I will describe recent progress on bootstrapping maximally supersymmetric Yang-Mills theory with higher-derivative corrections using analyticity and unitarity of 2-to-2 scattering amplitude. Specifically, I will show how upper and lower bounds on the Wilson coefficients result from assuming that the effective field theory arises as the low-energy expansion of a unitary "sensible" UV theory. I will show with few assumptions about the low-mass spectrum of the putative UV theory that there are interesting corners (kinks) in the bounds and that string theory (the Veneziano amplitude) is near a kink. I will discuss progress on bootstrapping the open string tree amplitude from a bottom-up EFT approach.