Is there a point where math becomes difficult for scientists?

[QuarkCharmer]

This may seem like a rather strange question, but whenever I stumble on to some math that is much harder than my current level, I have this horrible feeling that I won't be able to cut it.

I was out of Highschool for 10 years before I started college, and worked my way up from intermediate algebra. There was a time or two in Trig where I had to spend a day or two thinking about concepts like "why can there be multiple answers in questions using the law of sines" etc. but I always worked through it, "got" it, and then it was smooth sailing again.

Don't get me wrong, I don't think I am Mathematically inclined at all, if anything I simply have good review/study habits, but I see some of my peers, perfectly smart ones at that, struggling with some of the simpler Calculus topics and it gets me worried.

I suppose I am looking for some advice. At what point (if at all) did you hit a roadblock, or did Math become difficult?

 

[Nabeshin]

I suppose I am looking for some advice. At what point (if at all) did you hit a roadblock, or did Math become difficult?

For me it is making the transition into very abstract, proof-based mathematics. More specifically, a course on Lie groups/algebras (specifically, matrix groups).

 

[Frion]

When you meet a difficult instructor.

 

[yenchin]

 

[Klockan3]

It depends entirely upon who you are and how you define "difficult". I still don't see maths as difficult and I got roughly a masters but I am not that serious about it.

 

[MathematicalPhysicist]

It depends entirely upon who you are and how you define "difficult". I still don't see maths as difficult and I got roughly a masters but I am not that serious about it.

What does roughly mean in your case? Have you finished it?

 

[thegreenlaser]

Depends who you are. Personally I'm finding even basic proof-based math to be difficult, though I seem to excel in applied math (like math applied to physics). However, most people in my calc class are doing great at proofs, but really struggle with the applications. You'll understand what you understand, and you'll struggle with what you struggle with. Just keep working at it until you understand, and don't worry about what others do/don't understand. Everyone will excel/struggle with different things.

 

[Klockan3]

Edit: Gee, what a dry post this was, I feel ashamed for it...

What does roughly mean in your case? Have you finished it?

I got all the courses so I just got the thesis left but right now I don't really have the motivation to do it. I could have finished by now and even if I move it up half a year I would still finish early since I took extra courses throughout but I don't really care enough with the hassle that is looking for an advisor etc. I have some issues which makes such things demanding for me but I hope that I can muster the willpower to do it at least within a year from now. I would have no problem financially living in this limbo for a few years, taking some stray maths/physics courses, so I am not that worried, in the worst case scenario I could get a job as a teacher at some place.

The only times I thought that maths was hard was when I took courses which I lacked prerequisites for. Physics lost some of its magic once I started to get to higher level masters courses, much because the increased focus on numerical methods so I will probably do my thesis at the maths department. Mathematical proofs and such can also be gritty, but at least I can still see exactly what happens with everything. There are physics like that, yes, but I'd rather take my chances with maths for now. Maybe if I one day stop having all these problems, but that is not today.

 

[snipez90]

Pure math is difficult. If you're not Euler or Gauss or someone of comparable skill, you might have to spend a considerable amount of time to get anywhere. But you shouldn't encounter a new mathematical subject and wail in existential angst because you're afraid you won't understand everything the first time. Echoing Von Neumann, in math you don't understand things but rather get used to them.

Also, as Atiyah mentioned, the supremely confident mathematicians are the mediocre ones.

 

[mathwonk]

for most mathematicians it was their first real calculus or analysis class, the one with limits and continuity in it. for some its abstract algebra or higher dimensional linear algebra. then later it is often algebraic topology, with cohomology and homotopy and spectral sequences, or algebraic geometry with sheaves and cohomology and schemes...then for some it is trying to prove the riemann hypothesis...