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

  • Thread starter Swegner99
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In summary: In my undergrad, I struggled with differential equations and partial differential equations, because they're so logically and conceptually complex. The first time I saw them, I had no idea what was going on. It took a lot of work and practice to finally get a grip on them.
  • #1
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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  • #2
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
 
  • #3
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.
 
  • #4
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.
 
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  • #5
All math is hard for me :p
 
  • #6
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.
 
  • #7
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.
 
  • #8
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.
 
  • #9
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.
 

1. What is considered the hardest branch of math?

The hardest branch of math is subjective and can vary from person to person. Some may consider topics like abstract algebra or differential geometry to be the most challenging, while others may find statistics or mathematical logic to be the toughest.

2. What makes a math problem difficult?

A math problem can be considered difficult if it requires a high level of critical thinking and problem-solving skills, involves complex concepts and equations, or has multiple steps and layers of difficulty.

3. Is there a definitive answer to the hardest math problem?

No, there is no one definitive answer to the hardest math problem. In fact, there are many unsolved problems in mathematics that are considered extremely difficult and continue to challenge mathematicians.

4. How can one improve their skills in solving difficult math problems?

Practice, perseverance, and seeking help from others are key to improving skills in solving difficult math problems. It is also important to have a strong foundation in basic math concepts and to continually challenge oneself with new and challenging problems.

5. Can anyone solve the hardest math problems?

In theory, anyone can solve the hardest math problems with enough dedication and determination. However, some problems may require a high level of mathematical knowledge and expertise, making them more challenging for those without a strong math background.

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