Engineering: You can apply directly, but in the end it should be strict. But practice is ahead of theory. When calculus first came out, everyone thought it was very useful and powerful, but there was no strict analytical basis. The same is true of deep learning (don't hit me, run ... if everyone uses it well, then continue to use it; If problems are found in practical application, it doesn't matter, because these conjectures are difficult to solve, that is to say, the number of counterexamples is very small, even if they exist. Applications that use these conjectures can work with high reliability, and the failure probability caused by conjectural counterexamples may be lower than that caused by other engineering reasons, such as machine downtime. ). So we can still use it! Besides, every time you find a counterexample, you can save it for special judgment, which is a perfect algorithm ... Mathematicians can breathe a sigh of relief and finally don't have to prove this damn thing, because it is wrong. Haha! Mathematically: For several very important and highly reliable conjectures, we can use them with caution.