The Fishburn numbers, originally considered by Peter C. Fishburn, have been shown to enumerate a variety of combinatorial objects. These include unlabelled interval orders on $n$ elements, $(2+2)$–avoiding posets with $n$ elements, upper triangular matrices with nonnegative integer entries and without zero rows or columns such that the sum of all entries equals $n$, non–neighbor–nesting matches on $[2n]$, a certain set of permutations of $[n]$ which serves as a natural superset of the set of $231$–avoiding permutations of $[n]$, and ascent sequences of length $n$.
Soon after learning about these numbers in late 2013, George Andrews and I were led to study the Fishburn numbers from an arithmetic point of view - something which had not been done prior. In the process, we proved that the Fishburn numbers satisfy infinitely many Ramanujan–like congruences modulo certain primes $p$. In this talk, we will describe this result in more detail as well as discuss how our work has served as the motivation for related work by several others since then.