Mathematicians tell stories about dealing with mathematical "cranks" who try to do things like trisect an angle, prove Fermat's last theorem is true, or that 0.9999 ... is not equal to 1.
Do historians have the same problem, i.e. being contacted by amateur historians who are promoting some crazy pet theory? Are there common "crank" topics that pop up?
Most definitely. I work on the history of the atomic bomb. I have interacted with lots of cranks. Generally the most common crankish arguments I get sent my way are (in order of increasing looniness):
Germany or Japan actually got really close to making an atomic bomb!!! (not impossible, but not true — and they never really understand the technical or organizational evidence that would be necessary to prove such a thing; what makes it crankish is not so much the topic, but the way of approaching it, which is usually very uncritical, "look for what I want to find, ignore everything that gets in the way")
Germany made the atomic bomb and the USA took it!!! (same as the above plus ignoring all of the evidence we have about the US program, plus Nazi-technofetishism.)
Ancient India had atomic bombs!! (the combination of weird theories about the superiority of ancient cultures, strange (mis)translations of old texts, and a total lack of technical knowledge about the subject)
Atomic bombs are a hoax!!! (one of the goofiest theories I've ever seen, which is gaining more attention on the internet than you'd expect; the only technical argument involved is based on a complete misunderstanding of the science, and most of it seems to come from a self-conscious effort to make even the Apollo moon landing hoaxers uncomfortable)
Yes. See: Ancient Aliens (which promotes something called "ancient astronaut theory" or the belief that aliens did it), this video from Spirit Science, Holocaust denialists, JFK conspiracy theorists, Jesus mythers, and more.
/r/badhistory does occasionally go up against these history cranks.
There is a mailing list for a number of prominent Holocaust scholars by a denialist who periodically sends them new "research" proving that the Holocaust did not happen.
My favorite crank historian is P.N Oak, from India, my country. He is the darling historian of the Indian right wingers. Though extremely ridiculous, his ideas in one form or another have found many takers, and these stories have become part of the popular culture and discourse for the right wingers, chiefly lower middle class who have been exposed to the internet in the last five-ten years. Wiki has a nice summary for those interested- http://en.m.wikipedia.org/wiki/P._N._Oak
"Oak's claims, e.g. that Christianity and Islam are both derivatives of Hinduism, or that the Catholic Vatican, Kaaba, Westminster Abbey and the Taj Mahal were once Hindu temples to Shiva,[1] and their reception in Indian popular culture have been noted by observers of contemporary Indian society, who variously characterised Oak as a "mythistorian"[2] or more directly as a "crackpot".[3] In addition to this Oak again asserted that the Vatican was allegedly originally a Vedic creation called Vatika and that the Papacy was also originally a Vedic Priesthood."
Some of the most common ones in my area of study (20th Century US) are JFK conspiracy theorists, and people who think FDR knew about Pearl Harbor in advance. I actually had a nice long chat with the archivist at the LBJ Presidential Archives once about the JFK cranks - they are a constant presence there, and while the staff do their best to be nice/treat everyone well, I am sure it gets really old really fast.
But... Fermat's last theorem IS true.
You'll see the cranks in more modern periods, especially the really recent stuff. The good thing about studying really old history (Medieval here, 7-12th century in particular) is that you're freed from the cranks.
ETA *somewhat freed.
A book you might enjoy is Worlds of Arthur (Oxford, 2013) by Guy Halsall which systematically dismantles the myriad crank theories which have arisen about King Arthur in publication. Including one which suggested you could trace Arthur's campaigns by tracking the names of modern pubs!!!?? - very poor see me after class :(
It then balances this quite amusing snarkiness with some stellar scholarship which while not as satisfying as Arthur was [x] or [y] random person fo' sho does bring together what world he might have inhabited if he actually existed.
Templars. Bloody Templars, everywhere. Well, according to the nutters, anyway.
In askScience its people attempting to prove theyve found flaws in fundamental areas of Physics. You can tell, even if its not your field, when they ask a question that challenges some part of physics and when its explained why it DOESNT challenge current known laws they continue to argue that it does.