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What are the most glaring examples -- if any -- of when the professional scientists or mathematicians were wrong, but the nonprofessionals were right?

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    $\begingroup$ Two things: math was far ahead of nearly all fields of science in its rigor and procedures until relatively recently; and in nearly all cases "nonprofessionals" were right in a tiny percentage of their beliefs. They were correct by accident, not by insight. $\endgroup$ – Carl Witthoft Jan 18 at 13:24
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    $\begingroup$ I don't know the local standards but isn't this just a list question and hence should be closed? $\endgroup$ – Tim B Jan 18 at 16:00
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    $\begingroup$ @MasonWheeler: I don't know the history, but I would be really surprised if that was the case. Conservation of momentum is a very basic fact in Newtonian mechanis, so the idea of "I expel matter in one direction, I move in the other" should have been obvious to any physicist. $\endgroup$ – Martin Argerami Jan 19 at 5:20
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    $\begingroup$ @MasonWheeler You are undoubtedly thinking of this famous New York Times article, worth reading in its entirety: en.wikisource.org/wiki/The_New_York_Times/Robert_Goddard As you can see, it is actually an illustration of the opposite. Goddard, a professional scientist, was quite right about the dynamics of rocketry and how action and reaction actually work, while the amateur writer of the article was wrong. $\endgroup$ – Robert Furber Jan 20 at 9:09
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    $\begingroup$ It is particularly amusing when he says that only "Dr. Einstein" is "licensed" to change the laws of mechanics. $\endgroup$ – Robert Furber Jan 20 at 9:10

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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.

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    $\begingroup$ Eyewitnesses are routinely disbelieved because witness reports are the second-least-reliable source of information. $\endgroup$ – Mark Jan 19 at 0:48
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    $\begingroup$ @PedroA, an eyewitness report as relayed by a third party. $\endgroup$ – Mark Jan 19 at 2:30
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    $\begingroup$ @Mark: I thought that dishonour is reserved for facebook/twitter posts? $\endgroup$ – user21820 Jan 19 at 15:25
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    $\begingroup$ It doesn't help that ball lightning only lasts one turn. $\endgroup$ – Acccumulation Jan 22 at 21:13
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    $\begingroup$ What can be claimed without evidence can be dismissed without evidence... It's not that the scientists were exactly wrong, but it just took a long time to obtain the evidence. $\endgroup$ – UKMonkey Jan 23 at 19:58
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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 had an outstanding offer of £ 20,000 for a solution, and had trusted the astronomers at the Royal Observatory with awarding the prize. The prize was worth several times the modern-day Nobel Prize, and was famous at the time.

In 1731, a watchmaker named John Harrison solved the problem. The astronomers at the Observatory refused to believe him. Over the next 40 years, Harrison steadily refined his solution, but the astronomers never did award him the prize. It took an act of Parliament in 1773 before Harrison was finally given his prize, and east-west navigation could be made safe.

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    $\begingroup$ I don't think Harrison counts as a non-professional. His solution was to use an accurate clock, and he was a professional clockmaker. $\endgroup$ – David Richerby Jan 19 at 18:34
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    $\begingroup$ The question implies that it considers as "nonprofessionals" all those who aren't "professional scientists or mathematicians". So Harrison would appear to qualify. I am not sure, however, whether professional scientists or mathematicians thought he was wrong, and think the answer would benefit from links to relevant sources that demonstrate that. $\endgroup$ – njuffa Jan 20 at 0:14
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    $\begingroup$ @njuffa -- I linked to a book-length source that discusses the ways in which the professional scientists thought he had insufficiently answered the question. $\endgroup$ – Jasper Jan 20 at 3:46
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    $\begingroup$ For the history of the chronometer, it was not that scientists didn't believe that the chronometer could work. Rather, scientists believed that there should be a more "elegant" solution that does not simply rely on measuring time difference to determine longitude similar to how sextants can be used to measure latitude. $\endgroup$ – slebetman Jan 20 at 18:53
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    $\begingroup$ Everyone should read the wonderful book “Longitude”, by Dava Sobel. See en.m.wikipedia.org/wiki/Longitude_(book) $\endgroup$ – ZeroTheHero Jan 21 at 0:12
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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 that "a complete proof would require a rather large book".

However, after Martin Gardner talked about this claim in his column in Scientific American in 1975, it got to Marjorie Rice, a California housewife with a high school math education, who found four additional families, and Richard James, a computer programmer, who found another. Eventually, Michael Rao proved that there were exactly 15. You can read more about Rice in this article by the same author.

Admittedly, this is an instance of a single professional mathematician making a false claim without giving a proof, which mathematicians consider poor form, and a nonprofessional correcting him, rather than the general mathematics community being wrong.

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  • $\begingroup$ Isn’t there a similar story about Latin squares? $\endgroup$ – ZeroTheHero Jan 21 at 0:14
  • $\begingroup$ Thanks for the link to the interesting story about Marjorie Rice. It makes me wonder how much humanity is held back by gender and social inequality. How much talent wasted, how much potential unrealized. A shame even from a purely utilitarian viewpoint. What isn't there is not missed, but it must be a lot. $\endgroup$ – Peter - Reinstate Monica Jan 23 at 10:36
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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.

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    $\begingroup$ But the rate of correct answers was far higher among the educated (at least in math and physics) than among the great unwashed masses. $\endgroup$ – Carl Witthoft Jan 18 at 18:34
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    $\begingroup$ @ Carl Witthoft, do you have hard data about this or is it just a guess? $\endgroup$ – Karl Jan 18 at 18:37
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    $\begingroup$ This is not an accurate description of what happened. Marilyn Vos Savant thought she was answering the Monty Hall problem but was actually answering the evil Monty problem, which has a different answer. Lots of people wrote to explain to her that she was wrong and she stubbornly insisted that they were wrong. (In her statement of the problem, Monty offers to let you switch doors after he knows which door you chose with no requirement to do so. For all you know, Monty only extends this offer to people who he knows chose the right door. So switching could guarantee a loss in this variant.) $\endgroup$ – David Schwartz Jan 18 at 21:25
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    $\begingroup$ Also, please note that (1) the problem permeated the mathematics community far ahead of vos Savant's rise to prominence; (2) the large majority of professional mathematicians were right about the problem. "baskets of letters" does not necessarily represent "the professional ... mathematicians" as a whole. $\endgroup$ – Prune Jan 18 at 22:28
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    $\begingroup$ Karl, re Carl Witthoft's comment MvS wrote "Of the letters from the general public, 92% are against my answer, and of the letters from universities, 65% are against my answer." @David Schwartz, it's true that the problem has no solution unless you state Monty's general strategy; neither the asker of the question nor vos Savant did that; and from her explanations it's not clear that she understands how critical Monty's motivation is. However, the authors of the letters she quoted don't seem to understand that either, and no one mentioned evil Monty (or any other well-defined Monty). $\endgroup$ – benrg Jan 19 at 1:04
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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 of iron rocks weren’t real”. This state of affairs lasted until 1803, when Jean-Baptiste Biot established the reality of meteorites.

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    $\begingroup$ The WP link doesn't seem to support your interpretation. It sounds like the question was not even taken up by professional scientists until 1794, when Chladni, a professional scientist, published a book saying that they did fall from the sky. This was followed rapidly by the supporting evidence from Biot. $\endgroup$ – Ben Crowell Jan 18 at 15:58
  • $\begingroup$ Your link doesn't support that people before that time "knew" that no rock could fall from the sky... In addition it certainly doesn't say that a non professional scientist did the research on the rock $\endgroup$ – UKMonkey Jan 23 at 20:06
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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 purporting to show scientists were wrong. The "bumblebee can't fly" is one such. The truth behind the science/engineering theories is rather different.

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    $\begingroup$ Note that the actual statement in the bumblebee case is "the bumblebee can't fly using aerodynamic lift" -- and in fact, it doesn't. It flies using a different technique involving dynamic stall. $\endgroup$ – Mark Jan 19 at 1:01
  • $\begingroup$ @Mark I did know that; it's one of those cliches that has ignored the true source. Just like the "Let them eat cake," where 'cake' had a completely different meaning (leftover scalings from bakeries, not fancy dessert items) $\endgroup$ – Carl Witthoft Jan 19 at 21:31
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    $\begingroup$ @CarlWitthoft Although it's off topic, I don't know where you are getting that interpretation of "Let them eat cake". The origin of it that I know is that Jean-Jacques Rousseau attributed the phrase "Qu'ils mangent de la brioche." to a proverbial unspecified princess as part of a joke in his autobiography. $\endgroup$ – Robert Furber Jan 20 at 5:29
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    $\begingroup$ @Mark The bee thing always bothered me. The science wasn't wrong; no scientist ever claimed that bees can't fly or anything like that. The point was that using the science known at the time, they couldn't explain how bees were able to generate sufficient lift to fly, but, given that they clearly do fly, this hinted at principles of aerodynamics that were as yet not fully understood, thus pointing at new areas to research and new experiments to devise. It's not scientists being ignorant, it's scientists learning from observations. In other words, doing science. $\endgroup$ – anaximander Jan 22 at 14:12
  • $\begingroup$ Ironically, during the plague, the masks worn by doctors were stuffed with lavender (and other nice smelling flowers)... It had since been found this would have helped protect them from some diseases (though likely not the plague) because lavender is a natural anti biotic... $\endgroup$ – UKMonkey Jan 23 at 20:09
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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.

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    $\begingroup$ I guess "experts couldn't solve it" is not the same as "experts were wrong". $\endgroup$ – Gerald Edgar Jan 20 at 14:17
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    $\begingroup$ @GeraldEdgar Experts were wrong, since they didn't attempt to decipher those inscriptions assuming –as Ventris did– that they were written in a language related to Greek. $\endgroup$ – xxavier Jan 20 at 15:30
  • $\begingroup$ @xxavier Interesting. You should amend your answer with that detail, it makes it more relevant. It's also not untypical: Preconceived ideas sometimes prevent the professional from exploring new approaches. $\endgroup$ – Peter - Reinstate Monica Jan 23 at 10:38
  • $\begingroup$ @xxavier well no, there were attempt to decipher it via Greek but they moved on when they didn't have success. The question is if they were confident enough on the matter to be considered wrong for this question. It's tricky with ancient history as much of it is theories based on available evidence. Also, Ventris wasn't a profession in the field but his collaborator, John Chadwich, definitely was. $\endgroup$ – Kaithar Jan 27 at 8:46
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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.

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    $\begingroup$ That is an example from engineering, not science. For that very fact, the people at the Smithsonian weren't wrong, since they weren't even trying to be right. Engineering problems can have multiple solutions. $\endgroup$ – Jishin Noben Jan 22 at 12:29
  • $\begingroup$ The Wright Brothers do get full credit since they did their work independently; but weren't the first to achieve heavier-than-air manned flight. Richard Pearce's earlier (very similar) aircraft didn't have the same historical significance due mostly to its inventor's deteriorating mental state. $\endgroup$ – Jeremy List Jan 22 at 21:58
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    $\begingroup$ @JeremyList can you please provide a reference to Richard Pearce $\endgroup$ – russelld Jan 23 at 9:39
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    $\begingroup$ @JishinNoben the Wrights demonstrated scientific skills set associated with scientific inquiry. As in 1) Literature review 2) contacting other flight researchers; 3) Thought up hypothesis' which were tested to develop a theory ( of flight eg wing warping); 4) Controlled variables (chord ratio of wings) 5) Built equipment to test the hypothesis (eg wind tunnel); Pulling together research to successful outcome (eg controlled manned flight in heavier air device). NASA does the same process $\endgroup$ – russelld Jan 23 at 10:08
  • $\begingroup$ en.wikipedia.org/wiki/Richard_Pearse. Turns out there's a lot more uncertainty about his life and work than I had recalled, but this is still a very interesting read. $\endgroup$ – Jeremy List Jan 23 at 20:46
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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 same time many scientists thought this was impossible. (Rutherford is on record for saying this publicly, that nuclear energy will be never used).

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    $\begingroup$ HG Wells wrote many science fiction novels. That one happened to reflect something which later turned out to be correct is really just the dice falling right, with a whole bunch of other novels which turned out not to work out. Anyway, Wells was always about the concept, and the society, not the hard science. $\endgroup$ – Graham Jan 18 at 20:48
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    $\begingroup$ Can you provide a source that confirms the scientists did not believe the Green Flash was possible? The Wikipedia article mentions the photographs were published in 1960 and I clearly remember a 1920s children popular science book discussing green flash (after all, refraction has been studied for quite some time). Also, I find the idea that scientists changed their minds simply after looking at some photos dubious. $\endgroup$ – Denis Jan 20 at 16:26
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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 searching for a reason why traits wouldn't be continually diluted ... which was an answer that Mendel had already answered very neatly. (Darwin argued for pangenesis as he was sure from his observations that blending inheritennce would have diluted distinct traits)

I'd argue that Mendel would meet the criteria as being a 'non-professional' as while he did teach physics - he repeatedly failed the teaching exams so he wasn't qualified to teach high school or adults - only young children. A pedant may point out that as presented his experiments in a couple of meetings and published an ignored paper he should be regarded as a 'professional scientist' .. but since he own boss in the church banned him from studying mice as it was considered wrong to study animal reproduction - I'd safely argue that it was a very non-scientific profession he was in.

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    $\begingroup$ Actually, Mendel did once present his results to botanists. Most got bored of the lecture and left and none cared about what mathematics had to do with breeding plants. $\endgroup$ – slebetman Jan 22 at 5:00
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    $\begingroup$ @slebetman That sounds like a great anecdote. I would like to learn more about it. Do you have a reference? $\endgroup$ – Jishin Noben Jan 23 at 13:48
  • $\begingroup$ Mendel's work wouldn't have helped Darwin: Mendel didn't explain why traits didn't get continually diluted, but rather, he developed a mathematical description of the lack of dilution. $\endgroup$ – Mark May 6 at 21:30
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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 old schoolboy, Nicolo I. Paganini (no relation to the composer) found the previously unknown pair $(1184, 1210)$, which is actually the second smallest.

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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 equal volumes of water, one at 35 °C (95 °F) and the other at 100 °C (212 °F), and put them into a freezer, the one that started at 100 °C (212 °F) freezes first. Why?", only to be ridiculed by his classmates and teacher. After initial consternation, Osborne experimented on the issue back at his workplace and confirmed Mpemba's finding. They published the results together in 1969.

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    $\begingroup$ Do you have another source for this, because the article you link to does not agree with your statement you make. Apparently this was a well known but unexplained observation that a lot of very famous physicists had observed. $\endgroup$ – pipe Jan 21 at 2:39
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    $\begingroup$ @pipe I basically quote from the article but the wiki page is also good: en.m.wikipedia.org/wiki/Mpemba_effect $\endgroup$ – ZeroTheHero Jan 21 at 2:43
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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)

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protected by Danu Jan 21 at 19:06

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