alt Hacker NewsWith sufficient automation, there shouldn't really be a trade-off between rigor and anything else. The goal should be to automate as much as possible so that whatever well-defined useful thing can come out theory can come out faster and more easily. Formal proofs make sense as part of this goal.
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There are still many major oversimplifications in the core of math, making it weirdly corresponding with the real world. For example, if you want to model human reasoning you need to step away from binary logic that uses "weird" material implication that is a neat shortcut for math to allow its formalization but doesn't map well to reasoning. Then you might find out that e.g. medicine uses counterfactuals instead of material implication. Logics that tried to make implication more "reasonable" like relevance logic are too weak to allow formalization of math. So you either decide to treat material implication as correct (getting incompleteness theorem in the end), making you sound autistic among other humans, or you can't really do rigorous math.
The thing is if something is proved by checking million different cases automatically, it makes it hard to factor in learning for other proofs.
Let’s not forget that mathematics is a social construct as much as (and perhaps more than) a true science. It’s about techniques, stories, relationships between ideas, and ultimately, it’s a social endeavor that involves curiosity satisfaction for (somewhat pedantic) people. If we automate ‘all’ of mathematics, then we’ve removed the people from it.
There are things that need to be done by humans to make it meaningful and worthwhile. I’m not saying that automation won’t make us more able to satisfy our intellectual curiosity, but we can’t offload everything and have something of value that we could rightly call ‘mathematics’.