Symmetry

By J. Tits, J. Stillwell. The American mathematical monthly, 2000

2,030 citations recorded by the source corpus.

The word "symmetry" is used in mathematics quite differently from in ordinary speech. In everyday life one applies it mainly to two-sided, right-left symmetry; but not so in mathematics. Admittedly, the word sometimes has a more general meaning in everyday speech. For example, everyone recognises that Figure 1 is highly symmetric, although it has no two-sided symmetry. However, this is really an exception. (The example of Figure 1 calls for some comment: in preparing this lecture it struck me that one can easily run into political or religious symbols when seeking examples of highly symmetric figures. This shows that symmetry has always had a powerful effect on people.)

View Paper: https://www.semanticscholar.org/paper/19a8e229c6688bdb45856da3a7e67f0520add450

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Citations in the corpus

Comments on one-form global symmetries and their gauging in 3d and 4d (2018, background): “This theory was first studied in [20] and more recently in [23, 24].”
Stochastic mechano-chemical kinetics of molecular motors: A multidisciplinary enterprise from a physicist’s perspective (2012, background): “Insight into the actual kinetics of the motor can be gained by carrying normal mode analysis (NMA) which yields the spectrum of collective modes of the elastic network [393, 394, 395, 396, 397, 398, 399, 400].”
Robust Real-Time Periodic Motion Detection, Analysis, and Applications (2000, background): “Info rmally, spatial symmetry is selfsimilarity under a class of transformations, usually the gr oup of Euclidean transformations in the plane (translations, rotations, and reflections)[36].”
NOTES ON THE ARITHMETIC OF HILBERT MODULAR FORMS (2011, background): “Let us mention that this is a special case of well-known classical branching laws from GLn(C) to GLn−1(C); see Goodman-Wallach [17].”
Quantum speed limits, coherence, and asymmetry (2015, methodology): “6) and has been previously studied as a measure of asymmetry [21,26].”
Linear Algebra (2012, background): “A beautiful book that explores some of this area is [Weyl].”
Multiscale modeling of crowdion and vacancy defects in body-centered-cubic transition metals (2007, methodology): “approximated by the sine-Gordon equation [33, 34] makes the latter a convenient model for studying Brownian motion of defects at elevated temperatures.”
Learning to group discrete graphical patterns (2017, background): “Furthermore, while symmetries can be classified into a limited number of categories [Conway et al. 2008; Weyl 1952] and can all be well-defined mathematically, fluctuating symmetries [Graham et al. 2010], along with other grouping criteria such as continuity and proximity, are imprecise and can…”
Control of multistability (2014, methodology): “A dynamical model for the pattern of contour detecting neurons in the visual cortex has been developed by Wolf [112], who introduced a permutation symmetrywhich guarantees the emergence of contour detectors for all stimulus orientations.”