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Comment by hyperbovine | Hacker News Reader

> He responded that it was because people secretly "proved" everything to themselves in multiple ways, but only wrote up one proof.

I don't do pure math, but I write the occasional theory paper, and this resonates. So much ends up on the cutting room floor--usually you proved the key result three or four different ways before finding a proof that is actually incisive/aesthetically pleasing/whatever to justify signing your name to it sending it out the door. Also most mathematicians are extremely averse to even saying something that's incorrect, let alone putting in print. There's ton of sanity-checking and trying to break your own result that, again, is rarely if ever mentioned in the final publication.

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As a student working on some theory papers, I wish this kind of thing would go in an Appendix somewhere. Is it left out because it's not worth the effort to include compared to the number of people that would actually read it? Or is it something that runs the risk of negative perception by those established in the field?

It does seem like including a few alternative proofs would greatly aid in understanding.

I think it's fundamentally a question of incentives. A mathematician's career prospects and status depends heavily on being able to prove things that others can't. Why spend extra time helping your 'competitors'? Not saying this is ideal, but it seems to explain many behaviours in the community, and it seems unavoidable given the ever-increasing competition for jobs.

It's actually pretty tough to write out a proof, and going from a whiteboard where you're 99.9% sure it's right to something in LaTeX in a paper in your field is actually a long number of steps to take.

> As a student working on some theory papers, I wish this kind of thing would go in an Appendix somewhere.

For what it's worth, this kind of behavior isn't limited to theory papers. Papers presenting analysis and model development also generally only show the "finished" result, omitting most or all of the bad models, training models, development models, etc. that were used to get to the final result. Same thing with observational papers in astronomy and related fields. There's a lot of work done that builds the authors' confidence in the correctness of the result, but that doesn't lend itself to a clean "story" for the paper or perhaps also ends up being supportive but not necessary to demonstrate a result.

I remember being surprised as a student, to learn that papers aren't narrations of the path to a discovery, but rather a narrative to describe the idea in a compelling (and hopefully clear) fashion.

Oh for sure, I started out doing molecular biology so I dealt with missing methodology details all the time there - certainly some things make sense to leave out, but there were also cases where it took trial and error to replicate because details on intermediate steps were left out.

That is what it is, but in the case of theory I think the alternative proofs could actually be really educational. The exact details of a biology technique (and hyperparameter searching type stuff for that matter) don't have the same inherent interest to me.

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