Sadly, your inability to comprehend is noted which leaks your lack of expertise with the subject matter.
For a general overview, assuming good faith and a genuine willingness to learn, refer to https://iep.utm.edu/s-truth/
Its a remarkable intro into propositions, statements and sentences with vivid examples from the works of Tarski, Godel and others as to what constitutes truth.
Pay attention to Tarski’s T-Scheme (sentences and truths)
That is a dense extremely compressed version of my comment (on logic) and emphasizes the process (narrative selection) used and the purpose for the whole endeavor.
Each word in your sentence is load bearing.
Casual readers might find the density intimidating.
The act of stitching together, a series of sentences as true is what logic is.
If you make the stitching as airtight as possible, congratulations, you are in the realm of math.
If you are stitching together reasonably similiar to how the masses do, congratulations you have common sense.
If you stitch together completely random sentences, you are in the realm of nonsense and you may be classified as a retard.
The weapon is the same. The discipline differs and hence the effort to produce the chain.
So I am not at all worried about LLMs producing math proofs.
Godel with his incompleteness theorem helps one sleep easy. Rest assured no LLM can fly above Godel Incompleteness theorem.
There will always be statements that are true. So yes, it is time to celebrate.