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49

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.

45

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 ...

27

It is a play of words by Charles Babbage. Deism was a religious belief or rather a movement promoting the idea that God exists but it does not interfere with whatever happens in this world. This old philosophy according to the Wikipedia "...asserts God's existence as the cause of all things, and admits its perfection (and usually the existence of natural law ...

25

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 ...

23

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.

21

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 ...

19

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 ...

17

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.

16

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.

15

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 ...

14

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 ...

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

He wears the head wrap in combination with a silk banyan. In the 18th century... It was fashionable for men of an intellectual or philosophical bent to have their portraits painted while wearing banyans. Benjamin Rush wrote: Loose dresses contribute to the easy and vigorous exercise of the faculties of the mind. This remark is so obvious, and ...

8

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 ...

8

It would seem to be Euler. Dickson, in Ch. XVI of History of the Theory of Numbers, writes the following: "Euler discussed the numbers $a$ for which $a^2+1$ is divisible by a prime $4n+1=r^2+s^2$. Let $p/q$ be the convergent preceding $r/s$ in the continued fraction for $r/s$; then $ps-qr=1$. Thus every $a$ is of the form $(4n+1)m\pm k$, where $k=pr+qs$. ...

7

Rogue/Freak waves. It seems that reports of these were considered myths by science for a long time until they were finally recorded. (However this is not an exact answer to the question - no non-professional had a theory about these waves, it was more of "ignoring observed facts which don't fit the accepted theory)

7

Lu Jiaxi (1935 - 1983) was a self-taught Chinese mathematician who solved a major problem in combinatorial design theory. He was born in a poor family and his father died when he was in junior middle school. Working in the factory for several years, he self-studied and got into university majoring in physics. Fascinated by the Kirkman's schoolgirl problem ...

7

The first answer is excellent but just for context on the actual math: Newton notation for derivative of f(x): $\dot f(x)$ Leibnitz notation for derivate of f(x): $\frac {df}{dx}$ Newton's notation is fine for very basic single variable derivation and generally the derivative for the described cases but the Leibnitz notation is general purpose and ...

7

Yes, he did, multiple times. Singular double integrals (1814) In Mémoire sur les intégrales définies (1814) Cauchy studied why switching the order of integration in a double integral can sometimes lead to different results. This led him to introduce the notion of "singular integral". For $K = \frac{z}{x^2 + z^2}$ he showed that \$\int_0^1\int_0^1\frac{\...

7

The Grothendieck Circle site suggests a more innocent explanation for the loss these letters. Having left Montpellier in 1984.... In May of that year [1985] a secretary informed him that his office on the fourth floor of the institute had been cleared out. Seeing this incident as an egregious example of the general decline of mores, an outraged ...

6

C P Ramanujam, an Indian Mathematician, not to be confused with Srinivasa Ramanujan, one who worked with GH Hardy. Ramanujam's achievements at High School had been outstanding and he had shown that he was extraordinarily gifted, so he entered Loyola College with great expectations. He continued his interest in chemistry but it was mathematics that he ...

6

I don't know about the Fields medal, but he could not have won the Nobel prize since the only appropriate one would have been the one in Economics, which was awarded for the first time in 1969, 12 years after his death. And the Turing award was awarded for the first time in 1966, 9 years after his death.

6

It does not appear that Cambridge changed the policy for Ramanujan, although they did use a rather atypical degree they had for him (Bachelor of Arts by Research, not Bachelor of Science by Research). PhD in Mathematics was not traditional in Britain, and was only created after the First World War. Ramanujan was a beneficiary of the general conversion in ...

6

Mathematicians rarely describe the process which led them to their discoveries. One notable exception was Euler. Some books on the subject written by great mathematicians are: J. Hadamard, The Mathematician's Mind. The Psychology of Invention in the Mathematical Field (English translation). G. Polya, a) Mathematics and plausible reasoning. b) Mathematical ...

6

Kurt Gödel was certainly known as an eccentric in his life. In fact it is said that he starved to death when his wife died as he refused to take meals from anyone but his wife. In the language of today, he would probably be diagnosed as suffering from mental health issues.

6

You remember incorrectly. Calculus was found by Archimedes, G. Saint-Vincent, Galileo, Kepler, Descartes, Pascal, Cavalieri, Fermat, Barrow, Wallis, Brounker, Huygens, Leibniz, J. Gregory, N. Mercator, Newton, Cotes, Taylor, Torricelli, Bernoulli brothers, to name only the most famous ones. As every big enterprise, this was a collective enterprise. The ...

6

A significant obstacle to doing an online search for Fritz Peter is that both Fritz and Peter are common as German first and last names. The German Wikipedia provides some basic pointers, such as his 1923 dissertation in Göttingen. Arne Schirrmacher, "Establishing Quantum Physics in Göttingen: David Hilbert, Max Born, and Peter Debye in Context, 1900-1926." ...

6

You can find the quote (or something similar) in multiple places in the Théorie analytique de la chaleur, for example in Chapter I, paragraph (article) 14: "L'examen de cette condition fait connaître que l'on peut développer en séries convergentes, ou exprimer par des intégrales définies, les fonctions qui ne sont point assujéties à une loi constante, et ...

5

https://www.realclearscience.com/blog/2015/02/mathematicians_die_in_horrible_ways.html refers to Kellen Myers's list, and exemplifies with: Or what about Austrian American mathematician Kurt Gödel? Considered by some to be just as influential a logician and philosopher as Aristotle, he sadly succumbed to crippling paranoia later in life. In his sixties, ...

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