Over on the polymath blog, I’ve posted (on behalf of Dinesh Thakur) a new polymath proposal, which is to explain some numerically observed identities involving the irreducible polynomials $P$ in the polynomial ring ${\bf F}_2[t]$ over the finite field of characteristic two, the simplest of which is

$\displaystyle \sum_P \frac{1}{1+P} = 0$

(expanded in terms of Taylor series in $u = 1/t$).  Comments on the problem should be placed in the polymath blog post; if there is enough interest, we can start a formal polymath project on it.