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I'm interested mainly in mathematical and related fields, in which several important and famous open questions exist (e.g., Riemann Hypothesis). Almost every day a new "amateur" scholar (meaning, someone with no formal affiliation to a reputable research institute, or someone who does not have any track record of peer-reviewed publications in reputable journals or conferences in the area) publishes into cyber-space a new manuscript alleged to solve a major open problem in mathematics or related fields. Some established researchers then consider this a work of "cranckery" (i.e., an amateur attempt that is not only false, but is mostly meaningless and hence impossible to verify since the argument is so confused and unstructured that it is hard to identify any meaningful statement to verify). On the other hand, the amateur would usually claim that his/her proof is correct, and would feel frustrated that the established scholars ignore his/her breakthrough, perhaps because they are "outsiders", or that it is harmful for the "establishment" to acknowledge the breakthrough.

This leads to a simple question: is there a single example in the last 30 years in which such an amateur whose work was considered a crank when published, was in retrospect vindicated and proved correct?

Clarifications: examples of somewhat less known, but still established academics with a track record and an affiliation, who solved a moderately big open question do exist. I'm asking about a clear person identified as a "crank" whose work was then proved to be correct.


EDIT: I decided to accept Dan Romik's answer as the closest to a complete answer to my question. There were many good and surprising answers that I didn't know about. But my criteria were somewhat strict, so none of those fall within the desired quest: an (1) amateur, i.e., someone with NO research affiliation (2) whose work of a mathematical nature was (3) considered a "work of crank" (even when extending the time limit to ~80 years back, to make sure "affiliation" and "crank" have the same meaning as today).

The closest example is indeed Dan Shechtman's work that was dismissed as pseudoscience. But Shechtman was a researcher with a clear and respected affiliation. And as Dan Romik's comments, theories that are considered "crankery" at first can be vindicated in retrospect in the natural sciences, but much less so in mathematics. So Shechtman falls in both math and no affiliation criteria.

Another great example is that of 1952, Kurt Heegner, which I didn't know about. I would have accepted this I believe, had I not read in comments that Heegner was in fact considered a serious mathematician and not an amateur or an outsider.

Yitang Zhang's example is also close, but although he wasn't considered an established researcher, his work when published was never considered "crankery" as far as I know, but quite immediately identified as an important contribution.

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  • 6
    Some professionals produce results that are questioned for a long time as too convoluted to be easily grasped. It isn't solely the stage for amateurs. Actually, the opposite is probably more likely to happen when results are accepted but subtle errors in proof leave them suspect (but unsuspected for decades).
    – Buffy
    Jan 17 at 20:38
  • 4
    Marjorie Rice comes to mind, but her results — though significant — weren't as revolutionary as I think your question is asking for. And it was over 30 years ago anyhow. Jan 17 at 20:59
  • 8
    Unfortunately most answers seem to be ignoring the criteria listed in the question. I think this is reducing the impact, and ideally all those extraneous answers should be removed. Discussion: academia.meta.stackexchange.com/questions/5103/…
    – Arno
    Jan 17 at 21:50
  • 4
    Maybe "last 30 years" is a bit too restrictive? Mind you, that means post 1992. Sticking with modern examples seems important though. Maybe 50 years (or even 70, to make Heegner fit) would be better?
    – Arno
    Jan 17 at 21:52
  • 5
    One issue with a "last 30 years" restriction is that it can take a while for an apparent crank to be recognised as having made a significant discovery. At time of writing, the top voted answer (which is more than 30 years ago) had a gap of 17 years. If an apparent crank has attempted to publish a significant result in the last decade or two, it's very possible this is not widely known.
    – James_pic
    Jan 18 at 12:07

13 Answers 13

8

The correct answer is most likely “no”, but as with Russell’s teapot, it would be next to impossible to prove that an example of the scenario you’re describing does not exist.

By way of an argument to support my answer, that isn’t quite a proof of non-existence, I can suggest the following: for mathematicians it is usually very easy to recognize who is a crank and who isn’t. And a defining chracteristic of cranks is that when someone is a crank, they are a crank all the way; they can’t be a crank up to the time they suddenly start doing genuine (let alone groundbreaking) work. So the hypothetical situation described in the question is (essentially) impossible, almost by definition.

Edit: as @MaximalIdeal points out, there do seem to be genuine counterexamples to what I wrote above (at least one, dating from 1952). I stand by my reasoning above as being the justification for my belief, but acknowledge that what I wrote isn’t universally true and in rare situations someone can be regarded as a crank but still end up surprising everyone with legitimately good mathematical work.

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    I think I gave a counterexample to your post. Nonetheless I agree with your sentiment. Jan 17 at 21:29
  • 7
    It just isn't true that cranks are cranks all the way. Look at de Branges, Mochizuki, Lang (though his crankery was always non-mathematical). Jan 17 at 21:33
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    @NoahSnyder these are serious mathematicians who started believing they had proved something they didn’t. I wouldn’t consider them cranks, although I agree de Branges’ case is a borderline case. To me, they represent a phenomenon that, while interesting, isn’t quite the same as the phenomenon of cranks.
    – Dan Romik
    Jan 17 at 21:38
  • 3
    There are quite a few cranks that study torsion fields or decipher bible codes alongside doing actual research in mathematics.
    – Džuris
    Jan 18 at 12:27
  • 3
    @Džuris all of us are probably regarded as delusional by someone, somewhere for some belief that we hold that is unrelated to mathematics. If you stretch the definition of a crank to encompass this type of thing, the whole concept of a crank becomes pretty useless IMO. My answer is limited to mathematical cranks, which I think is closer to OP’s intent than what you’re suggesting.
    – Dan Romik
    Jan 18 at 16:48
60

This answer takes the following liberties:

(1) The field is experimental, not theoretical.

(2) The person had legitimate affiliation and wasn't amateur, but was publicly decried as being a crank by noted scholars.

Nevertheless, I'm adding it because it seems to be aligned with the spirit of the question.

Dan Shechtman is a metallurgist who reported for the first time the existence of 'quasi-crystals', an atomic arrangement which appeared to violate fundamental laws of crystallography. He was famously called a 'quasi-scientist' by the celebrated chemist & Nobel laureate Linus Pauling. His own team told him to read the textbook and not make ridiculous claims. These jibes are tantamount to accusations of crankery. Anyhow, the results were published and independently verified over decades, ultimately leading to Shechtman being awarded the Nobel Prize in 2011.

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    Interesting, but also not within the last 30 years as OP asks. I hate to make people feel old, but the last 30 years start with 1992. :) Jan 18 at 8:01
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    @FedericoPoloni- It was found to be true within the last 30 years, which is how I interpreted the question. Hence the 2011 Nobel. The work was certainly done earlier. Jan 18 at 8:22
  • 3
    Of course Pauling had some "interesting" ideas of his own in later life
    – Chris H
    Jan 18 at 14:33
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    @ChrisH: Yes, Linus Pauling was the real crank, promoting Vitamin C as a cure for all illnesses including cancer. Fortunately, Vitamin C is cheap, so he is hardly as bad as those quacks who promote their own hundred-thousand-dollar cancer treatment.
    – user21820
    Jan 18 at 15:12
  • 3
    Yes, that's a great example; though the guy was not an outsider at all.
    – Dilworth
    Jan 18 at 16:30
47

Note: As Federico Poloni pointed out, the OP requested an example from the last 30, and my example below is from ~70 years ago. This was careless on my part so I apologize. Nonetheless, I think my post is informative so I will keep it up. I guess it goes to show you how rare these examples really are.

Yes, a very concrete and relevant example exists. In 1952, Kurt Heegner published a proof resolving a very significant part of the class number problem. Some sources say he was an engineer while others say he was a high school teacher, but all accounts say he was someone interested in higher level math without being a mathematician by profession. Unfortunately, his proof was dismissed because it contained a few errors, and it was more or less agreed that his paper was not valuable. He died in 1965 before his proof was recognized as salvageable by Harold Stark in the late 1960s. The result is now called the Stark–Heegner theorem.

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    This is a good example, but it's worth noting that Heegner's paper was published in Mathematische Zeitschrift, and so apparently made it past some level of peer review. So he arguably wasn't regarded as a crank so much as an amateur who made a good effort but didn't quite pull it off. Still, very much in the ballpark of what was being asked for. Interesting story! Jan 18 at 5:04
  • 33
    This is a non-example. Heegner did not have a professor position, apparently he never sought one, but he was by no means an outsider or a crank. According to German Wikipedia, he had several math papers published in Crelle and Math. Zeit. prior to his famous one. He had a habilitation (!) in mathematics, and was in contact with a few established mathematicians, including E. Schmidt, Weber and Hasse.
    – Kostya_I
    Jan 18 at 7:48
  • 2
    Submitting this as a comment since it's another "timed out" case, I think that the Alvarez hypothesis regarding dinosaur extinction should be considered since Luis Alvarez was an outsider in the field of paleontology and his contribution was derided as a "crank theory" for a decade or more. I think that there are probably other examples of Manhattan Project physicists switching to other fields and- initially at least- being considered maverick outsiders. Jan 18 at 11:16
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    It would be interesting to know what exactly Heegner's academic status was. His English Wikipedia page calls him a "private scholar", which I suspect might be a mistranslation of Privatdozent. If so, that would place him at the very upper border of the difference between "amateur" and "professional". Jan 18 at 12:40
  • 6
    I’d heard this story many times and had no idea Heegner had a habilitation! This does not seem to be widely known among mathematicians. The German Wikipedia page has a lot more info than the English one and it would be a great service for someone bilingual to update the English page to include more of the info on the German page. Jan 18 at 22:21
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Research into mRNA-based therapy, including mRNA-based vaccines, was for a long time not considered positively by much of the scientific establishment. The word crank goes too far, but it appears the scientific consensus at the time was that this research was not promising. This continued well into the last 30 years.

For example, Katalin Karikó was demoted by the University of Pennsylvania in 1995 after several grant applications for mRNA-based therapy were rejected as her peers in the scientific community thought these to be not promising. She persisted, but her key finding of a chemical modification of mRNA to render it non-immunogenic was rejected by the journals Nature and Science, but eventually accepted by the niche publication "Immunity" in 2005 (quote from Wikipedia). Today, she works for BioNTech and, since 2020, has received numerous awards for her ground-breaking work preparing for mRNA-based therapy, including COVID-19 vaccines.

Further reading: Christina Frangou, Researchers looking for mRNA were ridiculed by colleagues. Luckily, that didn’t stop them.. In: MacLeans. Available online.

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    Wow! She should be on the cover pages given how many lives have her mRNA-based vaccines saved in this year alone. Jan 18 at 15:44
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    I dislike this example. It's not ridicule to point out reasons why an idea won't work, even if those reasons are then overcome in the future. The implication is that this advance was obvious, when in fact it was the result of careful work overcoming major technical hurdles. It does the scientists who did that work a disservice by minimizing how hard it was to do (and also fails to note that as soon as they had data to suggest the idea would work, they were buried in an avalanche of VC money).
    – user152275
    Jan 18 at 18:19
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    OP asked for outsiders/amateurs, and she definitely was not one. Jan 19 at 7:56
  • 3
    If grant and paper rejections means you're an outsider then we're all outsiders.
    – user152275
    Jan 19 at 14:30
  • 2
    @SamGinrich unfortunately in too many instances bad results still positively advertise themselves… Jan 19 at 22:41
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I'm adding another answer since it's fundamentally different from the other one I've written, being arguably not by an outsider, but it was groundbreaking and happened within the last 30 years.

Li Wenliang was one of the first to identify that 2019-nCoV was a new virus, but his hospital and immediate supervisors warned him about "publishing untrue statements". As I write this, we are still dealing with the fallout of that discovery.

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    Wasn't me more of a whistleblower silenced for political reasons than someone accused of being a crank, though?
    – gerrit
    Jan 18 at 8:12
  • 1
    @gerrit his colleagues apparently decided he was wrong and pushing an untrue position, however, which is similar to being a crank. It's still not an ideal example though, I agree.
    – Allure
    Jan 18 at 8:38
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    @Allure There is enough mix of politics to say that it is not clear whether the dismissal was due to scientific, academic, or political reasons.
    – Nelson
    Jan 18 at 9:13
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I can think of some examples of people who were thought of as cranks and then had a great result, but they're mostly not "outsiders" and mostly not within 30 years. For example, my understanding (from stories told at a conference I attended) is that Apéry was widely thought of as a crank at the time he proved his remarkable theorem. But he had a math Ph.D. and was a professor at a university.

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    Why is this downvoted? Jan 17 at 22:30
  • 1
    This question seems to attract a lot of downvoters :) (not me of course)
    – Dilworth
    Jan 17 at 22:59
  • I guess the nature of this question is pointing fingers on people we consider cranks. Those who disagree will be offended, I guess.
    – justhalf
    Jan 18 at 4:06
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    @MaximalIdeal Because it does not fit the requirements of the question, like many other answers here. Jan 18 at 8:10
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    @Kostya_I It surprises me, too, that the Heegner answer only has one downvote. FWIW, I downvoted them all. ¯\_(ツ)_/¯ Jan 18 at 12:34
10

Unfortunately right now I can't think of an example from the past 30 years. These go back 150 years.

  • Gregor Mendel was a priest when he wrote the defining papers of genetic inheritance. At the time his papers were largely ignored, but today Mendelian inheritance is widely taught in high school biology classes.
  • Alfred Wegener espoused the theory of continental drift and was met with ridicule, although it is widely accepted today. In his lifetime he was best-known as a meteorologist and polar explorer, not geologist; hence he was an outsider to the field.
  • Nicholas Christofilos developed strong focusing in accelerator physics that went unnoticed for several years until rediscovered independently by professionals.
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    Mendel and Christofilos seem different: the wider scientific establishment didn’t regard their work as wrong, they simply didn’t regard them. Wegener was certainly the example I thought of on seeing the question title, though.
    – KRyan
    Jan 18 at 4:49
  • Mendel's story always hurts me. Jan 18 at 15:47
  • Wegener is an interesting example, because it really did get a lot of ridicule. The others not so much, the normal state of research is for it to be mostly ignored. Jan 18 at 17:30
  • 2
    If you insist on going back more than a century, the best choice for someone who was widely considered a crank is probably Semmelweis. Mind you, I wouldn't really call him an outsider. @FailedScientist: If Mendel's story hurts you, I can't imagine what you'd think of Semmelweis.
    – Brian
    Jan 18 at 17:40
  • "Semmelweis's views were much more favorably received in the United Kingdom than on the continent, but he was more often cited than understood." Reminds me of Orwell's iconic line from 1984. How dearly I wish I could go back in time and support him.. Jan 19 at 5:28
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+50

It's not in maths, and it's just on the cusp of whether you'd consider it in the last 30 years, but...

Demonstrating that gastric ulcers are caused by bacteria

The key research for this was done in the 1980s, and all these researchers were written off as cranks. It isn't too strong to say that the medical profession were close to unanimous in this, despite the evidence.

Whether this counts depends on where you draw your 30-year line. Whilst major evidence was presented in the 1980s, in 1992 (30 years ago) the medical profession was still very largely opposed to this and to a large degree still considered them to be cranks. It took until the mid-late 1990s before it became more widely accepted, and the two key researchers were awarded the Nobel in 2005.

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    This is a very interesting case (in fact, one of the Nobel prize winners gave themselves an ulcer and then cured it). But OP defines "crank" as an amateur with no affiliation to a research institute -- in this case, both Marshall and Warren were were medical doctors, they applied for and received funding for this experiment, and they used their hospital's resources to help with the lab tests.
    – cag51
    Jan 19 at 10:17
3

An anonymous 4chan poster proved a lower bound on superpermutations in 2011, and an upper bound was then proved by SF writer Greg Egan in 2018. These have since been folded into a 2020 paper by Engen and Vatter, and validated by other mathematicians in the academy.

A small but important difference from your question is the requirement that they publish "into cyber-space a new manuscript alleged to solve a major open problem in mathematics". The "manuscript" here was a 4chan post on an anime board, and it didn't claim to solve the superpermutation problem in general, just the specific problem of how to watch all of the episodes of a particular show in every possible order.

Greg Egan, though mainly a science fiction writer, is the sort of hard SF writer who is very technical, who has many scientists as fans, and has even collaborated on a few scholarly publications in quantum computing. He posted it not as a LaTeX manuscript but as a HTML page, on his personal website, in full late nineties web brutalist style.

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  • I'm a little confused by the "late nineties" qualifier on web brutalist style, when the Egan page is from 2018, and the style guide is from 2021? Jan 24 at 2:25
  • Well, it's kind of a rhetorical aside, but I would argue web brutalist style was almost the only way to publish on the web in the late nineties. The brutalist manifesto is an attempt to describe and valorize that as an explicit style choice. Egan's personal website has been online since 2008 at that address, and previously at an ISP-specific address since 1999. He's stuck with relatively unadorned web pages throughout due to inertia or utility, and thus with the web brutalist style.
    – Adam Burke
    Jan 24 at 4:07
0

Galois is still the only example of an amateurish mathematician without even a high school diploma who solved a famous problem. He was getting no credit for this because famous mathematicians (Cauchy and others) considered him crank.

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    Great example, but I don't think he's the only such example, at a minimum there's also Ramanujan. Jan 17 at 21:27
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    @NoahSnyder I doubt Ramanujan was considered a crank. Just obscure in Britain.
    – Buffy
    Jan 17 at 21:51
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    OP asks "in the last 30 years" though. Jan 17 at 21:57
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    Ramanujan was not a crank. To the contrary, he was easily recognized by serious mathematicians as a mathematical talent of the first order. See here for example.
    – Dan Romik
    Jan 17 at 22:10
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    @BlueRaja-DannyPflughoeft that result has been known since Euler, so all this illustrates is that that professor was an incompetent mathematician himself, and unqualified to judge other people’s mathematical abilities. Again, Ramanujan was not a crank by any conventionally accepted definition of that term.
    – Dan Romik
    Jan 18 at 7:17
-1

Definitely not a "crank," as he was a PhD-holding lecturer at a small university (just didn't have the most prestigious publication record or anything), but Yitang Zhang may be the closest modern example of what you're looking for.

His work is related to the (still open) twin prime conjecture which states that there are infinitely many pairs of primes with difference 2 (like 3 and 5 or 11 and 13). His theorem showed that there are infinitely many pairs of primes with difference at most c where c is an explicit constant given in his paper. This result was published in the Annals of Maths, often considered to be the most prestigious math journal.

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    Right, there's outsiders who weren't cranks and cranks who weren't outsiders, but not people who were both cranks and outsiders. Jan 17 at 21:20
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    @NoahSnyder and there are people who are neither cranks nor (properly speaking) outsiders, such as Yitang Zhang.
    – Dan Romik
    Jan 17 at 22:18
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    Yes, I'm aware of him. But he was a reputable established mathematical, just not in a top-top US school. He was never considered a crank.
    – Dilworth
    Jan 17 at 23:02
  • @Dilworth : I don't think Yitang Zhang was "a reputable established mathematician", he had very few publications, and his work on the Jacobian conjecture was wrong, as far as I know.
    – akhmeteli
    Jan 18 at 12:45
  • @akhmeteli, well, he was reputable at least and has an affiliation. He wasn't considered top indeed.
    – Dilworth
    Jan 18 at 16:32
-11

I'll go one better, and suggest an entire field that was regarded as crankery, but now is viewed as a legitimate field of inquiry: ufology. Prior to the American government releasing declassified video evidence of UFO encounters and then issuing official statements that they're real and of unknown origin, it was widely regarded as the work of cranks.

Now, the head of Astronomy at Harvard is launching the Galileo Project to try to record hard evidence of them, without requiring the use of military equipment.

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  • I really wish that people who downvoted answers were courteous enough to at least leave a comment explaining why, and how the answer could be improved. I've added some links to relevant sources, if that helps any.
    – nick012000
    Jan 18 at 9:54
  • @apkg Well, the US government apparently has, according to their public statements to Congress, but almost all of the recordings are classified because they're reveal technical details about the capabilities of US military radar systems and the like. That's a fair point to make, though.
    – nick012000
    Jan 18 at 10:23
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    A field studying unidentified objects in the sky should not be conflated with the religion of assuming such objects are alien-operated spacecraft. Jan 18 at 12:48
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    I am one of the downvoters. The reason for my downvote is that, regardless of whether you think that ufology is now “a legitimate field of inquiry” (whatever that means), this actually has nothing to do with the actual question. OP asked about work that was considered crankery but was then validated and proved correct. Ufology has not been “validated and proved correct” in any meaningful sense.
    – Dan Romik
    Jan 18 at 18:13
  • 2
    @DanRomik, it wasn't proved correct, but it now became a legitimate area of study it seems. So the problem with this answer is that it is not mathematical, like all other non-mathematical answers here. Basically, I believe the only "formally correct" answers is yours.
    – Dilworth
    Jan 18 at 20:57
-15

This Riemann Hypothesis guy was not an amateur or a crank but he was not working at a major institution and bigwigs of his own métier had never heard of him.

Over a century ago Gosset, as an experimental brewer at Guinness' (and using the pseudonym, Student, lest he be accused of publishing industrial secrets by his employer), published his valuable work on the t-distribution.

I'd say there are quite a few "outsiders" (i.e not established names from universities, research institutes or national labs) but I doubt if many who have no professional qualification, e.g. at least a primary degree, would bother to publish in academic journals.

Those disclosing their innovations indirectly, like people applying for patents, are often without any formal qualification in the relevant field. James Dyson is an example of this sort of thing. His ~ 5,000 experiments on cyclone parameters showed that there was a way to use cyclones to separate particles less than 20 microns from air. This was a direct contradiction of numerous "experts" - several of them apparently professors of computational fluid dynamics - who denied it was feasible.

But what are you getting at with all this ? That someone seeking recognition for solving a major problem ought to prepare the ground for that by solving a series of less challenging - and therefore more easily verified and published - problems first ? That there is a sort of hierarchy or snobbery within the scientific community ? This is evident from the very manner of so many scientists inside and outside academia. And it's not confined to science either. You see it in how attention towards an individual is accumulated in the domain of sport, investing, community activism, the arts, even in religious affairs. Of course, it is stupid to overlook a potentially valuable contribution just because it comes from a newbee or someone whose previous contributions have been unimpressive. But it's all in the game of life and we have to handle it.

But yes, it certainly is healthy when someone unknown in a field defies the "breeders' guide" predictions of his/her talent. It gets everyone back to the basic task of scientific inquiry rather than following macrotrends like some old pol.

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    Your “Riemann hypothesis guy” didn’t actually solve the Riemann hypothesis, so that’s completely irrelevant to what OP is asking about. And your other examples also don’t answer the actual question.
    – Dan Romik
    Jan 17 at 21:00
  • I'm going on the OP's definition of a crank, i.e. someone with no formal affiliation to a reputable research institute, or someone who does not have any track record of peer-reviewed publications in reputable journals or conferences in the area. I think this definition covers both Gosset (since he published under a pseudonym) and Dyson.
    – Trunk
    Jan 17 at 21:05
  • 9
    That’s OP’s definition of an amateur, not of a crank. Two completely different things.
    – Dan Romik
    Jan 17 at 22:12
  • 7
    Note that your linked articles contradicts its own headline in the text. The headline clearly says he already won the million dollars from the Clay institute whereas the text says the Clay institue was not willing to comment on his proof. The article is already 7 years old and afaik the prize is still not awarded. The Daily Mail is not the most reliable source :-)
    – quarague
    Jan 18 at 12:10
  • example in the last 30 years in which such an amateur whose work was considered a crank when published Where amateur and crank have the definitions provided by the OP. Clearly (and OP's question didn't read so clear, at least to me) a pure crank is not what the OP is looking for. He wants a poorly regarded professional whose work, esp. w.r.t. to major questions, would be read as crankery by the big-names of that field.
    – Trunk
    Jan 19 at 21:03

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