"No matching distribution found" on all pip installations in PyCharm
<p>I'm on Windows 7 running PyCharm Community Edition 2016.1.2 and Python 3.4.3, and I have the following behavior:</p>

<ul>
<li>Installing new packages in PyCharm (from Settings -> Project Interpreter) failed with the error message <code>No matching distribution found for [package name]</code>, e.g. <code>No matching distribution found for numpy</code>.</li>
<li>Updating packages in PyCharm (from Settings -> Project Interpreter) claimed to succeed with a <code>Package successfully installed</code> notification, but did not change the package version in the table (and did not actually do the update).</li>
<li>Installing new packages on the command line with pip (e.g. <code>pip install numpy</code> failed with the same error message as PyCharm.</li>
<li>Updating packages on the command line gave the output <code>Requirement already up-to-date</code> and no update.</li>
</ul>

<p>What????</p>