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

这发生在自制程序安装之后，由于权限问题而发生。下面的命令解决了这个问题。

sudo chown -R _mysql:mysql /usr/local/var/mysql

sudo mysql.server start

对于我的例子，只需将host指定为127.0.0.1，而不是localhost:

$ bin/mysql -uroot -p -h127.0.0.1
Enter password:
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 8
Server version: 8.0.26

Copyright (c) 2000, 2021, Oracle and/or its affiliates.

Oracle is a registered trademark of Oracle Corporation and/or its
affiliates. Other names may be trademarks of their respective
owners.

Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.

mysql>

看起来你的mysql服务器没有启动。我通常运行stop命令，然后重新启动:

mysqld stop
mysql.server start

同样的错误，这也适用于我。

这个问题与/usr/local/var/mysql文件夹访问有关，我删除这个文件夹并重新安装mysql。

用brew卸载mysql: 卸载mysql 执行rm -r /usr/local/var/mysql Brew install mysql@8.0 Mysql -u root

这个解决方案很适合我! 但是你丢失了所有的数据库!警告!