53

It seems ball lightning was disbelieved by scientists until around 1960. See Wikipedia . I knew a geologist who told us how his eye-witness account of ball lightning had been ridiculed. He had learned not to mention it when he interviewed for jobs as a professor of geology.


48

In 1726's Gulliver's Travels, Jonathan Swift mocked the learned scientists of Britain for not having solved the Longitude problem: Figure out a way to keep track of one's east-west location to within a mile after making a round-trip across the Atlantic. This was one of the most important scientific challenges of the 18th century. The British Parliament ...


29

This isn't a topic I'm familiar with, just something I've read on Quanta, but according to this article, Richard Kershner of Johns Hopkins claimed to have a complete classification of convex pentagon tilings in 1968, though he notably said that "The proof that the list in Theorems 1 and 2 is complete is extremely laborious and will be given elsewhere" and ...


27

By way of throat-clearing, what is Occam's razor? John Baez has a useful essay giving the history and some examples. William of Ockham's original formulation was Entities should not be multiplied unnecessarily. In other words, don't assume the existence of something unless there is good evidence for it. Again quoting Baez, "In physics we use the razor to ...


25

I think a famous example is the Monty Hall problem` https://en.wikipedia.org/wiki/Monty_Hall_problem about switching doors. The problem was answered correctly by Marilyn vos Savant, but she got baskets of letters from experts that she is wrong.


23

Take meteorites, for instance. By the end of the XVIIIth century, educated people “knew” that no rock found on Earth could possibly have fallen from the sky, in spite of the evidence (eyewitnesses included) for their existence. As science journalist Kat Eshner wrote, “eighteenth-century rationalists […] thought the stories of rains ...


20

Just warning not to include pre-1920s medicine (and a lot of medical mantra thru the 20th century), as there was little to no science involved amongst physicians. Just look at how difficult it was for Lister et. al. to convince hospitals, midwives, etc. to wash their hands and sterilize operating theatres. There are dozens of incorrect anecdotes ...


18

Michael Ventris, an amateur philologist, (he was an architect) managed to decipher the Mycenean script known as Linear B, a problem that professional specialists had been trying to solve for decades.


18

The Wright Brothers, both bicycle mechanics, solved both the control and power problems of heavier-than-air manned flight in 1902, beating the well funded aeronautical academic scientists of the Smithsonian Institute, notably Samuel Pierpont Langley.


17

I'd be tempted to add Gregor Mendel, whose experiments on plants and his analysis demonstrated how genes work, to that list. It wasn't so much that the 'professional' scientists of the time considered that he was wrong — rather that they didn't even know of his results. In particular, Darwin puzzled over what the mechanism for transfer of traits was and was ...


16

Bertrand Russell wrote many books and essays on philosophy and social justice, and was awarded a Nobel Prize in Literature. And the Persian mathematician Omar Khayyám wrote poetry: quatrains that have been translated into English as the Rubáiyát of Omar Khayyám.


16

The Green Flash was described for the first time (at least in the Western literature) by Jules Verne, a science fiction writer. Many scientists did not believe until photographs were taken and published. Herbert Wells in 1914 described the use of nuclear energy for both bombs and peaceful applications. (His novel The world Set Free). At approximately the ...


15

Hausdorff wrote many literary and philosophical works, including poems and a play, under the pseudonym Paul Mongré.


14

The two most famous paradigmatic examples of de-unification are phlogiston and ether. The Kaluza-Klein theory of gravity and electromagnetism did not get to spread as far and wide before faltering. The splitting of jade into two distinct minerals, nephrite and jadeite, is a small scale example. The phlogiston/caloric theory was able to unify chemical and ...


13

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 ...


12

Many mathematicians wrote their autobiographies, see the answers to https://mathoverflow.net/questions/102597/history-question-autobiography-of-mathematicians/102676#102676 Quite a few also have engaged in writing literary fiction. For example, Sofya Kovalevskaya (apart from memories about her childhood) wrote a novel: Nihilist Girl, translated by Natasha ...


12

Check out these mathematicians: A father, and two sons, all of whom co-authored papers in various combinations. David Borwein, father Peter Borwein, son Jonathan Borwein, son Peter's memorial to his brother Jonahan, in which he speaks of writing papers together with his brother.


11

In the 1960s the mathematical structure of Turing degrees was conjectured to be rather simple and homogeneous. This was consistent with what was known at the time. It later turned out that the opposite is true in a sense: the Turing degrees are as complicated as can be. Details in Ambos-Spies and Fejer, History of degree theory.


11

Probably the most famous conflict that satisfies your requirements is the conflict between "Ptolemy system" and "Copernic system", though few people understand this even today:-) This conflict became so famous because of the intrusion of a non-scientific authority, that is catholic church. From the point of view of astronomy, there are two aspects: a) the ...


10

Quite a famous example from modern physics deals with the inherent randomness of quantum theory. In the early years of quantum mechanics when the formulation in terms of wave functions was developed, the question of interpretation arose. Copenhagen interpretation, developed mainly by Niels Bohr and Werner Heisenberg became the most accepted of all the ...


10

I'll give it a try but strictly speaking your conditions exclude pretty much everything. Breakthroughs considered such by competent people not prone to exaggeration probably were "real" in some sense, in hindsight perhaps for wrong reasons. What was once considered "real" is not anymore, old models that were seen as advances and made sense in their time are ...


10

The mathematician E. T. Bell (known for Bell numbers, and the first stirrings of umbral calculus) wrote many science-fiction novels under the name John Taine. Arthur C. Clarke considered John Taine one of his heroes. (According to Constance Reid's The Search for E. T. Bell: also known as John Taine, which is a wonderful work of history/biography.)


10

Elie and Henri Cartan (father and son) published a paper together, in 1931 (Les transformations des domaines cerclés bornés).


9

The Mpemba effect, named after a Tanzanian student who discovered that a hot ice cream mix freezes faster than a cold mix in cookery classes in the early 1960s was initially ridiculed. Quoting the wiki page on this topic: After [a lecture by Dr. Denis G. Osborne], Erasto Mpemba asked him the question, "If you take two similar containers with ...


9

Mathematicians have been looking for amicable numbers for millenia. The smallest pair $(220, 284)$ was known to the Pythagoreans, and several larger pairs and a formula for generating them were found by Hindu and Arab mathematicians during the Middle Ages. Fermat, Descartes, and Euler rediscovered some of these and found some more. But in 1866, a 16-year ...


9

Arthur Leonard Rubin co-authored at least two papers with his mother, Jean Estelle Hirsh Rubin, the first one below when he was 13 years old. Arthur L. Rubin and Jean E. Rubin, Extended operations and relations on the class of ordinal numbers, Fundamenta Mathematicae 69 #2 (1969), 227-242. Paul Howard, Arthur L. Rubin, and Jean E. Rubin, Kinna-Wagner ...


8

Leibniz and Newton never thought of manifolds outside of ambient space as far as I know, Newton is credited with forging the concept of absolute space, and Leibniz with reducing it to a relational fiction in the style of Aristotle. The most influential philosopher of science in 19-th century was Kant, specifically his "Copernican revolution" of ...


8

The standard example of "complete opposite" was N. Wiener. Anecdotes: Wiener walking on campus is stopped by someone and they start a mathematical conversation. After the end of the conversation Wiener asks: "In which direction I was walking before I met you?" -"This direction." -"OK, this means I already had my lunch!" Wiener bought a new house. On the ...


8

Several mathematicians wrote excellent recollections about their own life. Some of them are of high quality as literature. My favorite ones are by Weyl, Rudin and L. Schwartz. David Ruelle (a famous mathematical physicist) wrote some philosophical fiction.


8

One possibility is Ted Kaczynski, the Unabomber. He has been described as a mathematical prodigy and Allen Shields, his doctoral adviser, once told that Kaczynski was the best doctoral student he ever directed.


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