Is there a single example of an outsider considered a "crank" publishing a ground-breaking result that was found to be correct (in the last 30 years)?

Question

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.

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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.

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.

Answer 5

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.

Answer 6

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.

Answer 7

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.

Answer 8

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.

Answer 9

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.

Answer 10

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.

Answer 11

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.

Answer 12

Everyone ...

You might be shocked by this answer. It goes against the grain of the conventional wisdom. This answer is clearly the opposite of the accepted answer and OP's personal preference. But, do hear me out.

The OP defines an "amateur" as:

"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"

The rest of my answer focuses on amateurs who fall under the second category. The word "or" means that fulfilling only one of the two conditions is enough to identify an amateur and gives a precise answer.

To give a precise answer and avoid controversy, I will further narrow down to the subset of true amateurs who has not only no reputable journal ppaers, but also has published some mistaken works. "Publish" here means making things public. It includes papers, preprints, presentation slides, conference papers, and webposts.

I admit that I have been a true amateur. I have published some flawed works. I've made a lot of mistakes. I've made mistakes in an undergraduate paper that was later published in a college journal accessible to the public. I've made mistakes in the talks in my school (and those talks are open to the public). I've made mistakes in preprints. I've made countless mistakes in webposts. I am not a genius and it takes me a long time to understand a simple concept. I was and I am still a strict amateur. Yet, after nine years, I finally published in a reputable journal.

Am I alone? Of course not, almost all of my friends were similar. We were all once cranky, freshy, and amateury. We were all once naive, inexperienced, and unskilled. We were all once unprofessional, clumsy, and sloppy. We all made some blunders. Some blunders were silly, some were serious. Maybe Sally made fewer blunders because she was talented. Maybe Joe made more blunders because he took too many naps. But eventually, most of us managed to publish at least one paper. While I won't say one reputable publication is something ground-breaking, it is certainly an achievement and break-through in our narrow fields.

Before that paper, we had zero reputable publication. Our preprints got rejected everywhere, sometimes even without a line of comment.

Yes, we were cranks. Yes, we made mistakes. Yes, doing research is extremely difficult. Yes, it is even harder to get established researchers to recognize our works. Yes, there are many dark sides and unpleasant realities every day everywhere. But, a true hero will never forget their dream. A true hero will never give up. A true hero will stand against many challenges. A true hero will see the light through the dark clouds. A true hero will fight for the truth. A true hero will inspire others with their passion. A true hero will rise above their doubts and fears.

So let's finish my first sentence in the beginning of this answer.

... Everyone, in my small circle, was once an amateur, once a crank, once a misfit, stupid yet young, mediocre yet confident. But, you only fail when you lose hope.

Everyone has been there.

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Update: yesterday the OP updated their meaning of "affiliation to reputable research institute" to "tenure-track faculty, permanent scientists, and similar roles". This means that, according to the OP's definition, all students, visitors, research assistants and all other affiliates without a publication in reputable journal are amateurs.

So my answer strongly hold. Any students who made mistakes and later published a reputable journal fulfills all criteria. My answer applies to all students in fields that advisors are usually not heavily involved in student's research (for example, my small field), and applies to undergraduate students who does not have a very dedicated advisor. This answer does not apply to some scientific fields that advisors must be heavily involved and coauthor with students, and does not apply to extremely talented students who got their first paper quickly accepted in the first venue.

Answer 13

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.

Answer 14

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.