(this is a guest post by Theo Johnson-Freyd)
Occasionally on MathOverflow (and elsewhere on and off the internet), amateur mathematicians try to advertise their research results and solicit feedback from professionals. For example, recently HH Hannett (who holds a long-ago BS in mathematics, but has been doing non-math engineering work for many years) asked a well-meaning but inappropriate-for-the-forum question about Where to submit a recent paper, and how to cope with the negative or dismissive responses received from a previous journal submission. In a comment on a subsequent (now-deleted) post, Hannett wished “that there might be a mechanism whereby amateur (“non-PhD”) contributions can get a fair shake …. Perhaps some sort of delegated, tiered system that a paper has to survive.”
Discussing whether/what/how such a system should exist/be like/be set up is, to my mind, valuable. A potential answer is that the existing peer-review process is already adequate. I could certainly believe that the best answer is “no change necessary”: I’m young enough that I don’t really know the full extent of the current system; maybe we should just continue to avoid the cranks. But most amateurs don’t want to waste professionals’ time — they want to do math, and for the same reason (it’s fun!) that professionals do, and the current academic system, clearly, does not provide sufficient outlets for well-meaning amateurs (or “cranks” wouldn’t be a problem).
My hope with this post, then, is to constructively generate some ideas for relieving this pressure. In particular, it’s all well and good to ask that amateurs learn and follow reasonable advice, but my goal is to come up with things that professionals can do (pro)actively. These ideas could range from the fantastical (design a better peer-review system! establish free universal advanced mathematics education!) to the specific (make “respond to amateurs” part of universities’ “service” requirements!). An important note: My goal is not to establish yet another thread in which we can swap stories of all the dumb things amateurs have sent us. That’s certainly a fun game, but there are other outlets for it.
So, netizens: What, specifically, are the weaknesses and strengths of the current system when it comes to amateur mathematics? What would
be an ideal system through which amateur mathematicians could advertise their work and solicit feedback? How can professional
mathematicians help to set up such a system?
(this is an addendum by Ben)
Maybe I should save this for the comments, but I can’t resist abusing my blog privileges and throwing out an idea. I don’t think that any system that require a lot of input from people on the usual professional mathematics track is likely to succeed; it’s hard enough to get them to seriously read each other’s papers (for example, I’d much rather see a system whereby graduate students can read and give feedback on each other’s papers than one where they read amateur mathematicians). But perhaps we can ask amateurs to review each other’s work.
One could have a website where anyone can upload preprints and then give people function to vote on the preprints, write reviews and vote on the reviews. The power of your vote could be regulated using a page-rank type system where you only get real voting power as other people vote up your work. This wouldn’t have to restricted to amateurs only, but it’s hard for me to imagine it catching on quickly with professionals. Of course, it’s hard to know whether it would attract a big enough and diverse enough user base to effectively sort through papers, but you never know, it might.