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For questions requesting examples of a certain structure or phenomenon

10 votes

Applications of logic to group theory?

One area where logic really helped group theory is the theory of zetafunctions of torsionfree nilpotent groups. Define $\zeta_G(s)=\sum_{U\leq G} (G:U)^{-s}$, where summation runs over all finite inde …
Jan-Christoph Schlage-Puchta's user avatar
31 votes

Mistakes in mathematics, false illusions about conjectures

The simplicial homology of a simplicial complex is not a function of the complex, but of the complex together with a simplicial decomposition. The Hauptvermutung ("main conjecture") stated that simpli …