The paper by Hillar and Lim proves that many problems related to tensors are NP-hard. These include determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor has a given eigenvalue, singular value, or spectral norm, approximating these quantities, and determining the rank or best rank-1 approximation of a 3-tensor. The results show that even when restricted to symmetric tensors, these problems remain NP-hard. Additionally, the paper demonstrates that deciding nonnegative definiteness of a symmetric 4-tensor is NP-hard, and computing the combinatorial hyperdeterminant of a 4-tensor is NP-, #P-, and VNP-hard. The authors argue that these results highlight the boundary between tractable linear/convex problems and intractable nonlinear/nonconvex ones. The paper also discusses the computational complexity of tensor problems, including the NP-hardness of tensor eigenvalue problems, the #P-hardness of counting tensor eigenvectors, and the VNP-hardness of polynomial evaluation problems. The authors show that quadratic feasibility is NP-hard over real and complex numbers, and that graph 3-colorability is polynomially reducible to quadratic feasibility. The paper concludes that tensor problems are computationally hard, and that this has implications for the tractability of numerical computation.The paper by Hillar and Lim proves that many problems related to tensors are NP-hard. These include determining the feasibility of a system of bilinear equations, deciding whether a 3-tensor has a given eigenvalue, singular value, or spectral norm, approximating these quantities, and determining the rank or best rank-1 approximation of a 3-tensor. The results show that even when restricted to symmetric tensors, these problems remain NP-hard. Additionally, the paper demonstrates that deciding nonnegative definiteness of a symmetric 4-tensor is NP-hard, and computing the combinatorial hyperdeterminant of a 4-tensor is NP-, #P-, and VNP-hard. The authors argue that these results highlight the boundary between tractable linear/convex problems and intractable nonlinear/nonconvex ones. The paper also discusses the computational complexity of tensor problems, including the NP-hardness of tensor eigenvalue problems, the #P-hardness of counting tensor eigenvectors, and the VNP-hardness of polynomial evaluation problems. The authors show that quadratic feasibility is NP-hard over real and complex numbers, and that graph 3-colorability is polynomially reducible to quadratic feasibility. The paper concludes that tensor problems are computationally hard, and that this has implications for the tractability of numerical computation.