In a famous article, Freeman Dyson mentions an interesting relationship between the $\tau$ functions of number theory and the dimensions of finite-dimensional simple Lie algebras (section 2). He mentions there that the case $d=26$, remains unsolved. I am curious to know about the current status of this problem.
By the way, if I am not wrong, for bosonic String Theory to be consistent one must have $n=26$ where $n$ is the number of dimensions and the partition function of String Theory is a Dedekind $\eta$ function (in terms of which, the $\tau$ functions are defined). Is this a coincidence ?
I must add that I am far from being an expert on any of these and may be making silly mistakes above or asking something silly.
Thanks !