What is the hardest type of math and are there unsolved equations?

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  • Thread starter Thread starter Swegner99
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Discussion Overview

The discussion revolves around the perception of difficulty in various types of mathematics and the existence of unsolved equations. Participants share personal experiences and opinions regarding what they consider to be the hardest areas of math, as well as their thoughts on the challenges posed by different mathematical concepts and teaching styles.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Meta-discussion

Main Points Raised

  • Some participants suggest that the difficulty of math is relative and depends on personal understanding and preferences.
  • One participant recalls that in their experience, spherical trigonometry was once considered very challenging.
  • Another participant expresses that they found series, particularly absolute and uniform convergence, to be particularly boring and difficult to engage with.
  • A participant highlights the impact of teaching styles on the perceived difficulty of subjects, specifically mentioning Abstract Algebra as a challenging area due to its abstract nature.
  • Some participants humorously state that all math is hard for them, indicating a general struggle with the subject.
  • Complex number matrix manipulations and series solutions to differential equations are mentioned as particularly challenging due to the arithmetic involved.
  • One participant points out the confusion caused by varying notations and symbols used by different authors, suggesting that clarity in notation can aid understanding.
  • Another participant argues that math becomes easier with understanding and familiarity, noting that individuals may excel in different areas of math.
  • One participant shares their brief encounter with advanced topics like supersymmetry and non-commutative geometry as being among the hardest they have attempted.
  • Several participants reflect on the learning process in mathematics, describing a journey from confusion to understanding over time, with moments of clarity emerging after prolonged study.

Areas of Agreement / Disagreement

Participants generally agree that the difficulty of math is subjective and varies from person to person. However, there are multiple competing views on what constitutes the hardest type of math, and the discussion remains unresolved regarding specific areas of difficulty and the existence of unsolved equations.

Contextual Notes

Participants express varying levels of familiarity with mathematical concepts, and there are references to personal experiences that highlight the subjective nature of mathematical difficulty. The discussion includes a mix of opinions on teaching effectiveness and the role of notation in understanding mathematical ideas.

Swegner99
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In my introducation post, I stated that I am new to all this. My highest math education is elementary Algebra, but I am here to learn myself some new things. With that being said, what is the hardest type of math out there? I know its somewhat relative, based upon personal understanding... so personal opinion is welcome. Are there any math equations out there that haven't been solved?
 
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Swegner99 said:
I know its somewhat relative, based upon personal understanding... so personal opinion is welcome.

Very much so.

"In my day, as I remember it, we used to think spherical trigonometry about the hardest stuff of the lot." Stephen Leacock
 
Difficulty isn't the problem. It was the boring stuff I found impenetrable -- no surprise. For me that would be series. Absolute convergence, uniform convergence, that sort of thing. I just couldn't stay focused.
 
The biggest factor for me so far has been the professor. Certain subjects can be made quite manageable, or excruciatingly difficult depending on the expectations and teaching style of one's professor/instructor.

I had difficulty in Abstract Algebra, which is the study of the characteristics and properties of the algebraic structures named: groups, rings, and fields. Formulating a rigorous argument for something about which one has little-to-no intuition is not something many people are used to doing. It was a humbling experience for me, to say the least.
 
Last edited:
All math is hard for me :p
 
Anything that involves so much arithmetic that it is almost impossible to actually get it right. Complex number matrix manipulations with matrices bigger than 2X2 and series solutions to differential equations.
 
One of the biggest obstacles in many areas is just figuring out the barrage of symbols,and overall notation, and, even worse, different authors use different notation ( or even different names) for the same thing, or the same name is used for different things. And, on top of figuring the notation, you have indices and subindices, etc. I would suggest, if you want to look-up books, look for one where the notation used is described carefully, as I think it shows the author to be conscientious and has taken care and made an effort to be clear.
 
Math is not hard when you understand and get used to it. It all depends on what type of math you like. You may find yourself having trouble solving algebras but being really good at coordinate geometries.
 
WannabeNewton said:
All math is hard for me :p

I don't believe you lol :P

The hardest math I have seen/briefly attempted (I stress the BRIEFLY attempted) is that of supersymmetry and non-commutative geometry.
 
  • #10
The weird thing about maths is that once you get to higher level stuff, the first time you see it you have no idea what's going on. Then after a while you get your head around what the definitions actually mean, but still can't seem to answer the questions. After a long time spent of having little to no understanding, one day you get a spark and you're like "wait, that actually makes sense". Then after like a year or so, you look back at the stuff which you found absolutely impossible and think it's pretty straight forward. Instead you think the stuff you're doing currently is impossible... of course this opinion will change again some time from now.
 
  • #11
Marioeden said:
The weird thing about maths is that once you get to higher level stuff, the first time you see it you have no idea what's going on. Then after a while you get your head around what the definitions actually mean, but still can't seem to answer the questions. After a long time spent of having little to no understanding, one day you get a spark and you're like "wait, that actually makes sense". Then after like a year or so, you look back at the stuff which you found absolutely impossible and think it's pretty straight forward. Instead you think the stuff you're doing currently is impossible... of course this opinion will change again some time from now.

I feel the same way.
 

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