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Often professors in math and physics academia have inboxes full of people claiming to have solved deep problems such as dark matter, black holes, prime number conjectures and claim that many big names were actually wrong. Most of these "cranks" employ pseudo-scientific/mathematical arguments that often have no actual bearings on the subject. My question is how long has this been a trait of scientific academia. Did physicists like Einstein and Fermi have to sort through this type of spam?

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    $\begingroup$ Do you want to exclude all religion-based examples? Also, do you want to limit this to people who really believe their own work, as opposed to those who know they are comitting fraud? $\endgroup$ – Carl Witthoft Jan 31 at 12:52
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    $\begingroup$ @CarlWitthoft I think crank is characterized by unwavering belief that they are correct. Other than that I had no specifics. $\endgroup$ – Yemeen Jan 31 at 15:22
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    $\begingroup$ In S. Singh's book on Fermat's Last Theorem he mentions that Edmund Landau had form letters printed to reply to the numerous wrong proofs of FLT he received. Landau was a contemporary of Einstein and Fermi. (I would actually like a source for this story, and do not have the book at hand right now.) $\endgroup$ – Torsten Schoeneberg Feb 1 at 6:02
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There are lots of references to cranks in A Budget of Paradoxes, by Augustus de Morgan (1806–1871), who calls them “paradoxers”. There, he writes

[…] I say something on my personal knowledge of the class of discoverers that square the circle, upset Newton, etc. I suspect I know more of the English class than any man in Britain. I never kept any reckoning; but I know that one year with another — and less of late years than in earlier time — I have talked to more than five in each year, giving more than a hundred and fifty specimens. Of this I am sure, that it is my own fault if they have not been a thousand.

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    $\begingroup$ Paradoxers is a brilliant term for this. $\endgroup$ – Yemeen Jan 31 at 20:03
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In the foreword to G.H.Hardy's "A mathematician's apology" C.P.Snow writes

About his discovery of Ramanujan, he [Hardy] showed no secrecy at all. It was, he wrote, the one romantic incident in his life : anyway, it is an admirable story, and one which showers credit on nearly everyone (with two exceptions) in it. One morning early in 1913, he found, among the letters on his breakfast table, a large untidy envelope decorated with Indian stamps. When he opened it, he found sheets of paper by no means fresh, on which, in a non-English holograph, were line after line of symbols. Hardy glanced at them without enthusiasm. He was by this time, at the age of thirty-six, a world famous mathematician : and world famous mathematicians, he had already discovered, are unusually exposed to cranks. He was accustomed to receiving manuscripts from strangers, proving the prophetic wisdom of the Great Pyramid, the revelations of the Elders of Zion, or the cryptograms that Bacon had inserted in the plays of the so-called Shakespeare.

p.29f in the 1967 CUP edition, my emphasis

This suggests that this phenomenon occurs as early as 1913. According to Snow, Hardy himself has written this story, but Snow does not provide any references. As far as I can tell, it is not from "A mathematician's apology".

Einstein's works were published in the same period, so he has probably encountered the same phenomenon.

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    $\begingroup$ This suggests that this phenomenon occurs as early as 1913. --- Probably much earlier than this. Perhaps something about crank correspondence can be found in Augustus De Morgan's 1872 book A Budget of Paradoxes. $\endgroup$ – Dave L Renfro Jan 31 at 15:23
  • $\begingroup$ Right. I shall write about that. $\endgroup$ – José Carlos Santos Jan 31 at 19:13
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Alexander von Humboldt describes what we might call scientific cranks in 1799. His activities might also one of the earliest documented accounts of what we now call "public engagement with science".

Describing his visit to Cumana (Venezuela), where he arrived in July 1799, he describes how the local population is very interested in his research and he has to spend much time explaining science, but also meeting some rather complicated characters.

THE first weeks of our abode at Cumana were employed in verifying our instruments [...] If every thing around us was fitted to inspire us with the most lively interest, our physical and astronomical instruments in their turns excited strongly the curiosity of the inhabitants. We were distracted by frequent visits; and in order not to dissatisfy persons, who appeared so happy to see the spots of the Moon through Dollond`s telescope, the absorption of two gazes in a eudiometrical tube, or the effects of galvanism on the motions of a frog, we were obliged to answer questions often obscure, and repeat for whole hours the same experiments.

And now the cranks:

These scenes were renewed for the space of five years, every time that we took up our abode in a place where it was understood, that we were in possession of microscopes, telescopes, and electrical apparatus. They were in general so much the more fatiguing, as the person who visited us had confused notions of astronomy and physics; two sciences, which in the Spanish colonies are designated under the singular name of the new philosophy, nueva filosophia. The half-scientific looked on us with a sort of disdain, when they learnt that we had not brought in our collection of books the Spectacle de la Nature by Abbé Pluche, the Cours de Physique of Sigaud la Fond, or the Dictionary of Valmont de Bomare. These three works, and the Traité d`Economie politique of Baron Bielfeld, are the foreign, works most known and esteemed in Spanish America, from Caraccas and Chili to Guatimala and the north of Mexico. No one is thought learned, who cannot quote their translations; and it is only in the great capitals, at Lima, at Santa Fe de Bogota, and at Mexico, that the names of Haller, Cavendish, and Lavoisier, begin to take the place of those, that have enjoyed popular celebrity for these fifty years past.

But he is impressed by the curiosity of the native inhabitants and their eagerness to learn:

The curiosity excited respecting the phenomena of the heavens, and various objects of the natural sciences, takes a very different character among anciently civilized nations, and among those who have made but little progress in the unfolding of their intellectual faculties. Each of them exhibits in the highest classes of society frequent examples of persons unacquainted with science; but in the colonies, and among new people, curiosity, far from being idle or transient, arises from an ardent desire of instruction, and discovers itself with an ingenuousness and simplicity, which in Europe are the characteristics only of youth.

Quoted from: Alexander von Humboldt: Personal Narrative of Travels to the Equinoctial Regions of the New Continent during the Years 1799-1804, Vol 2, Chapter V, translated into English by Helen Maria Williams. - London 1818. Online version

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