in high school is very radical.

Small but important point. "there" --> "their"

Why is this English Nazi reminder important? Not paying attention in school comes back at you later in your professional life...

 

[xdrgnh]

Small but important point. "there" --> "their"

Why is this English Nazi reminder important? Not paying attention in school comes back at you later in your professional life...

I admit my Grammar sucks and if I encounter people in life that judge me on Grammar it won't be a good day. However I plan to just deal with it, no matter what those nazi's says it still won't impact the magnum opus of my academic training which will hopefully be physics.

 

[berkeman]

I admit my Grammar sucks and if I encounter people in life that judge me on Grammar it won't be a good day. However I plan to just deal with it, no matter what those nazi's says it still won't impact the magnum opus of my academic training which will hopefully be physics.

Unless you are an incredible savant in physics (or whatever), you will be judged on everything that you submit. So if you make that grammatical error on your resume to me when you apply for a job, I won't bother to interview you. So please pay attention and work on every aspect of your academic and professional presentation. And encourage others to do the same.

 

[xdrgnh]

Unless you are an incredible savant in physics (or whatever), you will be judged on everything that you submit. So if you make that grammatical error on your resume to me when you apply for a job, I won't bother to interview you. So please pay attention and work on every aspect of your academic and professional presentation. And encourage others to do the same.

If I am submitting a paper that's why I get people to proof read it most authors have people proof read there stuff. Not everyone learned grammar in school sadly I was one of them, but that hasn't stopped my doing well in College level and AP English classes I just proof read my stuff a lot. Thanks a lot for the advice.

 

[Fredrik]

I admit my Grammar sucks and if I encounter people in life that judge me on Grammar it won't be a good day. However I plan to just deal with it, no matter what those nazi's says...

It's actually "nazis", not "nazi's".

 

[Intervenient]

I think the problem isn't math elitists, but more the attitude that some have that NO ONE can succeed at math but them and their associates. College Confidential had a thread a while back about math majors where every several of them took graduate level math problems and gave them to the girl in question asking if she should major in math. They came to the conclusion that only they were able to hold the burden of being a math major, and because the girl couldn't do it with only AP Calc credit, she should stay away forever.

So yes, there is math elitism, but given the complexity of the subject, there's always a little room for gloating. But when you intentionally try to discourage someone who hasn't been exposed to upper level math and use that as a gate to prevent them from even trying, then you're just kinda being a douche.

 

[Bourbaki1123]

I think the problem isn't math elitists, but more the attitude that some have that NO ONE can succeed at math but them and their associates. College Confidential had a thread a while back about math majors where every several of them took graduate level math problems and gave them to the girl in question asking if she should major in math. They came to the conclusion that only they were able to hold the burden of being a math major, and because the girl couldn't do it with only AP Calc credit, she should stay away forever.

So yes, there is math elitism, but given the complexity of the subject, there's always a little room for gloating. But when you intentionally try to discourage someone who hasn't been exposed to upper level math and use that as a gate to prevent them from even trying, then you're just kinda being a douche.

Yes, I've actually seen that thread. It was absolute nonsense.

Anyway, here is my take: Mathematics is built from proofs, even if the proofs now are set theoretic, proofs in Euler or Gauss's day (not really much overlap of those lifetimes, but still) required a fairly rigorous chain of clever insights.

Physics is applied mathematics, you use mathematical tools (derived by mathematicians, or by scientists who derived new math, who I still consider mathematicians) to build mathematical frameworks to describe and reason about complex phenomena. Comparing mathematics and physics is, IMO, comparing apples to oranges. The best physicists and the best mathematicians are all brilliant, and they do different things.

If you aren't doing proofs, you aren't doing mathematics. If you're doing proofs, you might still be doing physics, depending on your point of view. Personally, I consider Witten to be primarily a mathematician with motivations in physics, because he works (does proofs in) with the mathematics that undergirds physical theory.

Now, I don't think that mathematics with full blown rigorous proofs is necessary for an engineer or an experimental scientist, or maybe even a lot of more theoretical scientists (of that I'm not entirely sure either way); definitely not at the undergraduate level. Why? Because it is often irrelevant to their field. Creating powerful innovations that improve the world is a team effort, and if everyone was sitting around doing proofs, we would still be in a stone age society, if that. Conversely, if we didn't have people doing complicated math, we would still be in the middle ages, with no understanding of navigation or electricity or any complex phenomena.

 

[Ryker]

Even AP calculus isn't good enough for them and should not be given college credit.

Huh, what does being in favour of separating high school and post-secondary education have to do with math nazis? If you think people telling you AP Calculus shouldn't be given college credit are math nazis, then you're the one having issues, not them. You probably wouldn't be in favour of giving out 5 ten-dollar bills for a single twenty-dollar one either, now would you?

 

[Functor97]

Without mathematical rigour there is no reason to accept any physical tautology. This is not a problem for an engineer as their goal is to develop new mechanisms for societies function. The problem is for physicists who use mathematics in a "hand waving" manner, claiming that because they get the answer that agrees with experimentation it must be correct.

 

[Functor97]

If you aren't doing proofs, you aren't doing mathematics. If you're doing proofs, you might still be doing physics, depending on your point of view. Personally, I consider Witten to be primarily a mathematician with motivations in physics, because he works (does proofs in) with the mathematics that undergirds physical theory.

That is not quite true. Witten's work has not focused upon proofs, but rather hints or clues about certain methods used in string theory which may be applied to more mathematical problems. Witten did prove the positive mass conjecture (in a simpiler manner to Yau) but most of his work has lacked the rigour which is the staple of pure mathematics. This does not mean that he lacks mathematical ability, he has that in spades, but this ability manifests itself in a form suitable for mathematical and theoretical physics. You are right though to say that he is more a mathematical physicist, than a straight out "physicist".

 

[Bourbaki1123]

That is not quite true. Witten's work has not focused upon proofs, but rather hints or clues about certain methods used in string theory which may be applied to more mathematical problems. Witten did prove the positive mass conjecture (in a simpiler manner to Yau) but most of his work has lacked the rigour which is the staple of pure mathematics. This does not mean that he lacks mathematical ability, he has that in spades, but this ability manifests itself in a form suitable for mathematical and theoretical physics. You are right though to say that he is more a mathematical physicist, than a straight out "physicist".

He does have a fields medal, I'm pretty sure it was awarded largely because of http://intlpress.com/JDG/archive/1982/17-4-661.pdf" . I think that qualifies him as both a mathematician and a physicist.

ETA: For someone like Witten, it's really just a matter of semantics I suppose.

 

[Functor97]

He does have a fields medal, I'm pretty sure it was awarded largely because of http://intlpress.com/JDG/archive/1982/17-4-661.pdf" . I think that qualifies him as both a mathematician and a physicist.

ETA: For someone like Witten, it's really just a matter of semantics I suppose.

I do not deny Witten is a mathematician, he certainly has skills which surpass mathematicians who work primarily in "purer fields" of mathematics. What i objected to was your claim that
"if you are not doing proofs, you are not doing mathematics". Witten's paper on supersymmetry did not contain what many mathematicians would consider as proofs. Witten is an applied mathematician, that does not mean he lacks the skill for pure mathematics, rather he has a different perspective and agenda. The fields medal may be given to any mathematician, whether he works in pure or applied mathematics. It is Witten's mathematical intuition which is so valued rather than his proof construction (once more not implying he lacks this ability in the least) I suggest you rescind the claim that a mathematician must be working on proofs to qualify for his title.

 

[jambaugh]

In response to the OP I would say, Don't confuse being able to use mathematics with being able to DO mathematics. Being able to use a cell phone well is not the same as being good at electronics.

Pure mathematics is that "Nazi" proof business. Mathematics is the study of logical implication, from axioms and definitions to theorems. Now given the large body of mathematics already accomplished by those "elitist" exemplars of rigor, we now have a very nice and large tool box for calculating and confirming solutions to many problems. Yes it is not necessary to know how to prove e.g. l'Hospital's rule in order to use it but...

And as a matter of opinion, I think:
--> Every driver should know the basics of how his engine works;
--> Every appliance user should know the basics of how household electricity behaves (e.g. so as not to dry their hair in the tub), and
--> every user of mathematical formulas should have some understanding of the axiomatic context, logic and rigor which goes into them (so again they don't "dry their hair in the tub" so to speak.)

 

[Bourbaki1123]

I do not deny Witten is a mathematician, he certainly has skills which surpass mathematicians who work primarily in "purer fields" of mathematics. What i objected to was your claim that
"if you are not doing proofs, you are not doing mathematics". Witten's paper on supersymmetry did not contain what many mathematicians would consider as proofs. Witten is an applied mathematician, that does not mean he lacks the skill for pure mathematics, rather he has a different perspective and agenda. The fields medal may be given to any mathematician, whether he works in pure or applied mathematics. It is Witten's mathematical intuition which is so valued rather than his proof construction (once more not implying he lacks this ability in the least) I suggest you rescind the claim that a mathematician must be working on proofs to qualify for his title.

Rescinded.

 

[chiro]

So what do you guys think about those math elitist that think that all math that is taught should be very rigorous and contains a lot of proofs in them. They usually I notice look down a lot on those who don't use math rigorous and use proofs like engineering and sometimes physicist. Personally I can't stand them at all they give math a bad name to whoever they encounter. Just to clarify most mathematicians I've met were wonderful people and were very humble and respectful of all uses of math. I'm just talking about a small amount of them.

Different people have different reasons for using math and therefore have a different idea and focus on what should be.

As long as say an engineer knows that the differential or integral calculus is correct with infinitesimals, then learning the absolute rigorous formulation of calculus is probably overkill: they have tonnes of other work to focus on and learning rigorous analysis is probably not going to help much with their perspective which is using math to solve other problems and I don't blame them. For those that do end up wanting to learn the formalities, then I think its good but I don't think that they are any lesser applied scientists/human beings than mathematicians.

Also one thing that people should realize is that mathematics is a man-made creation, even if the inspiration for that comes from studying the physical world in some form. Each new addition of mathematics has motivation behind it, and its important to realize that behind all the symbols, there was an idea which had some level of intuition that was born out of some creative differential from previous formulations. As time goes by, this becomes more organized and more refined and sometimes the intuition behind the rigor is lost on new students trying to understand something for the first time.

As far as elitism goes, I think its a little sad. Granted in the courses I am doing now I can say that the pure math courses are a lot harder than the applied statistics courses, but none the less both of those serve two completely distinct purposes. If people want to maintain an elitist attitude, then let them. If they ever get outside of their comfort zone or ivory tower they will realize the rest of the world and the fact that the world is full of extremely bright, hard working, and humble people who may not be able to prove analysis theorems, but build bridges, start businesses, make people laugh, and a wide variety of things that they do better than mathematicians do.

 

[Dale]

If I am submitting a paper that's why I get people to proof read it most authors have people proof read there stuff.

Here you again mean "their". "Their" indicates ownership, "there" indicates location. You have made this same mistake multiple times even after being corrected.

berkeman is correct, professionally your ability to communicate clearly will be much more important than your ability to do math or physics, even if you have a physics or engineering job. Also, while it is reasonable to rely on proofreaders for scientific manuscripts, you are unlikely to be able to do so for e-mails, presentations, and project reports.

If you are still going to school then I would recommend taking some communication classes and particularly some writing classes. You shouldn't need someone else to tell you the difference between "their" and "there" nor the difference between "Nazis" and "Nazi's".

 

[micromass]

Simply put, mathematics without proofs is not mathematics. And I feel that high school students should already be confronted to proofs early on. It will only enhance their understanding.

In Belgium, all physics majors and all engineering majors are required to do proofs. For example, physicists are required to take Analysis, Linear algebra and abstract algebra with proofs. And engineers have to take Analysis and Linear algebra with proofs. I think this is a good thing.

Being a math nazi isn't necessarily a bad thing. If you get to confront people with the limits of their understanding and if you get to get people thinking about how professional mathematicians do things, then this could only enhance your learning experience.

I've seen physics in high school, but I have no problem if a physicist comes a long and says that it wasn't real physics, because it wasn't real physics. I might get encourages and begin studying what real physics is all about. In the same manner, I don't think anybody should have a problem if I say that mathematics without proofs isn't mathematics. Because it isn't.

 

[Kindayr]

Simply put, mathematics without proofs is not mathematics. And I feel that high school students should already be confronted to proofs early on. It will only enhance their understanding.

In Belgium, all physics majors and all engineering majors are required to do proofs. For example, physicists are required to take Analysis, Linear algebra and abstract algebra with proofs. And engineers have to take Analysis and Linear algebra with proofs. I think this is a good thing.

Being a math nazi isn't necessarily a bad thing. If you get to confront people with the limits of their understanding and if you get to get people thinking about how professional mathematicians do things, then this could only enhance your learning experience.

I've seen physics in high school, but I have no problem if a physicist comes a long and says that it wasn't real physics, because it wasn't real physics. I might get encourages and begin studying what real physics is all about. In the same manner, I don't think anybody should have a problem if I say that mathematics without proofs isn't mathematics. Because it isn't.

QFT.

Would you attack chemists who claim that high school chemistry that teaches only the Bohr-Rutherford model isn't really chemistry? A lot of the discussion in the "Calculus" thread is about how accessible a lot of the content in calculus and pure mathematics actually is, if its just taught in a certain way. It isn't impossible to introduce relatively rigourous content to younger minds.

 

[micromass]

QFT.

Would you attack chemists who claim that high school chemistry that teaches only the Bohr-Rutherford model isn't really chemistry?

Well, it isn't really chemistry. But I don't want to attack anybody.

A lot of the discussion in the "Calculus" thread is about how accessible a lot of the content in calculus and pure mathematics actually is, if its just taught in a certain way. It isn't impossible to introduce relatively rigourous content to younger minds.

Indeed, in my country they already work with epsilon-delta's in high school. It can only enhance the understanding in my opinion.

 

[Kindayr]

Well, it isn't really chemistry. But I don't want to attack anybody.

Oh sorry, my point was to the OP. I believe a chemist has every right to say that high school chemistry isn't real chemistry, because it isn't. So I would expect a mathematician to share that right and be able to claim that high school math just isn't real math without receiving criticism.

I hope that clears everything up.

Indeed, in my country they already work with epsilon-delta's in high school. It can only enhance the understanding in my opinion.

I think that's amazing. It shouldn't be that in university calculus that we have to learn epsilon-delta proofs in an accelerated environment to get onto content that fundamentally relies on it! Especially when those concepts are accessible to younger minds and can be taugh earlier in a student's life.

 

[thegreenlaser]

I think the sentiment that high school calculus is not at the level of rigor required for university mathematics is being misinterpreted by the OP. To say that AP Calculus should not be counted for university credit has nothing to do with math elitism, it's simply a statement that it is not nearly as rigorous as a university calc sequence. I know of two people who say they really regretted opting out of Calc 1 because they took AP calculus and were allowed to do so. To say that AP calculus shouldn't count as a university course is no more elitist than saying that someone who hasn't learned how to drive properly should not be given their license. It's simply a question of whether or not someone has learned what they need to learn to move onto the next level. That *can* be the same as elitism, which would say that because you haven't learned math to the level I have, you're obviously much inferior to me, but in most cases it isn't.

That said, there are always elitists in every subject, and they'll trivialize your work to make themselves feel superior (first year engineering students at my school are BAD for that). I'm not denying that they exist, but you have to be careful to differentiate between people who are simply being realistic about what level of education you've reached in a certain subject area and people who are trying to put you down to make themselves feel smart.

 

[vela]

I admit my Grammar sucks and if I encounter people in life that judge me on Grammar it won't be a good day. However I plan to just deal with it, no matter what those nazi's says it still won't impact the magnum opus of my academic training which will hopefully be physics.

I think you may be underestimating how many people will judge you on your grammar. Most people probably won't say anything to you, but they will form an opinion of you based in part on what they read. If your writing is riddled with grammatical errors, you will be seen as being either careless or ignorant, which is not exactly the impression you want to give others.

 

[Dembadon]

I think you may be underestimating how many people will judge you on your grammar. Most people probably won't say anything to you, but they will form an opinion of you based in part on what they read. If your writing is riddled with grammatical errors, you will be seen as being either careless or ignorant, which is not exactly the impression you want to give others.

Well put!

 

[WannabeNewton]

I enjoy there being those individuals who push for the rigor in mathematics; elitist or not I find that having others who have a grand knowledge of a mathematical subject provides motivation to TRY and achieve the same. In fact, it was only after seeing many of micromass's posts on this site regarding proofs in analysis, topology, and differential geometry that I was motivated to go beyond the level of rigor provided in physics texts that utilize the aforementioned subjects. When someone, like micromass, can present material in such a rigorous manner it just makes you want to be able to do the same (and it allows for more intelligent/precise conversations) and since we are on the subject of academics I don't see anything wrong with this =D. Cheers!

 

[deRham]

There's nothing wrong with rigorous math and I'd like if it was taught more often but forcing everyone to take it and thinking that calculus shouldn't be taught in high school is very radical.

Yes, as a math person, I agree with you. I think people who place extreme emphasis on the rigor have it all wrong. You can appreciate the power of calculus a lot even with AP Calculus, because you can see how to analyze problems that are clearly linked to the calculus reasoning.

Throwing in an epsilon and delta here and there makes it more precise what you mean, but the intuition is the same, and is what will be used in the future anyway.

I don't think a lot of mathematics aspirants get that the big theorems in a subject are proved partially to confirm intuition, and partially to clarify it (i.e. make precise). Usually there is an idea that "Something like X is probably true..." but the big theorems make precise what exactly that is. Being able to regurgitate the details is not always important, although if you want to extend that field of research, you must be pretty well versed, at least usually.

Honestly, I think it's odd that you feel so angered over a different viewpoint. Aren't you being just as guilty as them, in the elitist sense, of your own point of view?

I think this is a bit like saying: "Hey, that guy is in favor of trashing my building because that space could be used in a better way. That opinion is as good as mine that I don't think the building should be trashed."

I don't think opinions really matter in and of themselves - after all, they are just opinions. It's the reasons for having them that matter. And when there is no reason and just elitism, that's plainly stupid and not befitting such a well-educated mind.

Why don't I tell you - well that was the opinion of the one who posted the original post, aren't you as guilty as he is? ;)

Not picking on this, just illustrating a point.

 

[920118]

That said, there are always elitists in every subject, and they'll trivialize your work to make themselves feel superior (first year engineering students at my school are BAD for that). I'm not denying that they exist, but you have to be careful to differentiate between people who are simply being realistic about what level of education you've reached in a certain subject area and people who are trying to put you down to make themselves feel smart.

And on what do you base this vilification? I find it very hard to believe that people treat your work unfairly to feel superior. It is more likely that they do so because they actually find it trivial. Your random assigning of subconscious motivational factors to people who "trivialize" the work of others is much more rude than that which they do.

 

[DrummingAtom]

In Belgium, all physics majors and all engineering majors are required to do proofs. For example, physicists are required to take Analysis, Linear algebra and abstract algebra with proofs. And engineers have to take Analysis and Linear algebra with proofs. I think this is a good thing.

I'm so envious. In my EE curriculum, I would be overwhelmed with trying to add a minor and finish in 4 years. I should move to Belgium.

 

[deRham]

I think the sentiment that high school calculus is not at the level of rigor required for university mathematics is being misinterpreted by the OP. To say that AP Calculus should not be counted for university credit has nothing to do with math elitism, it's simply a statement that it is not nearly as rigorous as a university calc sequence.

What does a university sequence offer in addition that is so clearly more rigorous?

 

[Tosh5457]

Mathematics is formal logic, therefore to assert something you must prove it. And mathematics apply to many fields, I wouldn't like something to be used on so many fields with no logic behind it. That doesn't mean doing proofs is the best way to learn mathematics, I think that just knowing what the proof uses, its general idea and why that concept was needed in the first place many times is enough to have a solid understanding of the concept.

 

[deRham]

Mathematics is formal logic, therefore to assert something you must prove it.

But formal logic is formal logic! Mathematics is conducted in the language of formal logic, sure.

Also, who said AP Calculus students don't make assertions and proofs? The question is how far you verify the details. You can go down to axiomatic set theory every time, but few do that.

Once you prove some theorems, actually a lot of proofs will not be far from what AP Calculus offers.

Now if you're in favor of forcing students to write in proper sentences, yes, if I taught AP Calculus ever, I'd do that. I would probably emphasize more details than is typical, but a clearly communicated explanation accounting for everything and acknowledging the assumptions is a proof!

 

[clope023]

Mathematics is formal logic, therefore to assert something you must prove it. And mathematics apply to many fields, I wouldn't like something to be used on so many fields with no logic behind it. That doesn't mean doing proofs is the best way to learn mathematics, I think that just knowing what the proof uses, its general idea and why that concept was needed in the first place many times is enough to have a solid understanding of the concept.

I study electrical engineering and the underlying concepts behind the math being used (usually calculus and differential equations) is not needed at all to do the engineering. Of course you would have to understand what a limit is, a derivative, and a differential equation is to understand the laplace transform and other such techniques like taking the maximums and minimums of functions but eventually it becomes second nature. I doubt most of my engineering classmates know many proofs but they can do the engineering because they have a minimum required understanding of the math so they can do the engineering, it's a trade off. I know some complex analysis, linear algebra, Fourier analysis, pde's, statistics and it's made the math in my engineering classes easier but I can't say it's helped my circuit designs.

 

[xdrgnh]

I enjoy there being those individuals who push for the rigor in mathematics; elitist or not I find that having others who have a grand knowledge of a mathematical subject provides motivation to TRY and achieve the same. In fact, it was only after seeing many of micromass's posts on this site regarding proofs in analysis, topology, and differential geometry that I was motivated to go beyond the level of rigor provided in physics texts that utilize the aforementioned subjects. When someone, like micromass, can present material in such a rigorous manner it just makes you want to be able to do the same (and it allows for more intelligent/precise conversations) and since we are on the subject of academics I don't see anything wrong with this =D. Cheers!

But that's the thing not everyone needs or wants rigor in their math. If you guys want to say that without lots of rigor and proofs math isn't math that is fine and you have a point. But for most people they use math as nothing but a tool. Rigorous math is very interesting and beautiful however to understand that beauty is very difficult and is something the individual has to be self motivated to do. Not all math students who sign up for a math class want that or need that. Forcing rigor into the class room is no different then forcing creationism in the classroom.

 

[deRham]

But that's the thing not everyone needs or wants rigor in their math.

I want to keep harping on this point - I agree with the spirit of what you're saying, but I want to also say that rigor is being misunderstood by many. The idea is to justify what you say.

That does NOT mean it has to be from the bare definitions. For instance, once you learn L'Hopital's rule, using it to show a limit is something or the other is perfectly valid.

The only difference is that some people want to give more details, and they are the ones who usually stand as "rigor-freaks" ... yet often they overestimate how much they are waving their hands, relative to someone who, say, does logic research.

I think rigor by my definition, namely being precise with what one means, is good. But giving "all" the details is often something implied by most people using the term, and that is what I find unnecessary.

 

[Vanadium 50]

Everyone is entitled to their opinion. It might convince more people if you gave new, cogent arguments, rather than just repeating inflammatory rhetoric.

 

[Tosh5457]

But formal logic is formal logic! Mathematics is conducted in the language of formal logic, sure.

Well, actually mathematics uses formal logic. Formal logic isn't a language.

But that's the thing not everyone needs or wants rigor in their math.

Sure, if you just want to apply maths you don't need to know the proofs or even what the proof uses. But then you won't know as much mathematics as the people who know how to relate the concepts (which is what proofs do), and knowing mathematics on that level can be really helpful even in applying mathematics.

 

[xdrgnh]

I'm not giving a rhetoric I'm giving facts, not everyone needs rigorous and proof based math, especially at the high school or freshmen college level. Forcing proof based math into the classroom is the same as forcing creationism. Of coarse it will probably never happen because this country prefers to dumb down the curriculum rather then make it more challenging which is if you ask me even worse then over emphasizing specialist concepts. By over emphasizing proofs time is taken away from problem solving and applications, something that most math students need. If you look at a honors calculus coarse the problems are more theory based then the ones in a non honors class. For those who don't want rigor they go into the non honors and for those who want to go into pure math they got into the honors one. Both types of math students have choices, what these math nazi's suggest is to remove choice and give everyone a proof based math curriculum.

 

[920118]

But that's the thing not everyone needs or wants rigor in their math. If you guys want to say that without lots of rigor and proofs math isn't math that is fine and you have a point. But for most people they use math as nothing but a tool. Rigorous math is very interesting and beautiful however to understand that beauty is very difficult and is something the individual has to be self motivated to do. Not all math students who sign up for a math class want that or need that. Forcing rigor into the class room is no different then forcing creationism in the classroom.

So you are saying that forcing rigor in a discipline, the theoretical side of which has always been aknowledged for its rigor, is like forcing people to learn about creationism? That just might be the worst analogy I have ever encountered.

It is likely that the "nazis" which you speak of by convention take "math" and "pure math" to coextend, which they do. Your problem seems to be that you want "doing math" to mean that you calculate by applying certain methods and theorems from the field of mathematics. To call pure math "math" and applied math "applied math" is custom.

 

[Kindayr]

I'm not giving a rhetoric I'm giving facts, not everyone needs rigorous and proof based math, especially at the high school or freshmen college level. Forcing proof based math into the classroom is the same as forcing creationism. Of coarse it will probably never happen because this country prefers to dumb down the curriculum rather then make it more challenging which is if you ask me even worse then over emphasizing specialist concepts. By over emphasizing proofs time is taken away from problem solving and applications, something that most math students need. If you look at a honors calculus coarse the problems are more theory based then the ones in a non honors class. For those who don't want rigor they go into the non honors and for those who want to go into pure math they got into the honors one. Both types of math students have choices, what these math nazi's suggest is to remove choice and give everyone a proof based math curriculum.

Okay first of all, stop calling us Nazis. It's offensive, especially when we aren't attacking you in any way, shape or form.

Secondly, do not compare rigour in mathematics to teaching creationism in the classroom. If anything, the analogy would be more likely comparable to introducing evolution to the classroom: teaching something that is actually relevant to the topic at hand. We aren't introducing faith into mathematics education, as your 'creationism' analogy implies.

Lastly, you claim that proof and rigour takes away from problem solving. I think its quite the opposite. When you teach the roots of a subject, it allows the students to understand where the concepts come from. I don't have a degree in education so this is only my opinion. However, I do know that I prefer to get a general sense of a subject before going into direct details as this helps me learn more efficiently.

Further, we're not asking for a jump to the most rigourous of teaching in mathematics, where we slap them on the hand for not explaining themselves axiomatically (as your use of Nazi implies). We ask for a general increase in the doing of actual mathematics in earlier years of a students life.

 

[xdrgnh]

Okay first of all, stop calling us nazis. Its offensive, especially when we aren't attacking you in any way shape or form.

Secondly, don't compare this to teaching creationism in the classroom. If anything, the analogy would be more likely comparable to introducing evolution to the classroom, as rigour and proof are real and applicable to the subject at hand. This isn't the introduction of faith to science.

Lastly, you claim that proof and rigour takes away from problem solving. I think its quite the opposite. When you teach the roots of a subject, it allows the students to understand where the concepts at hand come from. I don't have a degree in education, so this is my opinion. But I do know that I prefer to get a general sense of a subject before going into direct details helps me learn more efficiently. Though I cannot speak for anyone else.

Further, we're not asking for a jump to the most rigourous of teaching in mathematics, where we slap them on the hand for not explaining themselves axiomatically (as your use of Nazi implies). We ask for a general increase in doing of actual mathematics in earlier years of a students life.

When the emphasis of a class is proofs then it does take away from problem solving that could be used by engineers and scientists. Let me tell you about my AP calc BC class, I had a great math teacher for that class. When he introduced the topics he first proved them using appropriate mathematics for a 12th grade class, after the proof we all understood where it came from and why it was what it was. Afterward he gave us problems like finding the equation of motion of a falling object subject to air resistance or he would give something like finding the rate of change at which cars go through a intersections. What some radicals propose is that the emphasis should be on proofs and that rather giving problems like finding the equation of motion of a particle, the problems should be theory based and students should do many proofs on there own in a intro class. People who want to use math as a tool don't need that kind of math. Proofs even at a intro level are very difficult for students who have no interest in pure math.

It is like forcing creationism because it gets rid of choice in the end and like creationist these elitists think what they are doing is infallible. But I would like to say sorry if I offended you by using the term Nazi, I was trying to be parallel to grammar Nazis but I understand the weight of the word sorry. Doing proof based math in school was tried already in the USA and it failed during the 60s, topics like set and group theory were introduced in elementary school to foster greater understanding of numbers and it failed.

 

[deRham]

Well, actually mathematics uses formal logic. Formal logic isn't a language.

It might as well be. Of course there's such a thing formally defined in the study of logic as a language, a theory, a model, etc. But I guess in common speech, when we say "language," the logic is implied, and it's quite similar in the case of mathematics.

But aside from that, what you said is what I mean/agree with - mathematics uses formal logic. It isn't quite formal logic itself. You can say mathematics IS set theory, but in truth, it just uses it.

 

[deRham]

When the emphasis of a class is proofs then it does take away from problem solving that could be used by engineers and scientists.

And that's one step too far. You should read my latest posts. Rigor is not the same as giving all the details - it's about acknowledging what can and can't be assumed, and being precise. And frankly, without proper communication, there can be a weakness in understanding.

What some radicals propose is that the emphasis should be on proofs and that rather giving problems like finding the equation of motion of a particle, the problems

I don't know who they are, but most mathematicians I've talked to don't suggest any such thing. I'd be interested in those people's reasoning.

I dislike the harping on the word "proofs" though. A proof, as far as most math classes are concerned, is a precise explanation. That's all. And that's a good thing to expect. Jumping into esoteric theory is not necessary, of course.

"Proof" can of course mean something else to a logician, in terms of "deductive systems" or whatever. But the type of proof expected can vary greatly.

If you're suggesting emphasizing blind calculation, that's certainly bad. Calculation with the reasoning clearly stated is still, in a manner of speaking, a proof. Even very advanced math classes perform calculations.

 

[xdrgnh]

And that's one step too far. You should read my latest posts. Rigor is not the same as giving all the details - it's about acknowledging what can and can't be assumed, and being precise. And frankly, without proper communication, there can be a weakness in understanding.



I don't know who they are, but most mathematicians I've talked to don't suggest any such thing. I'd be interested in those people's reasoning.




I dislike the harping on the word "proofs" though. A proof, as far as most math classes are concerned, is a precise explanation. That's all. And that's a good thing to expect. Jumping into esoteric theory is not necessary, of course.

"Proof" can of course mean something else to a logician, in terms of "deductive systems" or whatever. But the type of proof expected can vary greatly.

If you're suggesting emphasizing blind calculation, that's certainly bad. Calculation with the reasoning clearly stated is still, in a manner of speaking, a proof. Even very advanced math classes perform calculations.

The people I am talking about those suggest in short that 1st year calculus should be like a light intro analysis class just look at any honors calculus class in college, most of the problems ask about the theory, not a actual calculation. Students who want to be engineers and scientists at first need to know how to do the calculations very well because that is what they will be doing for the first 2 or 3 years of college before the math becomes more abstract. There should be proofs or mathematical explanations but the emphasis should be applied problem solving in a standard 1st year college level class.

 

[Kindayr]

The people I am talking about those suggest in short that 1st year calculus should be like a light intro analysis class just look at any honors calculus class in college, most of the problems ask about the theory, not a actual calculation. Students who want to be engineers and scientists at first need to know how to do the calculations very well because that is what they will be doing for the first 2 or 3 years of college before the math becomes more abstract. There should be proofs or mathematical explanations but the emphasis should be applied problem solving in a standard 1st year college level class.

The problem roots from the fact that students are forced to rush through calculus in a very short amount of time. Like I've said in the "Calculus" thread, in Ontario we get 2.5 months of an introduction of calculus in our final year of high school, before going into university. A complete focus of application in university is just as hurtful to a student's education in mathematics than a rigourous analysis course in first year is. Without having knowledge or intuition of where the methods they are using come from, a lot of students fail to understand even the application of those methods.

In high school we were expected to understand a limit without explanation. This lead students to have the wrong intuition that the limit of any function is like the limit of a continuous function: that is, you just plug in the value to find the limit. So when we got to more complicated functions, their intuition failed them and they did poorly because they weren't taught what a limit really is. I'm not asking for a harsh and ridiculous notion of overwhelming epsilon-delta proofs at the first introduction of calculus (where they have no idea what a proof even is). Just a general sense of what a limit ACTUALLY is.

The state of the education of mathematics is ridiculous, and there needs to be some balance between rigour and application. For me, the solution would to introduce the ideas of reasoning your arguments at a younger age. This would allow teachers to introduce a little more theory, so students know what their doing and why it works in that way. Then all the time in the world could be used on application of those ideas.

But I'm just a 3rd year math student, so what do I know.

 

[deRham]

^ Yes it's unnecessary to make it like an intro to analysis class. However, emphasizing clear communication and understanding of the mathematics is a must.

You must be fair - not only engineers, but mathematicians too take the first course. It should involve clear reasoning, understanding the theory sufficiently to use it either in mathematics or other fields.

This means that one needn't know the proof of every theorem taught in standard calculus, but should be able to use them effectively, and with clear communication, both to solve intrinsically mathematical problems and inherently application-based problems, as I think at that basic level, even a pure mathematician should be exposed to the applications (it increases basic intuition).