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Hardest area in maths?

  1. Nov 19, 2006 #1
    Broadly speaking, which major area of mathematics is considered the (or has a reputation to be the) hardest by the majority of mathematicians?

    Note: I am aware that there are extremly hard unsolved problems in all areas of maths. I do not intend to be snobbish with this question but just an outsider wondering if there is an answer to this question.
     
    Last edited: Nov 19, 2006
  2. jcsd
  3. Nov 19, 2006 #2

    Office_Shredder

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    whichever area you're studying. It makes you sound smarter in comparison.

    Obviously, if a field of math was easy everyone would do it, and the knowledge base would expand to the point where it was hard. So the level of difficulty of a given field of math is always at a stable equilibrium point
     
  4. Nov 19, 2006 #3
    This case taken to the extreme would mean every field of study should be at an equilibrium. i.e. it is equally hard to do research in maths as in psychology. (I don't mean to belittle psychologists but I have a feeling resulting from a degree of personal experience that in general a mathematician can learn psychology much faster than a psychologist learn maths.) But that is not the case is it? So maybe you can think of my question as which area in maths has the most amount of 'bright' people working in. Hence that area will not have many easy questions left to answer, making it seem harder in comparison.
     
    Last edited: Nov 19, 2006
  5. Nov 19, 2006 #4

    Gza

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    I think it's difficult to single out any branch of math, and assign an arbitrary level of difficulty to it. Just like in sports, you have a wide range, such as basketball, football, baseball, and skillsets: (leaping ability, height, speed); in math you have the same situation, where much different skill sets are involved in each branch (computational ability, geometrical reasoning ability, etc.) Saying that football is harder than baseball, or topology is harder than vector calculus, is a question who's answer really depends on who you're asking.
     
  6. Nov 19, 2006 #5

    mathwonk

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    to me analysis is probably hardest.
     
  7. Nov 21, 2006 #6

    JasonRox

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    Research in Psychology isn't easier! Where the hell did you get this from?

    It looks harder in my opinion. You have to gather a bunch of data, test on people, and whatever else you have to do. There is lots to do.

    I'm in mathematics, and I don't think any other area is easier than mine except for things like Business, Popular Culture, Classics, and that kind of stuff.

    Things like Chemistry, Biology, Philosophy, Linguistics, and so on are just as hard a Mathematics.
     
  8. Nov 22, 2006 #7
    Although I am only an undergrad I feel it is hard has well mainly because it always deals with the infinite. Is that also your reason?
     
    Last edited: Nov 22, 2006
  9. Nov 22, 2006 #8
    I studies year 12 psychology and maths. And maths was much harder. However, I got a better grade in maths than psychology. The reason is because I spent so much more time in maths. Had I spent this much time on psychology I would have memorised the whole course and got 100%. Psychology research could be a different business altogether but compared to maths research, I still think maths would be harder - i.e. if you spend 30 years on a psychology research problem, you might get somewhere with it - i.e write a reasonable report. But the same time on a difficult maths problem, you might have gone nowhwere.

    Obviously there are different kinds of hardness. i.e for me the hardest subjects would be Labs and Classics. Although I believe I can overcome my incompetence in the former, the latter, I am not so sure - i.e. I could never understand a Shakespear play. The hardness in the latter I would describe as the problem of vagueness, something I hate. That is why I prefer maths even to a subject like physics.
     
  10. Nov 23, 2006 #9
    Artin's conjecture, involving Abstract Algebra and Number Theory, is considered a very hard field.

    The Ringel-Kotzig conjecture, that every tree has a graceful labeling, is also frequently mentioned as a difficult problem (Ringel calling the attempts to solve it a "disease").

    I know you are looking for areas of math, and not problems, but both of these problems drive their respective areas of math. Hundreds of people chip away at them bit by bit, every year.
     
  11. Nov 23, 2006 #10

    arildno

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    Dearly Missed

    My lecturer in complex analysis said he found discrete maths to be the hardest..
     
  12. Nov 23, 2006 #11
    Probability... It forces me to think instead of having to work with limits and physics.
     
  13. Nov 23, 2006 #12
    Certainly in high school, probability was much harder than say calculus, although I haven't done university probability. The formulas in elementary probability are not big so it really recquires one to really undertand the maths behind it in order to solve a wordy problem.
     
    Last edited: Nov 23, 2006
  14. Nov 23, 2006 #13
    from my experiences, math logic takes the cake.
     
  15. Nov 23, 2006 #14

    Hurkyl

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    Aww, logic is the most fun mathematics. :frown:
     
  16. Nov 23, 2006 #15

    Gokul43201

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    Maybe it takes the cake right in the face then?
     
  17. Nov 24, 2006 #16

    mathwonk

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    sheaf cohomology seems hard to me too. and compactifications of quotients of siegel domains. and minus signs, yes minus signs are definitely the hardest thing in math, and adding fractions is hard for my students.
     
  18. Nov 24, 2006 #17

    X=7

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    Yes, lunarmansion, JasonRox is surely mistaken on that one. I too have studied Classics:surprised & Maths and, Jason, absolutely cannot agree. You are well wrong on that one!

    Best wishes

    x=7
     
  19. Nov 24, 2006 #18

    matt grime

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    I think the modern take on geometry is hard. Or more accurately the way geometers present it makes it seem far harder than it actually is. If only they could just agree on one set of nomenclature.... it's easier than they let on, I'm sure. In fact, I've come round to the opinion that geometers are actually attempting to disguise how little they really can prove (which is distinct from what they 'know') - c.f. the need to assume something is Calabi-Yau, K3, Kahler, has log singularities, is Gorenstein,.... or whatever. (Yes, I am teasing, a little).
     
  20. Nov 25, 2006 #19
    number theory is the hardest FOR ME because I live in a metric space. In fact, anything like combinatoric, algebra, number theory are not my friends... lol
     
  21. Nov 25, 2006 #20

    mathwonk

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    I think MATT's post points up one source of difficulty, which for me is poor choice of nomenclature. why call something a K3 surface except for conceit. No one in geometry even knows what this stands for altho some say a conglomeration of names like kodaira, kahler,etc....

    as james milne said in commenting on a letter about why galois fields deserve to be called such, ok he did discover them, but calling them finite fields is still more descriptive.

    calabi - yau, k3, all this nonsense is just a way of naming manifolds analogous to elliptic curves, i.e. "flat" (trivial canonical bundle, and some other conditions).

    aS USUAL THERE ARE THReE WORLDS in geometry, positively curved, negatively curved, and flat, (spheres, elliptic curves, and all the rest), and the flat ones are often the most interestin, while the negatively curved ones are most common ("general type")

    i am being very rough here in my discussion, but not completely wrong.

    on the other hand, i like terms which suggest their meaning, such as group action, and codifferential, which is the dual of the frechet derivative or differential of a map.
     
    Last edited: Nov 25, 2006
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