article published yes Avi Wigderson author Yuval Wigderson author 2d0023a0-1567-11f0-833d-d5c1e476d4b5 We show how a number of well-known uncertainty principles for the Fourier transform, such as the Heisenberg uncertainty principle, the Donoho–Stark uncertainty principle, and Meshulam’s nonabelian uncertainty principle, have little to do with the structure of the Fourier transform itself. Rather, all of these results follow from very weak properties of the Fourier transform (shared by numerous linear operators), namely that it is bounded as an operator L1 → L∞, and that it is unitary. Using a single, simple proof template, and only these (or weaker) properties, we obtain some new proofs and many generalizations of these basic uncertainty principles, to new operators and to new settings, in a completely unified way. Together with our general overview, this paper can also serve as a survey of the many facets of the phenomena known as uncertainty principles. American Mathematical Society2021 eng 0273-0979 1088-9485 2006.1120610.1090/bull/1715 582225-261 yes Wigderson A, Wigderson Y. The uncertainty principle: Variations on a theme. <i>Bulletin of the American Mathematical Society</i>. 2021;58(2):225-261. doi:<a href="https://doi.org/10.1090/bull/1715">10.1090/bull/1715</a> Wigderson, Avi, and Yuval Wigderson. “The Uncertainty Principle: Variations on a Theme.” <i>Bulletin of the American Mathematical Society</i>. American Mathematical Society, 2021. <a href="https://doi.org/10.1090/bull/1715">https://doi.org/10.1090/bull/1715</a>. A. Wigderson, Y. Wigderson, Bulletin of the American Mathematical Society 58 (2021) 225–261. Wigderson, A., &#38; Wigderson, Y. (2021). The uncertainty principle: Variations on a theme. <i>Bulletin of the American Mathematical Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/bull/1715">https://doi.org/10.1090/bull/1715</a> Wigderson, Avi, and Yuval Wigderson. “The Uncertainty Principle: Variations on a Theme.” <i>Bulletin of the American Mathematical Society</i>, vol. 58, no. 2, American Mathematical Society, 2021, pp. 225–61, doi:<a href="https://doi.org/10.1090/bull/1715">10.1090/bull/1715</a>. A. Wigderson and Y. Wigderson, “The uncertainty principle: Variations on a theme,” <i>Bulletin of the American Mathematical Society</i>, vol. 58, no. 2. American Mathematical Society, pp. 225–261, 2021. Wigderson A, Wigderson Y. 2021. The uncertainty principle: Variations on a theme. Bulletin of the American Mathematical Society. 58(2), 225–261. 221752026-06-29T10:57:49Z2026-07-14T09:02:39Z