14 votes

Almost All Polynomials Are Irreducible

4 comments

  1. [2]
    tiredlemma Link
    Thought I would try this here, see if there is any math interest on ~. One thing that came to mind for me reading this article is how much of what we think about mathematically is the special...

    Thought I would try this here, see if there is any math interest on ~. One thing that came to mind for me reading this article is how much of what we think about mathematically is the special case! Whether it's integers or rationals or factorable polynomials, the objects that are easy to reason about in mathematics so often turn out to be incredibly rare in the scheme of the reals, or as in this case, the set of all polynomials with integer coefficients.

    Like so much other work, this rests on the Riemann Hypothesis proving true--something that I very much hope is resolved one way or another in my lifetime.

    4 votes
    1. Algernon_Asimov Link Parent
      It looks like there is.

      Thought I would try this here, see if there is any math interest on ~.

      It looks like there is.

      3 votes
  2. [2]
    DonQuixote Link
    I'm a mathematics observer, meaning I didn't study it in school beyond 2nd year calculus. But like to read about it and try to understand it. Your article mentioned Riemann and got me going down...

    I'm a mathematics observer, meaning I didn't study it in school beyond 2nd year calculus. But like to read about it and try to understand it. Your article mentioned Riemann and got me going down that rabbit hole (not the first time. ) I gleaned a passage in Wikipedia that I thought was interesting:

    Riemann held his first lectures in 1854, which founded the field of Riemannian geometry and thereby set the stage for Albert Einstein's general theory of relativity. In 1857, there was an attempt to promote Riemann to extraordinary professor status at the University of Göttingen. Although this attempt failed, it did result in Riemann finally being granted a regular salary.

    A different age and time, but they must have had either pretty high standards at Gottingen or no money or both.

    3 votes
    1. tiredlemma Link Parent
      I don't know how university appointments used to work, but I know that you often see things like "X got Y an appointment to Z after A paper was circulated" and "B received a salary from C...

      I don't know how university appointments used to work, but I know that you often see things like "X got Y an appointment to Z after A paper was circulated" and "B received a salary from C university after D achievement". So I often wonder how that actually worked, as you note it seems like there was a difference between being associated with a university and actually getting paid by one. My best guess is that he got a regular salary like we think of today instead of getting paid piecemeal for courses taught or papers published??