The documentation says the following:

> A built-in function object is a wrapper around a C function.  Examples of built-in functions are `len` and `math.sin` (`math` is a standard built-in module).

However, `math` is not always a built-in module, as can be seen in on my own Python installation (Windows 10, WSL 1, Python 3.7.7 installed via conda).

>>> import sys
>>> sys.builtin_module_names
('_abc', '_ast', '_codecs', '_collections', '_functools', '_imp', '_io', '_locale', '_operator', '_signal', '_sre', '_stat', '_string', '_symtable', '_thread', '_tracemalloc', '_warnings', '_weakref', 'atexit', 'builtins', 'errno', 'faulthandler', 'gc', 'itertools', 'marshal', 'posix', 'pwd', 'sys', 'time', 'xxsubtype', 'zipimport')

Therefore, I have submitted a pull request to remove the statement "(`math` is a standard built-in module)" from the documentation.

What happens when you type, "import math" and "print(type(math))"?

Here's the output from my terminal comparing the `math` standard library module (not always built-in) against the `sys` standard library module (always built-in).

On Windows 10 x64, WSL 1, Ubuntu 18.04.02 LTS, Python 3.7.7 installed via conda: math is not a built-in module.

$ python
Python 3.7.7 (default, Mar 26 2020, 15:48:22)
[GCC 7.3.0] :: Anaconda, Inc. on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import math
>>> print(math)
<module 'math' from '/home/chris/miniconda3/envs/py37/lib/python3.7/lib-dynload/math.cpython-37m-x86_64-linux-gnu.so'>
>>> print(type(math))
<class 'module'>
>>> import sys
>>> print(sys)
<module 'sys' (built-in)>
>>> print(type(sys))
<class 'module'>


On Windows 10 x64, Python installed directly from Python.org: math is a built-in module.

C:\>python
Python 3.7.3 (v3.7.3:ef4ec6ed12, Mar 25 2019, 22:22:05) [MSC v.1916 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import math
>>> print(math)
<module 'math' (built-in)>
>>> print(type(math))
<class 'module'>
>>> import sys
>>> print(sys)
<module 'sys' (built-in)>
>>> print(type(sys))
<class 'module'>

FWIW, the word "built-in" is being used in two different ways here.  It is used in a strict sense for sys.builtin_module_names and in a general sense in the datamodel docs.

The former only includes modules compiled into the core exe or dll file.  The latter includes anything in compiled extension such as the math module.  The latter is part of the standard build in the sense that it is included in setup.py and parts of the library depend on it being present:

    ~ $ python3.8
    Python 3.8.3 (v3.8.3:6f8c8320e9, May 13 2020, 16:29:34)
    [Clang 6.0 (clang-600.0.57)] on darwin
    Type "help", "copyright", "credits" or "license" for more information.
    >>> import sys
    >>> 'math' in sys.builtin_module_names     
    >>> False
    >>> import math
    >>> type(math.sin)
    <class 'builtin_function_or_method'>

I understand the two uses of the phrase "built-in":

1) to refer to things included with the Python interpreter (e.g. modules in sys.builtin_module_names, and built-in functions like len() and ord())
2) to refer to things included with Python that are written in C

However, I find it fairly difficult to distinguish between the two uses in the context presented:

> A built-in function object is a wrapper around a C function.  Examples of built-in functions are `len` and `math.sin` (`math` is a standard built-in module).

Within the Python Language Reference (docs.python.org/3/reference), this is actually the only case where definition (2) applies, as far as I can tell: https://www.google.com/search?q="built-in+module"+site%3Ahttps%3A%2F%2Fdocs.python.org%2F3%2Freference%2F

Also, I am not sure that the parenthetical about `math` being a module written in C adds any additional clarity.