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Imagine you are minding your own business when you receive an email from someone who claims to have discovered the Answer to the Ultimate Question of Life, the Universe, and Everything. He provides some "details" about his theory, then says he wants to meet you and / or arrange a time for a phone conservation to discuss it. What should you do?

The only thing I've seen is this 1983 article by Underwood Dudley about what to do when the trisector comes. Dudley says not to examine the trisector's proof, and also not to direct the trisector to the proof that trisection is impossible. Instead one should send computer-generated results showing that the trisection is imperfect. Problem with this is that it only works for questions that can be attacked by computers - there was a recent question here on Academia SE challenging conservation of angular momentum which this won't work for.

What are some general guidelines for dealing with these situations?

Edit: ignoring an email is easy, but what if the crank calls or visits in person?

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    insti.physics.sunysb.edu/~siegel/quack.html – Count Iblis Jun 19 '18 at 1:42
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    Related 1 Related 2. Additionally, an approach I remember seeing somewhere, but couldn't find: When sent a proof by a crank, the professor would send them a previously received crackpot proof, and state that they would go over the new crank's work if and only if the crank could find at least one of the errors in the other one. – Ray Jun 19 '18 at 20:47
  • I really like this article, which could be seen as a modern follow up to Dudly (and also one that is focused more on physics than on math): aeon.co/ideas/… – Vincent Jun 20 '18 at 12:00
  • Comments are not for extended discussion; this conversation has been moved to chat. Please do not use comments to answer the question. – Wrzlprmft♦ Jun 20 '18 at 12:07
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This happens far less frequently than inappropriate requests for postdocs that have absolutely nothing to do with your area, invitations to participate in conferences that have nothing to do with you, invitations to serve as section editor on predatory journals, .....

Handle them all the same. Use your delete button.

A call or visit is harder to deal with. A polite "... very interesting, but I don't have the time to follow up on this" might get you off the hook. If the person shows up at your door more than once, I recommend calling security.

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Ignore the crank.

Unless you are in some location where you are required by law to respond to communications (I remember reading here about one country where it was indeed the case that it was required to answer emails as part of "open records" laws), you are under no obligation to waste your time on a crank's musings.

If it amuses you to respond, feel free to do so, but you waste your time at your own peril!

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    I work for a German government research institute. We are required by law to respond to communication from citizens that was directed to the government. We once had to answer a crank who claimed photosynthesis doesn't use CO2 as a substrate. My colleague had fun for about two years with that one. You are much better off if you can ignore them. – Roland Jun 19 '18 at 6:28
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    @Roland, perhaps you could clarify whether the legal obligation is satisfied by a reply which states simply "Your correspondence has been received and noted." – Peter Taylor Jun 19 '18 at 8:12
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    There are expectations to make citizens feel heard and taken seriously. – user781 Jun 19 '18 at 23:10
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    The last line seems incomplete without some reference to James Veitch, so I hereby add that. For more entertaining details, search YouTube or TED.com. – WBT Jun 20 '18 at 0:36
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    I honestly would like every governmental university (or research institute) to answer such questions in some way. Many of these questions are genuine. It is sad that most academics talk so bad about "cranks" which are just so unfornate to not have collage educatoon and do thus not understand the rules of academia. – Udank Jul 6 '18 at 16:30
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Follow the peer-review model with some tweaks:

If the work is clearly flawed and so off the mark that nothing can come out of it, ignore. [Desk reject]

If the work may have some iota of sense, but it isn't worth your time to get into it, write back suggesting a different forum, like a blog post. [Reject and suggest transfer]

If you are marginally interested, but not sure whether it's worth it, ask them to try presenting it better/differently with more proof. [Reject and resubmit]

If you think it deserves a chance, but can't get into it yourself, lightly share with your colleagues/students over the coffee table and if anyone seems interested, let them take it up. Alternatively, as suggested by @jpmc26, you could ask them directly if they would be interested to detect preliminary errors that could be pointed out. Purely voluntary, of course.[Assign reviewers]

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    Would asking your students to review it for errors or if they're interested in doing so be a reasonable variation on the last one? This might act as a sort of initial smell test. – jpmc26 Jun 19 '18 at 6:20
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I agree with @aeismail that you should try to avoid the crank. That may not be possible though. Underwood Dudley wrote a book "Mathematical Cranks" (an MAA press book) about the subject. He has a chapter (Case Study of a Crank, I think; if not, The Making of a Crank) devoted entirely to a crank he refers to as G. K.. This person happened to be an alum of the school at which I taught. When I assumed the Chair of the Mathematics Department, I began to receive "stuff" from G.K., which I stuck in my files and ignored. My luck ran out one day when he happened to reach me by phone in my office (we did not have caller ID at the time). He asked me what I thought about the things he had been sending and I told him that I thought his ideas were without mathematical merit. He proceeded to call me all sorts of vile things and eventually hung up. I have no idea what he said about me in subsequent writings, and don't really care.

Interestingly enough, he had called my residence some time before this and my teenage daughter fielded the call. She reamed him out about it and invited him never to call my home again, which he never did.

Along the way (cranks can be very persistent) he asked me for a recommendation for the national medal of science or something. I ended up calling the organization for advice on what to do. They asked me who the person was and I told them. The person on the phone laughed and told me to throw the form away.

Among G.K.'s mathematical achievements were the "discovery" of "subzero pi," and the recognition that since $e=mc^2$ we must have $e=m(a^2+b^2)$ via the Pythagorean theorem.

I corresponded with Dudley and George Andrews about my encounters with G.K., which they found quite amusing. Although I found G.K. to be harmless, a colleague of mine in the department, who had been a classmate of G.K., was afraid he would come to school and use his military commando background to harm members of the department who didn't praise his dubious achievements. That didn't happen, but I cannot say I dismissed his concerns completely.

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    +1 since $e=mc^2$ we must have $e=m(a^2+b^2)$ via the Pythagorean theorem --- This is totally priceless! I must confess to spending more time than I should have 15-20 years ago reading stuff by this guy, especially the diaries he posted on usenet when he made road trips. – Dave L Renfro Jun 19 '18 at 18:50
  • @Dave L Renfro - This is the first I have heard of Archimedes Plutonium. I'm going to look into him further. My guy was also a megalomaniac. He had translated the bible into verse, and received some award from the Beaux Arts Society in New York. I recall a piece about him, I think on CNN, after his bible translation. He always insisted that his name be followed by the letters FRM, for being the world's foremost renaissance man. I would mention his name, but I don't want to speak ill of the dead (he died just a few years ago). – Chris Leary Jun 19 '18 at 19:23
  • @Dave L Renfro - A small edit: the initials were RM. for being America's foremost renaissance man. – Chris Leary Jun 19 '18 at 19:32
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    @AlecosPapadopoulos, $a$ and $b$ are left as an exercise for the reader. – shoover Jun 20 '18 at 21:51
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    @shoover - Considering he filled out his application for the national science medal and expected me to just sign and submit, I'm sure he had an obit composed and ready to go. – Chris Leary Jun 21 '18 at 4:07
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I read somewhere that a professor dealt with this issue by introducing such cranks to other cranks. "You might want to talk to Bob about your theory, I'll introduce you."

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A general guideline for these situations is to communicate your message (whatever you decide) to this person in a polite and gentle way.

The most successful people in my university are those who are excellent in their field and extremely nice, respecfull and humble because they understand the best how much they don’t know.

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I knew a very eminent astrophysicist who would receive hundreds of these emails claiming to disprove Einstein and relativity, discovering life on Mars, alien visitations, space mirrors, critiques of the big bang, flat earth, etc.

He would respond in a vaguely positive way, "This is very interesting work, but I don't know the answers to these important points you raise. Let me point you to someone who can help:" and give them the email address of another random crank that had previously contacted him.

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