Edward Witten discusses the unexpected properties of perturbative scattering amplitudes in Yang-Mills theory, such as the holomorphy of maximally helicity violating (MHV) amplitudes. He proposes Fourier transforming these amplitudes from momentum space to twistor space, suggesting that the transformed amplitudes are supported on certain holomorphic curves. This interpretation is linked to an equivalence between the perturbative expansion of $\mathcal{N}=4$ super Yang-Mills theory and the $D$-instanton expansion of a specific string theory, namely the topological $B$ model on the Calabi-Yau supermanifold $\mathbb{CP}^{3|4}$. The paper explores how this string theory interpretation can explain the holomorphy of MHV amplitudes and the differential equations obeyed by higher-order amplitudes. Witten also discusses the physical implications of these results, including the possibility of understanding the closed string sector of the $B$ model and the connection to conformal supergravity. The paper concludes with a discussion of the extension of these ideas to $\mathcal{N}=4$ supersymmetry and the generalization to other field theories.Edward Witten discusses the unexpected properties of perturbative scattering amplitudes in Yang-Mills theory, such as the holomorphy of maximally helicity violating (MHV) amplitudes. He proposes Fourier transforming these amplitudes from momentum space to twistor space, suggesting that the transformed amplitudes are supported on certain holomorphic curves. This interpretation is linked to an equivalence between the perturbative expansion of $\mathcal{N}=4$ super Yang-Mills theory and the $D$-instanton expansion of a specific string theory, namely the topological $B$ model on the Calabi-Yau supermanifold $\mathbb{CP}^{3|4}$. The paper explores how this string theory interpretation can explain the holomorphy of MHV amplitudes and the differential equations obeyed by higher-order amplitudes. Witten also discusses the physical implications of these results, including the possibility of understanding the closed string sector of the $B$ model and the connection to conformal supergravity. The paper concludes with a discussion of the extension of these ideas to $\mathcal{N}=4$ supersymmetry and the generalization to other field theories.