This article does a fine job of disspelling the myth that group theory has no post-classification future. There is no scientific basis for this myth, since groups emerge wherever there is symmetry, and symmetry emerges wherever there is nature.

I really like the author's analogy (chemistry and the extension problem), however I wish to point out one small caveat that as well contributes to the intractability of the extension problem. Whereas every molecule is comprised of atoms, it is not the case that every finite group is comprised of finite simple groups. I speak here of the "nonsplit extension". To fit this case into the author's analogy (at least the 2-step version), one would have to imagine a molecule that consists of only one atom, but also some additional material that is defnitely not an atom. However, were that atom in this molecule to collapse to a singularity, then the molecule iteself would become another atom ... evidently one that was never present in the molecule to begin with.

Again, excellent article.

- Doc