Mathematicians are good at counting. We can count the number of ways to roll a 7 with two dice. (Answer = 6.) We can count the number of ways to shuffle a deck of cards so that every card is not in its original position. (Answer = $!52$ = 29672484407795138298279444403649511427278111361911893663894333196201.) We can count the number of lines on a cubic surface in $\mathbf{CP}^3$. (Answer = 27.) Sometimes we can count, but we don’t really know what the actual *number* is, such as when we count the minimum number of guests that must be invited so that at least $m$ will know each other or at least $n$ will not know each other. (Answer = the Ramsey number $R(m, n)$.) Many times, it is better to use an asymptotic estimate, such as Stirling’s formula. When we can’t estimate, we can bound, such as Conrey’s result that more than two-fifths of the zeros of the Riemann zeta function are on the critical line. Lately, we (along with our colleagues in other disciplines) have started counting citations. Continue reading