Editing Singularity theory (section)

===Arnold's view===
While Thom was an eminent mathematician, the subsequent fashionable nature of elementary [[catastrophe theory]] as propagated by [[Christopher Zeeman]] caused a reaction, in particular on the part of [[Vladimir Arnold]].<ref>{{harvnb|Arnold|1992}}</ref> He may have been largely responsible for applying the term '''''singularity theory''''' to the area including the input from algebraic geometry, as well as that flowing from the work of Whitney, Thom and other authors. He wrote in terms making clear his distaste for the too-publicised emphasis on a small part of the territory. The foundational work on smooth singularities is formulated as the construction of [[equivalence relation]]s on singular points, and [[germ (mathematics)|germs]]. Technically this involves [[Group action (mathematics)|group action]]s of [[Lie group]]s on spaces of [[jet (mathematics)|jet]]s; in less abstract terms [[Taylor series]] are examined up to change of variable, pinning down singularities with enough [[derivative]]s. Applications, according to Arnold, are to be seen in [[symplectic geometry]], as the geometric form of [[classical mechanics]].