Yesterday, 1:17 AM
I honestly think maths is one of the easiest subjects, but high school maths is a truly awful experience. During high school I was terrible enough at it that my teacher told me to give up on extension maths (which I did). I thought it was grindy and not fun or interesting at all. Now I'm doing a PhD in it. Go figure.
For the most part, I found the difficulty of the maths courses I took as an undergrad to be inversely proportional to how much I enjoyed them. I didn't do very well with probability / statistics even though it's generally considered to be one of the easier topics. I found it really uninteresting.
There were two exceptions to this: algebraic geometry and, to a lesser extent, algebraic topology (not to be confused with point-set topology, which I think was easy and so much fun - I think the only easier courses I took were category theory and PDEs). Even though I found them really interesting, those topics are genuinely hard, especially algebraic geometry.
I think algebraic geometry is one of the deepest topics in research level mathematics and it takes a very long time to become comfortable with, but regardless of what you're studying it has a nasty habit of appearing in the background when you least expect it. Roughly speaking, I think of it as the study of certain nice algebraic objects whose global behaviour is captured well by their local behaviour. It appears a lot in my research and I'm currently doing my best to avoid it at all costs, it's way too scary.
For the most part, I found the difficulty of the maths courses I took as an undergrad to be inversely proportional to how much I enjoyed them. I didn't do very well with probability / statistics even though it's generally considered to be one of the easier topics. I found it really uninteresting.
There were two exceptions to this: algebraic geometry and, to a lesser extent, algebraic topology (not to be confused with point-set topology, which I think was easy and so much fun - I think the only easier courses I took were category theory and PDEs). Even though I found them really interesting, those topics are genuinely hard, especially algebraic geometry.
I think algebraic geometry is one of the deepest topics in research level mathematics and it takes a very long time to become comfortable with, but regardless of what you're studying it has a nasty habit of appearing in the background when you least expect it. Roughly speaking, I think of it as the study of certain nice algebraic objects whose global behaviour is captured well by their local behaviour. It appears a lot in my research and I'm currently doing my best to avoid it at all costs, it's way too scary.
