Fascinating discussion including showing how LLMs are helping push the state of the art:<p>> I still did not see how to prove this inequality, but I decided to try my luck giving it to ChatGPT Pro, which recognized it as an {L^1} approximation problem and gave me a duality-based proof (based ultimately on the Fourier expansion of the square wave). With some further discussion, I was able to adapt this proof to functions of global exponential type (replacing the Fourier manipulations with contour shifting arguments, in the spirit of the Paley-Wiener theorem), which roughly speaking gave me half of what I needed to establish (2).<p>> As a side note, this latter argument was provided to me by ChatGPT, as I was not previously aware of the Nevanlinna two-constant theorem.<p>This mirrors my experience with these tools for math. Great for local problems and chatting through issues. Still can’t do the whole thing in one shot but getting there.