## La chartreuse de Parme and f(p), briefly

These last few weeks I’ve gone to some public lectures that are impossible to mention without name-dropping. Habermas’s talk last week had some good points, but could have been shorter; since he was not using a board, what was the point of standing up for more than an hour, other than enduring suffering? A French public intellectual gave a marathonic seminar during which she gave a dazzling literary interpretation of an event in the history of computing – based, alas, on an error: while Turing may have seen Snow White, and was obviously familiar with the apple from popular retellings of the Garden of Eden story, Macintosh’s bitten apple was not a coded reference to Turing’s method of suicide.

Agamben’s talk a couple of weeks ago – on the origin of the concept of will – was pretty excellent. Apparently the notion of will, as clearly distinct from the related concept of power, arose after the Greek Classical period. I recall that things started going with Aristotle, and somehow our good friend Pelagius got involved, but I’m not sure where I’ve put my notes.

I started reading La Chartreuse de Parme a few years ago. I put it down a bit before the middle, and picked it up again a few weeks ago. I just finished it today, more or less at sunrise. A thrilling ride, really, and it was almost a pity it had to end. I believed every bit in those characters I was clearly not supposed to believe in (in part because of that very same fact). Now I know where Godard got the idea that it was socially acceptable to finish his movies (Contempt, Vivre sa vie) in that fashion.

These days I’m also retaking something I put down a few years ago, but on the end of mathematical production rather than novelistic consumption. A long version of my paper on f(p) should be ready soon. (A summary version appeared in a conference proceedings volume a few years ago.) Take a cubic polynomial f without repeated factors (say, $f = x^3 + 2$). Erdős showed that (granted the obviously necessary local conditions, fulfilled by $f = x^3 + 2$ but not by $4 (x^3 + 2)$ or $2 (x^3 + x^2)$) there are infinitely many integers n such that f(n) is square-free, i.e., is not divisible by any squares other than 1. Are there, however, infinitely many primes p such that f(p) is square-free? This is what Erdős asked but – unsurprisingly in retrospect – couldn’t do. This is also what I did – it used plenty of the theory of elliptic curves, including modularity, and it was fun.