Reported Speech

Hello.
Reported speech means go back in tenses, doens't it?
But when I don't go back? When it's a proverb or a universal true(2+2=4)?

And what I have to change?
Today ->That day
Yesterday->The previous day
Tomorrow->The next day????
Last week->The previous week?

Can you add more? Or is it all?
Thank you :)

One point at a time.

When the word introducing the reported speech is in a past tense (said, told, thought, etc), then it is almost always correct to backshift, i.e. move the tense one step back:

"I like..." - He said that he liked ...
"I have seen her." - He told me that he had seen her
"I will try ..." - He said that he would try.

If the situation spoken of is still true at the moment of reporting, then we can backshift, but we do not have to:

"I love you." - (reported soon after:) He told me that he loves/loved me.
"We are leaving at 6.30" - (reported before 6.30:) He said that we are/were leaving at 6.30.
"Czechs drink more beer than Germans." - The guide claimed that Czechs drink/drank more beer than Germans.

And what about words today,....? do I have to backshift them?

It depends where you are in terms of time.

10 am: John says "I will do it later today."
1 pm: I say "John said he would do it later today.

Three days later: John said that he would do it later that day. Did he get it done?

Jan 1: John says "I want to go to Prague this year."
June 15: John said that he wanted to go to Prague this year.

Otherwise, yes, the prior/previous day/week/month/year, or the next day/week/month/year depending on how much later it is when you say it.

Hello, I have a question again :)
If a universal truth musn't be backshifted, what about this:

Columbus discovered America.
It's a universal truth. Do I have to backshift it, or not?:?:

Nobody said that a universal truth must not be backshifted. It can, but it does not have to be.

ScarlettBegoni claimed that Columbus discovered America.

The past perfect is possible, but the past simple is fine.