下面我包括了最新的说明从brew安装mysql，以便更新搜索这个问题可以受益:

$ brew install mysql
==> Downloading https://homebrew.bintray.com/bottles/mysql-5.6.26.yosemite.bottle.1.tar.gz
######################################################################## 100.0%
==> Pouring mysql-5.6.26.yosemite.bottle.1.tar.gz

To connect:
    mysql -uroot

To have launchd start mysql at login:
  ln -sfv /usr/local/opt/mysql/*.plist ~/Library/LaunchAgents
Then to load mysql now:
  launchctl load ~/Library/LaunchAgents/homebrew.mxcl.mysql.plist
Or, if you don't want/need launchctl, you can just run:
  mysql.server start

在我的情况下，我现在通过launchctl load加载mysql ~/Library/LaunchAgents/homebrew.mx .mysql。Plist，然后能够启动$ mysql和我的方式。

这可能是因为MySQL已经安装但还没有运行。

要验证它正在运行，打开活动监视器，在“所有进程”下，搜索并验证你看到了进程“mysqld”。

你可以通过安装“MySQL.prefPane”来启动它。

以下是帮助我的完整教程: http://obscuredclarity.blogspot.in/2009/08/install-mysql-on-mac-os-x.html

在我的mac m1 macOS Monterey上安装MySQL后，使用brew安装MySQL，我得到了以下信息:

[System] [MY-013169] [Server] /opt/homebrew/Cellar/mysql/8.0.27_1/bin/mysqld (mysqld 8.0.27) initializing of server in progress as process 3624

[ERROR] [MY-010457] [Server] --initialize specified but the data directory has files in it. Aborting.

[ERROR] [MY-013236] [Server] The designated data directory /opt/homebrew/var/mysql/ is unusable. You can remove all files that the server added to it.

[ERROR] [MY-010119] [Server] Aborting

[System] [MY-010910] [Server] /opt/homebrew/Cellar/mysql/8.0.27_1/bin/mysqld: Shutdown complete (mysqld 8.0.27)  Homebrew.

还有这个警告:

Warning: The post-install step did not complete successfully You can
try again using:   brew postinstall mysql

之后，我尝试使用brew services启动MySQL，我得到了这个错误:

ERROR 2002 (HY000): Can't connect to local MySQL server through socket
'/tmp/mysql.sock' (2)

我设法修复它使用:

> rm -rf ~/opt/homebrew/var/mysql/
> brew postinstall mysql

现在您可以使用mysql -uroot或mysql -uroot -p连接。

在做了几个小时之后，对我有用的是 进入/etc/mysql/，编辑my.cnf文件。添加以下内容

[client]
port = 3306
socket = /var/run/mysqld/mysqld.sock

我经历了这个问题，我设法运行mysql服务器使用下面的解决方案

通过.dmg(https://dev.mysql.com/downloads/mysql/5.7.html)安装mysql，你会在系统首选项中看到mysql服务面板，然后从面板中启动mysql并尝试

Mysql -u root -p

附图供参考

执行命令:brew info mysql

按照说明做。由公式中的描述可知:

Set up databases to run AS YOUR USER ACCOUNT with:
    unset TMPDIR
    mysql_install_db --verbose --user=`whoami` --basedir="$(brew --prefix mysql)" --datadir=/usr/local/var/mysql --tmpdir=/tmp

To set up base tables in another folder, or use a different user to run
mysqld, view the help for mysql_install_db:
    mysql_install_db --help

and view the MySQL documentation:
  * http://dev.mysql.com/doc/refman/5.5/en/mysql-install-db.html
  * http://dev.mysql.com/doc/refman/5.5/en/default-privileges.html