History of Mathematics: Conventions

It is strange that it should be so, but it is true all the same, that many of the most debated aspects of Mathematics concern matters that are really completely trivial.  They arise from questions of how we make our definitions.  Such matters are referred to as conventions. Start with a simple example:
Is $1$ a prime number?
One very common definition of a prime number is that it is a natural number that has no divisors other than itself and $1$.  If we use this definition then clearly $1$ is prime.