[goldenkey]

This even extends to the hardest problems in mathematics and science. Solve the Riemann Hypothesis for real? Good luck getting the community to actually take a look at your paper and award you for it. Us problem solvers like these "pure" fields because we idealize a world where the work indisputably speaks for itself. Unfortunately without the sales and connection bullshido, no one will ever look at your profound work to see that it is world changing. Yeah, fuck everything about this. That's why Coq and Lean and all the other formal systems are ideal. I solve a problem, the system validates it. Now listen Clay, give me the motherfucking million!

[Penyngton]

That's not my experience at all. To be fair, I've never solved the Riemann Hypothesis, but in my experience it is possible to find professional academic mathematicians who were willing to meet me (as an outsider) to discuss their work and my ideas in a serious way.

Obviously, you have to bear in mind that high-profile mathematicians do get contacted by cranks and they have to weigh up what's worth spending their time on, but I have no doubt that if I did chance upon a genuine proof of the Riemann Hypothesis, I'd be able to find a decently respected mathematician to look at it and help me to publish it in a form acceptable to the academic community.

On the other hand, I agree with your comment about formal proof systems, and I'd love to use them in my (pure mathematical) research, but I've found the usability isn't there for me yet.

[derbOac]

I have mixed experience publishing in math and statistics. I've had some of the best and worst experiences there compared to more applied fields. There's just been much more variability.

The comments and feedback, handled by the right editor, have been some of the most thoughtful, logical, and rigorous I've had of all my papers. The sort that, even when I disagree, think are very good questions to ask of the submission. Those that catch errors, and those that improve the paper in new, thoughtful directions.

At the same time, my worst peer review experiences have also been in more "pure" math and statistics. When they're bad, they're bad. The worst corruption and obvious jealousy have been in publishing in these areas, so convoluted that it would almost take an entire blog post series to explain. Reviewers can get really caught up on missing the forest for the trees and not understand the applied utility of something, even if it's technically correct, if it's not part of standard procedure. Othertimes it's been obvious (in the sense that if I published the entire review publicly I'm confident public opinion would come to that conclusion) reviewers have been jealous, and have tanked submissions in journals by piling up small criticisms that have nothing to do with the primary theses being argued. Usually in these cases, the failure ultimately comes down to an editor not wanting to ruffle the feathers of someone prominent.

These things all happen in applied fields too, but it seems like there, there's a softening around the edges of sorts, so the problematic behaviors aren't as extreme or obvious, and people sort of expect that fuzziness, so everything is taken with a grain of salt. I think the rigorousness of things like pure math can cut both ways, in that when it's correct, and everyone is behaving rationally, and the process is working with integrity, it produces very rigorous, solid work at the end. However, when it's incorrectly applied, and people are behaving irrationally (these are humans, it is inevitable), and the process is tainted, it can stifle novel work, or lead to really misleading conclusions.

I suspect that, if it's not already happening, I think one of the next phases in documentation of the reproducibility crisis and academic problems is in the areas of math, stats, and computer science. These fields have a veneer of rigor which can be true, but can also lead to false assumptions about the process that produces results. I think you're already seeing this a bit on HN with posts about reproducibility of AI findings, and with things like Taleb's criticism of academic models (FWIW Taleb has his own problems, but I think as a public figure he's correct to point out these things), but there's a lot more going on behind the curtain.

[Penyngton]

Yes, certainly things like corruption, jealousy and ego games do exist in pure maths, but I just wanted to contest the other comment's assertion that pure mathematics is completely closed to outsiders, let alone ones who could resolve the Riemann Hypothesis.

Furthermore, I could believe that the above issues and, as you also mention, reproducibility, are worse in pure mathematics or theoretical CS than in other fields because so little is at stake. Which is not to say I think most maths papers are false, but just that they're not all _entirely_ true either. Their audience is so small and the readers/reviewers "know what they mean" anyway, most of the time. And others are just false and no-one noticed because they couldn't be bothered to check the details, because the result was inconsequential to their own work and the author was a nice enough chap...