NumPy 1.21.2 may not yet support Python 3.10

If on Windows, numpy has not yet released a precompiled wheel for Python 3.10. However you can try the unofficial wheels available at https://www.lfd.uci.edu/~gohlke/pythonlibs/#numpy . Specifically look for

• numpy‑1.21.2+mkl‑cp310‑cp310‑win_amd64.whl or
• numpy‑1.21.2+mkl‑cp310‑cp310‑win32.whl

depending on you system architecture.

After downloading the file go to the download directory and run pip install "<filename>.whl".)

(I have personally installed numpy‑1.21.2+mkl‑cp310‑cp310‑win_amd64.whl and it worked for me.)

Since you are on MS-Windows you can also make use of pipwin - this windows only utility is pip installable and can download and install a number of "unofficial" builds (provided by the excellent Christoph Gohlke) of scientific from the https://www.lfd.uci.edu/~gohlke/pythonlibs/ but takes the guesswork out of which file(s) to download and install.

A session might run:

pip install pipwin
pipwin install numpy

Alternatively you could use the py launcher as in:

py -3.10 -mpip install pipwin
py -3.10 -mpipwin refresh
py -3.10 -mpipwin install numpy

The middle step tells pipwin to populate its list of what is currently available.

If you don't mind using Docker and Debian, the official python:3.10 (==python:3.10-bullseye) docker container has pip pre-installed. And some packages like numpy can be installed using pip install and run under python 3.10 (good luck with other packages though:).

Here's some PoC and proof that numpy really works there:

$ docker run -it --rm --name python310 -u 0 python:3.10 bash -c 'pip --version; pip install numpy --user --no-cache; pip show numpy; python -c "import numpy as np; print(np.ones(5))"'

..which should output:

pip 21.2.4 from /usr/local/lib/python3.10/site-packages/pip (python 3.10)
Collecting numpy
  Downloading numpy-1.21.4-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (15.9 MB)
     |████████████████████████████████| 15.9 MB 36.9 MB/s 
Installing collected packages: numpy
  WARNING: The scripts f2py, f2py3 and f2py3.10 are installed in '/root/.local/bin' which is not on PATH.
  Consider adding this directory to PATH or, if you prefer to suppress this warning, use --no-warn-script-location.
Successfully installed numpy-1.21.4
WARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv
WARNING: You are using pip version 21.2.4; however, version 21.3.1 is available.
You should consider upgrading via the '/usr/local/bin/python -m pip install --upgrade pip' command.
Name: numpy
Version: 1.21.4
Summary: NumPy is the fundamental package for array computing with Python.
Home-page: https://www.numpy.org
Author: Travis E. Oliphant et al.
Author-email: 
License: BSD
Location: /root/.local/lib/python3.10/site-packages
Requires: 
Required-by: 
[1. 1. 1. 1. 1.]

I use Ubuntu and I had the same issue but when changed the version from 1.19.5 to 1.22.1 my issue fixed