Why is math so hard? Can anyone truly understand it?

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SUMMARY

The discussion centers on the challenges faced by students in advanced mathematics, particularly in Calculus III and complex analysis. Participants highlight the disconnect between intuitive understanding in earlier math courses and the overwhelming nature of higher-level topics like the Cauchy Goursat theorem and complex integration. The conversation emphasizes the importance of visualization and practical applications, such as using physics concepts to aid comprehension. Additionally, the role of teaching quality in mathematics education is debated, with some asserting that poor teaching contributes to students' struggles.

PREREQUISITES
  • Understanding of Calculus I and II concepts, including integration and derivatives.
  • Familiarity with the Cauchy Goursat theorem and complex integration.
  • Basic knowledge of vector calculus and differential equations.
  • Ability to visualize mathematical concepts in multiple dimensions.
NEXT STEPS
  • Explore the applications of the Cauchy Goursat theorem in engineering contexts.
  • Study complex analysis through resources like "Visual Complex Analysis" by Tristan Needham.
  • Investigate the relationship between calculus and physics, particularly through the lens of Maxwell's equations.
  • Research effective teaching methods in mathematics to understand how they impact student learning.
USEFUL FOR

Students in engineering and mathematics, educators seeking to improve teaching methods, and anyone struggling with advanced mathematical concepts.

  • #31
I was a mostly terrible college student (for a lot of reasons) but I managed to get one of my degrees in Math. Upon learning a concept (while studying) I often found myself wondering why did the teacher make this seem so hard in class.

Although I had one really great math teacher who inspired me and I took four classes with him. Once I had a really great math teacher I realized what I had been missing . . .
 
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  • #32
John d Marano said:
Most math professors have absolutely no training in teaching

True for most professors. Why single out math?

John d Marano said:
Additionally a mind that excels in mathematics usually lacks in soft skills like communicating

Evidence, please?

John d Marano said:
We all know it.!

That is not evidence.

John d Marano said:
The self absorbed math genius makes a poor teacher!

What evidence do you have that most math professors are "self absorbed math geniuses"? And for that matter, what evidence do you have that they make poor teachers?

You said some offensive things. Are you going to back them up or not?
 
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  • #33
A lack of soft skills in STEMs ---> "Employers are increasingly concerned about STEM students’ lack of preparedness in soft skills" https://www.eab.com/research-and-insights/continuing-and-online-education-forum/expert-insights/2016/soft-skills-gap

There's this https://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html?_r=0

My opinion about math teachers is mostly an opinion. I feel a good teacher has a command of the subject, command of the classroom, humor and makes themselves accessible to students. "The self absorbed math genius makes a poor teacher!" aka Sheldon Cooper was a joke
 
  • #34
It occurs to me that math may be the only field where there is abstraction for its own sake. Abstraction certainly has great benefits in math. Are there other fields like that?

PS. It will not hurt my feelings if you tell me that is a dumb statement. I may be saying more about my limited perspective than anything.
 
  • #35
FactChecker said:
It occurs to me that math may be the only field where there is abstraction for its own sake. Abstraction certainly has great benefits in math. Are there other fields like that?

Philosophy . . .
 
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  • #36
John d Marano said:
Philosophy . . .
Maybe that's why Bertrand Russell was famous for both.
 
  • #37
symbolipoint said:
You confused difficulty with complexity. These are very different things.
I try not to philosophize too much on PF, I won't argue.

Maths is easy if you have the patience to do the grind work that goes with it, obviously those that don't like to work, i.e lazy people, they will find maths as a really big pain.
 
  • #38
FactChecker said:
Maybe that's why Bertrand Russell was famous for both.

Deductive reasoning, logic and set theory all gave me a real advantage in the one philosophy course I took. The course was called "World Religions" and the professor was an atheist; the class was a blast!
 
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  • #39
FactChecker said:
It occurs to me that math may be the only field where there is abstraction for its own sake. Abstraction certainly has great benefits in math.

It seems to me that these two sentences contradict each other. If the abstraction was for its own sake, it wouldn't be there because of a benefit external to the abstraction. If the abstraction has benefits, then the abstraction isn't for its own sake.

That being said there are other fields with sub-disciplines which use a lot of abstraction. Cellar biology, organic chemistry, the various cognitive sciences, economics, and linguistics all benefit a great deal from abstraction in various forms.
 
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  • #40
MathematicalPhysicist said:
I try not to philosophize too much on PF, I won't argue.

Maths is easy if you have the patience to do the grind work that goes with it, obviously those that don't like to work, i.e lazy people, they will find maths as a really big pain.
In other words, Mathematics is not easy.
 
  • #41
symbolipoint said:
In other words, Mathematics is not easy.
It is.

Anything that is worthwhile requires work, I would think that mundane work as wiping the floor are harder than doing maths.
 
  • #42
symbolipoint said:
In other words, Mathematics is not easy.
MathematicalPhysicist said:
It is.

Anything that is worthwhile requires work, I would think that mundane work as wiping the floor are harder than doing maths.
Okay; you are a genius.
 
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  • #43
beamthegreat said:
I used to like math when I was in high school. Calculus (integration and derivatives) seem intuitive to me and made me understand math so much better.

Now I'm currently in university majoring in civil engineering taking Calc III and I feel overwhelmed by everything taught in class. No matter how hard I try, I cannot understand things intuitively and everything feels disconnected. I can solve problems given by my professor but I have no clue what I am doing or what the answers even mean.

Why is math so hard?
I just love maths. I am also an Engineering graduate. And am sure that for the first 2 years, I scored the highest marks for maths. Try doing the problems again and again. Work out similar problems. Maths is not too hard. :)
 
  • #44
MathematicalPhysicist said:
I would think that mundane work as wiping the floor are harder than doing maths.
There is much more to floors than one would think at first glance.
 
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  • #45
Krylov said:
There is much more to floors than one would think at first glance.
As a joke it's a poor one.
 

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