It's well known that you can construct the octonions using triality. One statement of triality is that $\operatorname{Spin}(8)$ has nontrivial outer automorphisms of order 3. On the other hand, the| MathOverflow
How and when did the word "normal" acquire this meaning? When I first thought of this, I couldn't really come up with any explanation that wasn't complete speculation -- pretty much all I...| MathOverflow
Is there a name for the class of groups in which every two-generator subgroup is free, and any sort of characterization? Free groups and surface groups are in the class, but presumably there are many| MathOverflow
Since the old days, many mathematicians have been attaching monetary rewards to problems they admit are difficult. Their reasons could be to draw other mathematicians' attention, to express their ...| MathOverflow
Given $X = \{x_1, ..., x_n\}$, how many collections $C$ of subsets of $X$ are there such that $C$ is the listing of all open balls of some metric space? The first nontrivial example is $n=3$; let's...| MathOverflow
Let $x$ be a formal (or small, since the function is analytic) variable, and consider the power series $$ A(x) = \frac{x}{1 - e^{-x}} = \sum_{m=0}^\infty \left( -\sum_{n=1}^\infty \frac{(-x)^n}{(n+...| MathOverflow
Simple linear algebra methods are a surprisingly powerful tool to prove combinatorial results. Some examples of combinatorial theorems with linear algebra proofs are the (weak) perfect graph theor...| MathOverflow
