Re: Heuristics for number theory?

"Stephen White"
> Hello,
>
> It seems that there is a horrific dearth of manageable heuristics
> for number theory. People have always told me it is supposed to be a
> very elegant and beautiful branch of mathematics, but I find it to be
> ugly, indeed hideous. In a good branch of mathematics, you'll find
> yourself guessing ahead of the book at the general idea of a proof; not
> so in number theory, where the proof will just pull things out of a hat
> out of nowhere. You read a proof and you're left scratching your head
> and saying "ok, who on earth just arbitrarily decided to consider (some
> huge, ugly, complicated auxiliary function)?" It isn't _natural_, it's
> forced, and there is no *understanding* (ok, I can (very
> painstakingly) verify line by line the proof of pi's irrationality, but
> it sheds absolutely zero insight into the matter).
What was the content of your course? Proving that pi is irrational
is rather untypical in a first course in NT. What else went on?
And was this course intended for math majors only, or did it
aim at students of information technology? That would have
an influence on the instructor's choice of problems, I expect.
LH

> People say some of
> the stuff becomes more digestable when you look at it from some higher
> algebraic / complex analysis / analytic number theory viewpoint.....
> so why bother with an elementary number theory class at all? I feel
> I've gained virtually nothing from this class, and the problems have
> been more frustrating than all my other classes combined.
>
> Exhausted,
> M. Toede
>


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Relevant Pages

  • Heuristics for number theory?
    ... very elegant and beautiful branch of mathematics, but I find it to be ... In a good branch of mathematics, ... so why bother with an elementary number theory class at all? ...
    (sci.math)
  • chapter on the halting of ill-definitions in math such as irrational #225
    ... yes I do have an easy resolution of escaping the ill definition ... Since mathematics never defined Finite versus ... So we see that the concept of Irrationality and that of ... composite which are intrinsic properties of math. ...
    (sci.math)