The art of counting

Mathematics is certainly not limited to "performing calculations on numbers". However, the problem of counting objects is more stimulating than it seems: can we count everything exactly, or at least approximately? Is it useful to have a precise numerical value, or is an estimate sufficient? In each situation, the mathematical techniques used will be different: enumerations, combinatorial reasoning, algebraic tools, set bijections. To count a population, one will prefer statistics, models, estimators. Counting is no small feat!

Positive integers are the simplest to conceive, they are even called 'natural'. Yet they contain rich and surprising properties. Some of them bear the name of the person who studied them, or even, one might say, discovered them. Whether they answer a counting question, possess remarkable arithmetic properties, or denote orders of magnitude that are difficult to conceive, encountering some of these 'numbers named after…' is an opportunity to explore the history of mathematics.