Most scientists 'can't replicate studies by their peers'

A lot of this is because of the incentives that result from grant-based funding of science. Your ability to continue to do science is contingent on your ability to find someone to pay for it; it's much easier to convince someone to pay for it if you can point to headlines that say "Breakthrough research! Is the end of cancer in sight?"

The old system of "gentleman science" (where only independently-wealthy heirs did science, as a hobby) had a lot of problems and wouldn't really be workable today, but one thing it had going for it was that the scientist could count on the funding being there tomorrow, and so had much less of an incentive to overstate their work.

I work as an applied mathematician. In general, I would say that this is incorrect. Virtually all of the papers that I read I would contend have full proofs. That said, I can sympathize with the sentiment in a certain sense.

Just because a paper contains a proof doesn't mean that the proof is correct nor that it's comprehensible. Further, even if a paper went through peer review, it doesn't mean that it was actually reviewed. I'll break each of these down.

First, a proof is just an argument that an assertion is true or false. Just like with day to day language, there are good arguments and bad arguments. Theoretically, math contains an agreed upon set of notation and norms to make its language more precise, but most people don't abide by this. Simply, very, very few papers use the kind of notation that's read by proof assistant tools like Coq. This is the kind of metalanguage really required for that precise. Now, on top of the good and bad argument contention, I would also argue that there's a kind of culture and arrogance associated with how the community writes proofs. Some years back, I had a coauthor screaming at me in his office because I insisted that every line in a sequence of algebraic reductions remain in the paper with labels. His contention was that it was condescending to him and the readers to have these reductions. My contention was that I, as the author of the proof, couldn't figure out what was going on without them and if I couldn't figure it out with all those details that I sincerely doubt the readers could either. Around the office, there was a fair amount of support for my coauthor and removing details of the proof. This gives an idea of the kind of people in the community. For the record, the reductions remained in the submitted and published paper. Now, say we removed all of these steps. Did we still have a full proof? Technically yes, but I would call it hateful because it would require a hateful amount of work by the readers to figure out what was going on.

Second, peer review is tricky and often incredibly biased. Every math journal I've seen asks the authors to submit to a single blind review meaning that the authors don't know their reviewers, but the reviewers know the authors. If you are well known and well liked in the field, you will receive the benefit of the doubt if not a complete pass on submitted work. I've seen editors call and scream at reviewers who gave "famous" people bad reviews. I feel like I was blacklisted from one community because I rejected a paper from another "famous" person who tried to republish one of their previous papers almost verbatim. In short, there's a huge amount of politics that goes into the review process. Further, depending on the journal, sometimes papers are not reviewed at all. Sometimes, when you see the words "communicated by so-and-so" it means that so-and-so vouched for the authenticity of the paper, so it was immediately accepted for publication without review. Again, it varies and this is not universal, but it exists.

What can be done? I think two things could be done immediately and would have a positive affect. First, all reviews should be double blind, including to the editor. Meaning, there is absolutely no good reason why the editor or the reviewers should know who wrote the paper. Yes, they may be able to figure it out, but beyond that names should be stripped prior to review and readded only at publication. Second, arbitrary page limits should be removed. No, we don't need rambling papers. If a paper is rambling it should be rejected as rambling. However, it removes one incentive to produce difficult to follow proofs since now all details can remain. Virtually all papers are published electronically. Page counts don't matter.

In the long run, I support the continued development of proof assistant tools like Coq and Isabelle. At the moment, I find them incredibly difficult to use and I have no idea how I'd use them to prove anything in my field, but someday that may change. At that point, we can remove much of the imprecision that reviewers introduce into the process.

Code/design/engineer are considerably different than say biology, because you can (and should) publish artefacts. The actual code/algorithms (not pseudo code) needs to be shared and archived with the journal.

There has been some work for archiving code with some journals and some allow video uploads as well for segments from the actual experiments.

I would say that most scientists, at the top of their game, who have years of trusted publications behind them, should be given some latitude to publish discovery science without the requirement of reproducibility, so long as they share their results in detail, and accept postdocs who then take the resulting research materials to their new labs.

I didn't always believe this, but after spending a bunch of time reading about the numerous times in history when one scientist discovered something, published the results, and were told they were wrong because other people couldn't reproduce their results, only to be shown correct when everybody else improved their methodology (McClintock, Cech, Boyle, Bissell etc).

This ultimately came to a head when some folks critized the lack of repeatability of Mina Bissel's experiments (for those who don't know, she almost singlehandledly created the modern understanding of the extracellular matrix's role in cancer).

She wrote this response, which I originally threw on the floor. http://www.nature.com/news/reproducibility-the-risks-of-the-... After rereading it a few times, and thinking back on my experience, I changed my mind. In fact, Dr Bissel's opinion is shared by nearly every top scientist I worked with at UCSC, UCSF, and UC Berkeley. The reason her opinion has value is that she's proved time again that she can run an experiment in her lab that nobody else in the world is capable of doing, and she takes external postdocs, teaches them how to replicate, and sends them off to the world. In other cases, she debugged other lab's problems for them (a time consuming effort) until they could properly reproduce.

I believe reproducibility is an aspirational goal, but not really a requirement, for really good scientists, in fields where reproduction is extremely hard.

That's an absurd degree of cynicism. I just finished my PhD in chemical engineering, and I did the reverse of this. In fact, I successfully migrated the younger members of my research group to a completely open-source software stack for chemical simulations, so that in principle anyone with a Linux box could reproduce our results. We published all our code and plain text versions of the data.

I'm not saying you're wrong about the incentives - scientists are often incentivized toward secrecy - but I deny that we have to follow such incentives.