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A comment on The Connection That Changed Number Theory. Parent comment
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
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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