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This is more a question for mathematics academia, but may apply more broadly.

I have left academia long ago, but there are a few problems and conjectures, not especially famous but that I find really interesting, that I would like to see solved. Nobody seems to be really working on them, at least in the past 10 years.

I am considering either putting up a prize or hiring talented folks to work on them.

What's the best way to proceed : where to advertise for that? Or should I just email some experts or grad students whose research records hints they might make headway if they accept? Or organise a sort of workshop and invite folks (with some contraint that what has been tried or found be written up)?

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  • What size of problem and money are we talking about here? Are you planing to offer enough money to fully fund the respective research?
    – Wrzlprmft ♦
    Commented Oct 5, 2023 at 12:15
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    @Wrzlprmft The problem are difficult, no doubt. What bothers me is the limited activities on them : I'm unsure if folks are trying but it's too difficult, or nobody is looking. The amount I was thinking to use, either for a prize, a workshop organisation, or direct pay, is $US 5000.
    – Archie
    Commented Oct 5, 2023 at 12:20
  • Obviously this amount is more adapted for a prize or week of pay. A workshop would be online, say a mixture of introductory talks and then a polymath type wiki/blog, and the money used to reward participants somehow (books,...)
    – Archie
    Commented Oct 5, 2023 at 12:41
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    You can place an ad in Notices of the AMS.
    – Moishe Kohan
    Commented Oct 5, 2023 at 12:41
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    @Archie I doubt anyone who has a PhD will pay attention for only $5000.
    – Anonymous Physicist
    Commented Oct 5, 2023 at 14:00

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There's a historical precedent for this - in 1993 businessman and amateur mathematician Andrew Beal formulated a conjecture that would imply Fermat's Last Theorem as a corollary. He wrote to 50+ journals & professors about it, and received responses affirming the novelty of the conjecture. He then offered a prize (currently standing at $1,000,000) for a proof or counterexample.

You could do something similar. The conjectures you want people to investigate are already known, so you can skip the part where you ask journals & mathematicians and write directly to the American Mathematical Society.

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  • It is indeed a precedent for prize, but on much more difficult question, still open. And precisely, Beal has probably waited for years and not seen advances. This is why I'd very much prefer a direct hire or a workshop : precedents for these would be very useful
    – Archie
    Commented Oct 5, 2023 at 13:21

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