My calculus classes were looking at $$ \int e^{x^2} \, dx $$ today. I let them struggle with finding a solution. when I shared that the solution was impossible using the functions we know, and that we needed to define the “error function” to do this job, they asked me:
How do we know there is no “known” solution to this integral? Have we proven we cannot find one with our regular algebraic functions?
