在 macOS 升级到 10.13.1 之后，原来安装的 MySQL 就多多少少出现了问题。于是决定重装：

// 1、先移除之前错误的；

$ brew remove mysql
Uninstalling /usr/local/Cellar/mysql/5.7.20... (324 files, 233.7MB)

// 2、brew重新安装mysql

$ brew install mysql
Updating Homebrew...
==> Downloading https://homebrew.bintray.com/bottles/mysql-5.7.20.high_sierra.bo
Already downloaded: /Users/kokia/Library/Caches/Homebrew/mysql-5.7.20.high_sierra.bottle.tar.gz
==> Pouring mysql-5.7.20.high_sierra.bottle.tar.gz
==> Caveats
We've installed your MySQL database without a root password. To secure it run:
    mysql_secure_installation

MySQL is configured to only allow connections from localhost by default

To connect run:
    mysql -uroot

To have launchd start mysql now and restart at login:
  brew services start mysql
Or, if you don't want/need a background service you can just run:
  mysql.server start
==> Summary
🍺  /usr/local/Cellar/mysql/5.7.20: 324 files, 233.7MB
kokiadeMacBook-Pro:var kokia$ mysql -uroot
ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO)

// 3、直接使用 mysql -uroot，出现如下错误提示：
// 原因是 mysql 服务没有启动，故尝试 mysql.server start，结果如下，依然出错。

$ mysql -uroot
ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO)


$ mysql.server start
Starting MySQL
... ERROR! The server quit without updating PID file (/usr/local/var/mysql/kokiadeMacBook-Pro.local.pid).

最终的处理方式是 mysqld ：

通过 mysqld 直接启动 mysql。
由于 HomeBrew 安装的 mysql 默认root账户没有设置密码，故按照提示输入 mysql_secure_installation 来设置密码。
设置完成以后，就可以正常操作 mysql 了。

$ mysqld

$ brew services start mysql
Service `mysql` already started, use `brew services restart mysql` to restart.

$ brew services restart mysql
Stopping `mysql`... (might take a while)
==> Successfully stopped `mysql` (label: homebrew.mxcl.mysql)
==> Successfully started `mysql` (label: homebrew.mxcl.mysql)

$ mysql -uroot
Welcome to the MySQL monitor.  Commands end with ; or \g.
Your MySQL connection id is 3
Server version: 5.7.20 Homebrew

Copyright (c) 2000, 2017, Oracle and/or its affiliates. All rights reserved.

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> show databases;
+--------------------+
| Database           |
+--------------------+
| information_schema |
| mysql              |
| performance_schema |
| sys                |
+--------------------+
4 rows in set (0.00 sec)

mysql> 

mysql_secure_installation 密码长度8，12345678

$ mysql_secure_installation

Securing the MySQL server deployment.

Connecting to MySQL using a blank password.

VALIDATE PASSWORD PLUGIN can be used to test passwords
and improve security. It checks the strength of password
and allows the users to set only those passwords which are
secure enough. Would you like to setup VALIDATE PASSWORD plugin?

Press y|Y for Yes, any other key for No: y

There are three levels of password validation policy:

LOW    Length >= 8
MEDIUM Length >= 8, numeric, mixed case, and special characters
STRONG Length >= 8, numeric, mixed case, special characters and dictionary                  file

Please enter 0 = LOW, 1 = MEDIUM and 2 = STRONG: 0
Please set the password for root here.

New password: 

Re-enter new password: 

Estimated strength of the password: 50 
Do you wish to continue with the password provided?(Press y|Y for Yes, any other key for No) : y
By default, a MySQL installation has an anonymous user,
allowing anyone to log into MySQL without having to have
a user account created for them. This is intended only for
testing, and to make the installation go a bit smoother.
You should remove them before moving into a production
environment.

Remove anonymous users? (Press y|Y for Yes, any other key for No) : y
Success.


Normally, root should only be allowed to connect from
'localhost'. This ensures that someone cannot guess at
the root password from the network.

Disallow root login remotely? (Press y|Y for Yes, any other key for No) : y
Success.

By default, MySQL comes with a database named 'test' that
anyone can access. This is also intended only for testing,
and should be removed before moving into a production
environment.


Remove test database and access to it? (Press y|Y for Yes, any other key for No) : y
 - Dropping test database...
Success.

 - Removing privileges on test database...
Success.

Reloading the privilege tables will ensure that all changes
made so far will take effect immediately.

Reload privilege tables now? (Press y|Y for Yes, any other key for No) : y
Success.

All done! 

http://linfuyan.com/install_mysql_via_brew_on_osx_eicapitan/