After running the following SQL statements, you will see that, MySQL has automatically created the non-unique index question_tag_tag_id_tag_id on the tag_id column for me after the first ALTER TABLE statement has run.

But after the second ALTER TABLE statement has run, I think MySQL should also automatically create another non-unique index question_tag_question_id_question_id on the question_id column for me.

But as you can see from the SHOW INDEXES statement output, it's not there.

Why does MySQL forget about the second ALTER TABLE statement?

By the way, since I have already created a unique index question_id_tag_id_idx used by both question_id and tag_id columns. Is creating a separate index for each of them redundant?

mysql> DROP DATABASE mydatabase;
Query OK, 1 row affected (0.00 sec)

mysql> CREATE DATABASE mydatabase;
Query OK, 1 row affected (0.00 sec)

mysql> USE mydatabase;
Database changed
mysql> CREATE TABLE question (id BIGINT AUTO_INCREMENT, html TEXT, PRIMARY KEY(id)) ENGINE = INNODB;
Query OK, 0 rows affected (0.05 sec)

mysql> CREATE TABLE tag (id BIGINT AUTO_INCREMENT, name VARCHAR(10) NOT NULL, UNIQUE INDEX name_idx (name), PRIMARY KEY(id)) ENGINE = INNODB;
Query OK, 0 rows affected (0.05 sec)

mysql> CREATE TABLE question_tag (question_id BIGINT, tag_id BIGINT, UNIQUE INDEX question_id_tag_id_idx (question_id, tag_id), PRIMARY KEY(question_id, tag_id)) ENGINE = INNODB;
Query OK, 0 rows affected (0.00 sec)

mysql> ALTER TABLE question_tag ADD CONSTRAINT question_tag_tag_id_tag_id FOREIGN KEY (tag_id) REFERENCES tag(id);
Query OK, 0 rows affected (0.10 sec)
Records: 0  Duplicates: 0  Warnings: 0

mysql> ALTER TABLE question_tag ADD CONSTRAINT question_tag_question_id_question_id FOREIGN KEY (question_id) REFERENCES question(id);
Query OK, 0 rows affected (0.13 sec)
Records: 0  Duplicates: 0  Warnings: 0

mysql> SHOW INDEXES FROM question_tag;
+--------------+------------+----------------------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+
| Table        | Non_unique | Key_name                   | Seq_in_index | Column_name | Collation | Cardinality | Sub_part | Packed | Null | Index_type | Comment |
+--------------+------------+----------------------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+
| question_tag |          0 | PRIMARY                    |            1 | question_id | A         |           0 |     NULL | NULL   |      | BTREE      |         |
| question_tag |          0 | PRIMARY                    |            2 | tag_id      | A         |           0 |     NULL | NULL   |      | BTREE      |         |
| question_tag |          0 | question_id_tag_id_idx     |            1 | question_id | A         |           0 |     NULL | NULL   |      | BTREE      |         |
| question_tag |          0 | question_id_tag_id_idx     |            2 | tag_id      | A         |           0 |     NULL | NULL   |      | BTREE      |         |
| question_tag |          1 | question_tag_tag_id_tag_id |            1 | tag_id      | A         |           0 |     NULL | NULL   |      | BTREE      |         |
+--------------+------------+----------------------------+--------------+-------------+-----------+-------------+----------+--------+------+------------+---------+
5 rows in set (0.01 sec)

mysql>