The paper by Carl M. Bender explores the concept of non-Hermitian Hamiltonians in quantum mechanics, where the standard requirement of Hermiticity (complex conjugation and transposition) is replaced by the physically transparent condition of space-time reflection symmetry ($\mathcal{PT}$ symmetry). $\mathcal{PT}$ symmetry ensures that the energy spectrum is real and time evolution is unitary, even if the Hamiltonian is not Hermitian. The author discusses the mathematical and physical implications of $\mathcal{PT}$ symmetry, including the construction of a positive-definite inner product and the existence of physical states with positive norms. Examples of $\mathcal{PT}$-symmetric Hamiltonians, such as $H = \hat{p}^2 + i\hat{x}^3$ and $H = \hat{p}^2 - \hat{x}^4$, are presented, showing that their energy levels are real and positive. The paper also addresses the Lee Model, a non-Hermitian Hamiltonian with a "ghost" state, which is reinterpreted as a $\mathcal{PT}$-symmetric Hamiltonian with a physical state having a positive norm. The author emphasizes that $\mathcal{PT}$ symmetry is a fundamental discrete symmetry of the world, as it is part of the Lorentz group, and discusses the development of the field of $\mathcal{PT}$-symmetric quantum mechanics, including the discovery of new Hamiltonians and the rigorous mathematical proofs of their properties.The paper by Carl M. Bender explores the concept of non-Hermitian Hamiltonians in quantum mechanics, where the standard requirement of Hermiticity (complex conjugation and transposition) is replaced by the physically transparent condition of space-time reflection symmetry ($\mathcal{PT}$ symmetry). $\mathcal{PT}$ symmetry ensures that the energy spectrum is real and time evolution is unitary, even if the Hamiltonian is not Hermitian. The author discusses the mathematical and physical implications of $\mathcal{PT}$ symmetry, including the construction of a positive-definite inner product and the existence of physical states with positive norms. Examples of $\mathcal{PT}$-symmetric Hamiltonians, such as $H = \hat{p}^2 + i\hat{x}^3$ and $H = \hat{p}^2 - \hat{x}^4$, are presented, showing that their energy levels are real and positive. The paper also addresses the Lee Model, a non-Hermitian Hamiltonian with a "ghost" state, which is reinterpreted as a $\mathcal{PT}$-symmetric Hamiltonian with a physical state having a positive norm. The author emphasizes that $\mathcal{PT}$ symmetry is a fundamental discrete symmetry of the world, as it is part of the Lorentz group, and discusses the development of the field of $\mathcal{PT}$-symmetric quantum mechanics, including the discovery of new Hamiltonians and the rigorous mathematical proofs of their properties.