In a sense even this is not true, as in any sufficiently complex (which turns out to be quite simple) formal system you can create proofs that are true and untrue at the same time creating a contradiction. In other words, mathematics works by setting up useful axioms and following up on the logical consequences, but they usually can be used to create contradictory proofs even if useful in many problems.

I recommend learning about Gödel’s incompleteness theorem behind it all.

For a pop science book that explains it nicely I recommend ”I am a strange loop”. The wiki intro is also quite good

https://en.m.wikipedia.org/wiki/G%C3%B6del%27s_incompletenes...