October 3, 2006
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A Serious Theorem
Serious
“I don’t think the ‘diamond theorem’ is anything serious, so I started with blitzing that.”
– Charles Matthews at Wikipedia, Oct. 2, 2006
“The ‘seriousness’ of a mathematical theorem lies, not in its practical consequences, which are usually negligible, but in the significance of
the mathematical ideas which it connects. We may say, roughly, that a
mathematical idea is ‘significant’ if it can be connected, in a natural
and illuminating way, with a large complex of other mathematical
ideas.”– G. H. Hardy, A Mathematician’s Apology
Matthews yesterday deleted references to the diamond theorem and related material in the following Wikipedia articles:
Affine group
Reflection group
Symmetry in mathematics
Incidence structure
Invariant (mathematics)
Symmetry
Finite geometry
Group action
History of geometryThis would appear to be a fairly large complex of mathematical ideas.
See also the following “large complex” cited, following the above words of Hardy, in Diamond Theory:
Affine
geometry, affine planes, affine spaces, automorphisms, binary codes,
block designs, classical groups, codes, coding theory, collineations,
combinatorial, combinatorics, conjugacy classes, the Conwell
correspondence, correlations, design theory, duads, duality, error
correcting codes, exceptional groups, finite fields, finite geometry,
finite groups, finite rings, Galois fields, generalized quadrangles,
generators, geometry, GF(2), GF(4), the (24,12) Golay code, group
actions, group theory, Hadamard matrices, hypercube, hyperplanes,
hyperspace, incidence structures, invariance, Karnaugh maps, Kirkman’s
schoolgirls problem, Latin squares, Leech lattice, linear groups,
linear spaces, linear transformations, Mathieu groups, matrix theory,
Meno, Miracle Octad Generator, MOG, multiply transitive groups, octads,
the octahedral group, orthogonal arrays, outer automorphisms,
parallelisms, partial geometries, permutation groups,
PG(3,2), polarities, Polya-Burnside theorem, projective geometry,
projective planes, projective spaces, projectivities, Reed-Muller
codes, the relativity problem, Singer cycle, skew lines, sporadic
simple groups, Steiner systems, symmetric, symmetry, symplectic,
synthemes, synthematic, tesseract, transvections, Walsh functions, Witt
designs.
