This overview paper treats the sampling theorem of signal analysis, and especially a variety of its applications in mathematics. These include fractional and infinite series forms of classical combinatorial identities, such as the Chu-Vandermonde convolution formula and some identities due to Hagen, the Gauss summation formula for hypergeometric functions, sampling of Stirling functions of first kind in terms of Stirling numbers, formulae expressing higher order fractional derivatives in terms of infinite sums involving higher order differences, connections between the Riemann zeta function and Stirling functions as well as conjugate Bernoulli functions. Some open problems are mentioned.