My current understanding is that work submitted to journals has mathematicians look over it for errors. Mathematics is deductive, yet with this being the burden of proof, how can we know for sure there have been no mistakes and we are demanding enough rigour in our burden of proof?
For example, in the 20th and 19th century I know there were some issues when calculus was not formalised rigorously enough, leading to contradictions. Also, when you go to higher levels mathematics, you find that your previous acceptable burden of proof was totally inadequate. I am concerned because, if we cannot be sure, then mathematics instead becomes very empirical - we use a certain burden of proof only because that has not led to any contradictions yet.
I read the comments in >implying we can discuss mathematics, title 'I recently came into an innocent-looking discussion, which leads me to ask the following: Do you think mathematics is a science? Why? Why not?'
I also read these articles, but haven't found a satisfactory answer yet. Thanks!
https://www.newscientist.com/article/mg19125661-400-mathematics-the-burden-of-proof/
https://thesociablesolipsist.com/2018/08/26/is-mathematics-empirical/