toosimpletobe

Non-primality of 1 is a design decision made by the mathematical community. A convention with which one can agree or disagree.

But it is part of a general pattern that certain objects are "too simple to be simple" [0].

Here "simple" should be thought of as atomic, indecompossible, without smaller parts.

- prime numbers are simple wrt multiplication, 1 is too simple to be prime

- the zero ring is too simple to be a field

- the trivial group is too simple to be a simple group

- the empty topological space is not connected

- etc...

It turns out that if one adheres to this convention, then theorem statements generally become shorter, and have fewer side conditions.

[0]: https://ncatlab.org/nlab/show/too+simple+to+be+simple