The paper "The Uncertainty Principle: A Mathematical Survey" by Gerald B. Folland and Alladi Sitaram provides an overview of various mathematical aspects of the uncertainty principle, including Heisenberg's inequality and its variants, local uncertainty inequalities, logarithmic uncertainty inequalities, results related to Wigner distributions, qualitative uncertainty principles, theorems on approximate concentration, and decompositions of phase space. The authors emphasize that the uncertainty principle has both physical and mathematical significance, describing limitations in quantum mechanics and classical physics. In quantum mechanics, it states that the values of canonically conjugate observables like position and momentum cannot both be precisely determined. In classical physics, it relates to the limitations on time-limited and band-limited signals. The paper also discusses the historical development of the uncertainty principle, from Heisenberg's 1927 paper to modern research, and highlights its impact on areas such as signal analysis, wavelet theory, and communication theory. The authors fix notation and terminology, defining key concepts like Fourier transforms, probability measures, and variance, and provide a foundation for the mathematical exploration of the uncertainty principle.The paper "The Uncertainty Principle: A Mathematical Survey" by Gerald B. Folland and Alladi Sitaram provides an overview of various mathematical aspects of the uncertainty principle, including Heisenberg's inequality and its variants, local uncertainty inequalities, logarithmic uncertainty inequalities, results related to Wigner distributions, qualitative uncertainty principles, theorems on approximate concentration, and decompositions of phase space. The authors emphasize that the uncertainty principle has both physical and mathematical significance, describing limitations in quantum mechanics and classical physics. In quantum mechanics, it states that the values of canonically conjugate observables like position and momentum cannot both be precisely determined. In classical physics, it relates to the limitations on time-limited and band-limited signals. The paper also discusses the historical development of the uncertainty principle, from Heisenberg's 1927 paper to modern research, and highlights its impact on areas such as signal analysis, wavelet theory, and communication theory. The authors fix notation and terminology, defining key concepts like Fourier transforms, probability measures, and variance, and provide a foundation for the mathematical exploration of the uncertainty principle.