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In many areas of mathematics it is informative to conduct numerical experiments.

But, it not uncommon that the searches do not lead to the examples or data one was hoping for. Since the numerical searches can be quite time consuming, it seems useful to share these negative results, so that others avoid spending time attempting the same searches.

What would be best practices in this regard? And would setting up and maintaining an open-access database be a realistic prospect?

As an example, consider the question of the (non-)existence of $n$-body choreographies when allowing the bodies to have different masses and different time-lags (see "$n$-body choreographies" by Montgomery for background as of 2013, and Minton's fine applet for the type of numerical searches that one could try to adapt). I'd be interested to know what has been already attempted by others. I could ask experts, but it may well overlook work by other experts and by Ph.D. students.

LSpice
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Thomas Sauvaget
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    I think this previous MO discussion will be helpful: https://mathoverflow.net/q/406896/11260 – Carlo Beenakker Mar 22 '22 at 13:03
  • @CarloBeenakker: yes, thank you, although I'm stressing that my interest here is on purely numerical and correct work, as opposed to 'failed proofs'. And less for a journal with refereeing, rather a way to share in a precise fashion the parameter ranges inspected and the code used (since bugs in the code can happen). – Thomas Sauvaget Mar 22 '22 at 13:22

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An easy and reliable way to share code is via Zenodo --- works much like arXiv, you get a DOI, can update your files, and it's free. We use it regularly to document computer simulations in physics, I imagine computational mathematics is not that different.

Note that Zenodo explicitly welcomes both positive and negative results.

Carlo Beenakker
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