The mere fact that people are doing experiments which explore time travel, and publishing their results in respected peer-reviewed journals is pretty damn amazing. The article, https://www.physorg.com/news/2011-03-grandfather-paradox.html talks about a series of experiments that are being performed by folks at MIT and elsewhere to see exactly what is preventing the grandfather paradox from occurring during time travel.
“Ah!” You might say – just make time travel against the laws of physics, and you can avoid the whole issue. Unfortunately, or perhaps fortunately, travel on the so-called “closed timelike curves,” or “CTCs” is allowed by general relativity. The problem has been how to resolve issues like the case when you show a mathematician a proof from the future and she proceeds to publish _that_proof_. The question about where that proof came from is left as an exercise for the reader. For all the details, you can read the complete paper at Physics Review Letters: https://prl.aps.org/abstract/PRL/v106/i4/e040403