A past tense in the main clause may be followed by a present tense in the subordinate clause when the subordinate clause expresses a universal truth.
Galileo maintained that the earth moves around the sun. (More natural than ‘Galileo maintained that the earth moved around the sun.’)
The teacher said that honesty is the best policy.
Newton discovered that the force of gravitation makes objects fall.
When the subordinate clause is introduced by than, it may be followed by any tense.
He liked you better than he likes me.
He valued your friendship more than he values mine.
When the verb in the main clause is in the present or future tense, the verb in the subordinate clause can be in any tense.
I believe that she is there.
I believe that she was there.
I believe that she will be there.
He will think that we are there.
He will think that we were there.
Note that when the subordinate clause indicates purpose, it must be in the present tense if the verb in the main clause is in the present or future tense.
We eat that we may live. (NOT We eat that we might live.)
She works hard that she may pass.