I believe I have solved a famous open problem. How do I convince people in the field that I am not a crank?

Question

I am interested in the situation where you have a very interesting result. For instance, you have solved a very important open problem. However, you are not known in the field and do not have any remarkable publications. Your supervisor thinks the work is good and you submit the work to a high profile journal, but you get rejected.

The thing is that the contribution is very strong. It breaks what most people believe or what they have already proven: e.g., you solve the P vs. NP problem or any other well known open problem.

The reviewers strongly reject your work with no justification and they do not state why the result is wrong. Examples of reviewer comments include:

• "The proof must be wrong."
• "You cannot achieve such a result."
• "You do not understand well the notion of ..."

My question is what to do in this situation? Where to go? If your advisor accepts the work, but the reviewers from the top journal reject the work without even explaining the mistakes, what should you do?

Answer 1

Your question has some issues. Given some of the (now-deleted) questions you have asked on other SE sites in the last few days, I have some reservations about whether your question is being asked in good faith, but taken on its own merits it is a reasonable question so I will try to answer it.

The main issue is that, even in asking this relatively simple question, your writing is far from clear. If you cannot write clearly in this situation, your chances of writing up a difficult piece of mathematics or theoretical computer science are less than good. For instance:

His/Her supervisor(s) accept the work and they published it in a highly known journal and they get rejected.

Laying aside issues of subject/verb agreement and consistency of tense, the entire sentence doesn't make sense: you can't publish a paper and get rejected.

It breaks what most people believe

I don't know what it means to "break what most people believe".

or what they have already proven,

What? Are you saying that your proof contradicts other proven results? Taken literally, that would mean that you have shown mathematics to be inconsistent. In practice this could only mean that if your result is correct then some previously published work is incorrect. If that's the case then you need to be very clear about that and explain the flaws in the earlier work. It distresses me that you don't really seem to believe this but are just throwing it off as loose language.

i.e., He/She solves the P vs. NP problem or any other well known open problem.

Solving an open problem would not "break what people have already proven"....that's what it means for the problem to be open. Also saying "P vs. NP problem or any other well known open problem" is a strange bit of coyness: there is no other problem in theoretical computer science (and very few to none in mathematics as a whole) which is "like" P vs. NP. So it doesn't make sense to give that as an example. It's like saying "i.e., he found the Holy Grail or some other famous cup".

In other questions you have spoken specifically about having a proof of P vs. NP and then upon questioning have retreated from this. This sort of vacillation about what you have done is a red flag of "crankiness" that will make professionals wary.

The reviewers strongly reject his/her work with no justification and they said that the result must be wrong.

Saying that the result must be wrong is not just a justification for rejection, it's the best justification. No professional reviewer will say something is wrong lightly. Almost any reviewer who says this will point to at least one specific error. If they do not, then in practice it almost certainly means that the entire document did not make enough sense to them to be more specific.

If your advisor accepts the work, the reviewers reject the work without even explain the mistakes (it is the "best" journal in his/her domain) then what he/she must do?

If you submit a paper to the top journal in your field claiming a solution to the top problem in your field, and your paper does not make sense or does not evince even a correct understanding of the problem, then the editors are likely not to want to spend much time in response. On the other hand, if you are sincerely interested in getting their expertise, it seems reasonable to write back very politely and ask for more specifics about the error. If your response is in any way argumentative then you risk the editorial staff thinking that you will keep hounding them ad infinitum, and at some point they have to stop replying. So you should write back saying that you are not considering resubmitting the paper to that journal but for your own progress it would be extremely helpful to know what is wrong with it. You could also mention that your supervisor found the paper to be correct.

In fact you could be getting more help on this from your supervisor. If you have really "solved P vs. NP problem or any other well known open problem" and your supervisor believes your solution to be correct, why isn't your supervisor moving heaven and earth to be sure your work is getting the attention it deserves? That doesn't add up. The two possible explanations seem to be (i) your supervisor is being too polite with you: s/he does not actually believe that you have solved P vs. NP; and (ii) your advisor's imprimatur does not carry any weight in the community whatsoever. The latter unfortunately means his/her opinion on the correctness of your work is not worth very much.

A good way to find out whether it's (i), (ii) or -- I do admit that anything is possible! perhaps the top journal in your field is unfairly ignoring your revolutionary work -- is to seek your advisor's help in getting another faculty member to evaluate the work, preferably someone in the department that you can speak to recently.

Finally, you seem to have some real worries that if an unknown person solves a famous problem then it somehow doesn't count. This is really not the way academia works, provided the unknown person is capable of presenting the work in a way which makes sense to the experts (and if not, what a shame, but what else could one possibly expect?). Have you heard of the recent example of Yitang Zhang? Zhang was a non-tenure-track lecturer at the University of New Hampshire when he stunned the mathematical world by proving the existence of bounded prime gaps. He submitted his work to the top mathematical journal...and by all accounts they accepted it with unusual speed. In other words, they received a paper from someone they had probably never heard of, looked at it quickly and saw that it was a plausible attack on a huge open problem, and as a result they sprung into action much more rapidly and thoroughly than for most submissions they get. This is an amazing story, but a true one, and it shows how the community responds to a real situation like this.

Answer 2

First, make sure you are not really a crank before trying to convince others. Read these common characteristics of cranks. If they apply to you then get professional help.

For the rest of the answer I will assume that you have really solved a famous open problem. In the following "he" refers to a typical non-expert claiming to have a solution for a famous open problem and "she" refers to an expert in the topic.

1. There is no easy shortcut for you!
   If you are looking for a simple easy shortcut to get your solution verified by an expert then this answer is not for you and I can assure you what you want is not going to happen.

2. Understand the magnitude of your claim!
   E.g. If you are claiming to have a proof of P is not equal to NP then you are the guy who is claiming to have a design for a rocket that can be built with the currently technology and resources to take a human to Andromeda and back safely while experts are having hard time sending a human to mars. If you are claiming to have a proof of P is equal to NP then you are the guy who is claiming to have a time travel machine.

3. Understand why experts are reluctant to directly engage non-experts.
   Many experts would be interested to know about any major progress in their field. E.g. there are complexity theorists who do read every P vs. NP related paper posted on arXiv (arXiv has a very lenient acceptance policy regarding P vs. NP claims). They will definitely let other experts know if they notice something interesting. But

• You are not the only one with such claims.
  There are thousands of people who regularly make such claims.

• All previous ones suffered from trivial issues no expert would have made.
  It is your job to show you are not one of them.

• Her time is valuable.
  For most it is not really monetary. But I think giving some numbers would be helpful. In my university a graduate student is paid over $40/hour to mark simple undergraduate assignments. This is nothing compared to what an expert might charge for consulting in the industry.

• Non-experts often lack basic skills and knowledge to understand her replies.
  E.g. he lacks mathematical maturity, he does not know basic definitions and terminology, etc. It is not uncommon that an expert tells a non-expert what he has is not a proof. She does not mean the proof is incorrect, she means it is not even a proof in the sense that an apple is not a proof. He does not understand when he is told it is "not even wrong!". To make him understand her reply she would have to teach him those required skills and knowledge, too much work just to convince him he does not have a solution. Often he is not patient nor interested in learning (e.g. reading a textbook), he is only interested in a confirmation of what he believes to be a solution. Way too much work in that case.

• It is often impossible to satisfy him.
  Because of the points mentioned above, he often insists on the validity of his claim even after she tells him it is not. At other times where he understands the reply he considers it a simple easy-to-fix error, not a fundamental one. He tries to fix it and get her verify it. This leads to back and forth.

• He underestimates the required time and effort on her part to answer his claim.
  He thinks it is a simple easy job for her to answer his claim. E.g. he expects her to give him a counterexample where his algorithm fails. Finding a counterexample for an algorithm is a very difficult task (as anyone who has marked undergraduate algorithms or complexity theory assignments would know). Finding an explanation why an idea is fundamentally flawed and cannot work is even more difficult.

4. He does not understand it is not a puzzle.
   She is not interested in the question just for its own sake. She expects the solution to the question will be accompanied with major advances in her field. E.g. complexity theorists do not care about P vs. NP just for its own sake. They expect the solution for P vs. NP will come with major progress in our understanding about the nature of efficient computation and its limitations. Often he does not understand this. He thinks of the question as a game or puzzle that he thinks he has won and that is it. This attitude is frustrating for experts.

---

Now here are some tips:

0. Be humble.
   It is much easier to get her to have a look at your solution if you are genuinely humble and eager to learn and accepting if you are told that you are wrong.

1. Make sure you understand what is required to solve the question.
   E.g. understand that a program that seems to efficiently solve an NP-complete problem is not a proof, understand that an idea does not make a proof, make sure you understand the definitions and terminology, etc.

2. Know the basics.
   I keep repeating this: read a good textbook on the topic and solve its exercises. It is beneficial for you as you will know more and will be more convincing. It is beneficial for her because you will not waste her time with simple mistakes that you would have noticed yourself if you had read a good textbook. It is annoying to deal with people who claim to have solved P vs. NP but repeatedly make basic mistakes that a good student who has taken an undergraduate course on the topic will not make.

3. Use your real name.
   Not using your real name indicates that you are trying to avoid suffering any potential negative consequence of your claim being incorrect. Using your real name indicates that you are sure enough to be ready to suffer potential negative professional consequences if you are mistaken, so you can be taken more seriously. If you are not completely sure about your claim do not waste her time.

4. Don't shirk work. Do your share before expecting help from others.
   If you want her to look at your solution you should spend 10 times more time and effort than she will spend helping you. For claims about P vs. NP you have to do way more.

5. You will not get more than one chance.
   Make it count. If on the first page of your paper she finds a silly mistake or a basic error (e.g. you do not even know the definitions of P and NP) then she will be done with your claims forever.

6. Understand the known obstacles for solving the question and why they do not apply to your solution.
   E.g. if you are claiming P is not equal to NP then you should have a good idea why relaltivization and natural proofs barriers do not apply to your solution. Similarly if you are claiming P is equal to NP.

7. Try to prove simpler more acceptable claims.
   E.g. if you have a proof of P is equal to NP then you should also have a proof of simpler weaker major results like Factoring is in P. If you can extract a clean proof for such claims then you can first try publishing them. Such results can be much easier to get verified as they are considered more likely.

8. Make sure your solution is not too strong.
   In other words, make sure it does not contradict other known results. E.g. if your argument for P is equal to NP would also show that P is equal to ExpTime (which we know is false) then you are in trouble (Scott Aaronson mentions a few more cases of too strong results in his blog post Eight Signs A Claimed P≠NP Proof Is Wrong).

9. Check your solution.
   Make sure there are no mistakes. All steps should easily seen to follow from the previous ones. Make sure you do not make extra assumptions at any point.

10. Recheck your solution.
    Put your proof aside completely for two weeks or more. Do not think about it. Then go back and recheck it with a fresh mind as if you were checking someone else's solution.

11. Build evidence for your claims.
    E.g. if you have a really efficient algorithm (i.e. its running time is a polynomial with small constants) which you have proven to solve an NP-complete problem then it should not be a difficult task to beat the state-of-art SAT-solvers or to break various cryptographic protocols based on hardness conjectures (those conjectures will be false if P is equal to NP).

12. Write easy-to-read concise clean abstract and introduction.
    Do not put any unnecessary background/history/philosophical consequences/discussion of importance/general commentary. It is a famous open problem; every expert knows its significance. Save them for your final version. Right now you should focus on convincing her that your claim is correct. She first wants an easy-to-read short error-free convincing high-level explanation of your solution. It should also explain why any known obstacles do not apply to your solution. It should also contain any other evidence that can support the correctness of your claim. If you fail the reader is not likely to continue reading.

13. Make sure the rest of your paper matches your abstract and introduction.
    If you fail the reader is not likely to continue reading.

14. Make sure every detail in your paper is correct.
    Follow the standard structure of papers in the topic. Check a few famous well-written papers in the area that have solved major open problems. All definitions should be clear, easy to understand, and rigorous. Every theorem (lemma, etc.) should be clearly and rigorously stated, and the proof of each of them should follow their statement. She should be able to see why each claim in the proof is correct based on the previous steps, definitions, and lemmas without too much trouble. If you fail the reader is not likely to continue reading.

15. Have a general expert who personally knows you check your solution.
    I am assuming that you do not know personally any expert in the area of the question. The closer the general expert is to the area of the question the better it will be. E.g. for P vs. NP, you can ask a mathematician, preferably a theoretical computer scientist. Opinion of people who are not experts in the topic may not have much weight but it will make sure you are not making some simple mistake.
    Understand that at this point someone who does not know you personally has no reason to check your solution.

16. Have another general expert who knows you personally check your solution.
    Rome was not built in a day. You have to build confidence in your solution little by little. Those you convince can become your bridges to reach the experts.

17. If they are convinced ask them to show your solution to an expert they know.
    E.g. for P vs. NP, ask them to show it to a complexity theorist they know. At this point you are less likely to be making a basic mistake and you have good evidence to support your claim. Your solution now requires the expertise of an expert in the topic.

18. If she is convinced she will definitely show it to other experts.
    News about any major progress in an area will spread very fast among the experts in that area. Other experts (complexity theorists in the case P vs. NP) will recheck your solution independently. If they are convinced you will probably get an invitation to submit your paper to a famous journal (something like JACM in the case of P vs. NP).

19. Do not claim to solve a famous open problem more than once.
    As I wrote above, you will not get more than one chance! You do not have a right to ask her to see what is wrong with your fixed solution if you made a mistake. (The exception is when she explicitly asks you to try to fix your solution and send the fixed version back to her.)

20. Do not expect an explanation for why your idea cannot work.
    It is unlikely that someone would be able to show formally that an informal idea cannot work. If the idea is formal enough then the reason that it cannot work can be a new interesting result in itself; however, proving such results can be even more difficult than solving the original question. In the case of P vs. NP, if you are claiming to have an efficient algorithm for an NP-hard problem you should not expect her to find an input where your algorithm fails.

---

In summary,

Understand that she is not required to help you. If she is helping you she is doing so out of generosity. She has a right to stop it whenever she pleases without any explanation. Be mindful of her time, do not waste it for what you could/should have done yourself, try to make her job in helping you as easy as possible, and do not do anything that will make her regret trying to help you.

Answer 3

Regardless of whether the work is correct or not, the following statement applies:

The burden of proof is on the author to convince the reader of the result.

The community (e.g., editors, reviewers) has no responsibility to evaluate your work to your satisfaction. If the reviewers made a good faith effort to read your paper and were not convinced, then you must make your argument more convincing.

(This does not mean, make a few trivial edits and resubmit. This means, prove your results so thoroughly and in such excruciating detail, and with such demonstrably excellent understanding of the problem context, that they become inarguable. Then figure out a way to express the results in a convincing way.)

If in the process of doing so you find an error, well, you'd be in good company.

Answer 4

If your interpretation of events is: "I have a heartbreaking work of staggering genius and the only obstacle to acceptance is that I am not well known and the elites are blocking my work", then you're unlikely to get good advice on what to do here or elsewhere.

The problem, as Raphael indicates, is that while it's possible that this interpretation is correct, it's far more likely that in fact your result does NOT solve the major open problem that you think it does.

Once you admit that this possibility exists, then many steps present themselves, all listed in the very good links provided. Reaching out to people who might comment on your work, looking at the literature to see if approaches like yours have been tried before and have failed, seeing if your solution also solves related (simpler) problems, and so on.

Answer 5

What does your advisor say about all this?

If she really believes you have solved this major problem, she should be moving mountains to help you publish and disseminate it. (It sounds like her name is on it too, so she has an even greater incentive.) But you've used the rather lukewarm phrasing that she "accepts" it. Better get her completely on board first, or get her to explain in more detail her reservations (which may indeed turn out to reveal fatal flaws).

The advantage you have over the average crank is that, as a student, you already have ties to the scientific community, through your advisor. Take advantage of this. Once you and your advisor are satisfied that your manuscript is of the best possible quality (see ff254's answer), post it on arXiv, and circulate. Your advisor surely knows experts in the field, and should have enough reputation that she can get them interested in it.

I'm not sure about your field, but in mathematics, this currently tends to be the way that the community handles solutions to major open problems. You don't just submit it to Annals, have the referees approve it, and then wait a few months until everyone gets their issue of Annals in the mail and is astonished. Instead, you get the community to study it first. You convince a few experts that it is plausible enough to be worth their attention, and they look at it. Either they find a critical flaw right away (the most common case), or they find a lesser flaw that you or someone else fixes, and maybe, gradually, a consensus develops that it is probably right. That's when you send it to Annals.

One thing that worries me in what you wrote is:

It breaks what most people believe or what they have already proven...

Which is it? The distinction is crucial. If it contradicts people's intuition, that raises the bar a little, but scientists are used to being surprised. If it contradicts something previously proved, that raises the bar a lot. It puts on you the burden of not only showing that your work is right, but showing specifically why the previously accepted work was actually wrong. (You can't just say "Mine is right, therefore theirs must be wrong.") You didn't say anything about having done that. (And if you can't find a flaw in the previous work, then your claim is in fact along the lines of "Mathematics is inconsistent". The bar on that one is more or less on the moon.)

Answer 6

By attacking your own proof even stronger than the others do.

Seriously, there is a reason why people in your discipline haven't been able to find the answer for centuries. The a priori probability that you are wrong is so high that even when you have created a good looking proof, the a posteriori probability that you are right is way too low. This means that, if you know enough of your own discipline, you should not be convinced that you solved it. Given a problem which has resisted solution for a long time, being convinced that you solved it just because you have a proof you believe in is a sure sign of a crackpot.

So non-crackpot behavior in such a case will be to try to take the proof apart, shoot it down, tear it to pieces from all possible angles. This is what your peers will be doing, and this is what they will expect you to be doing. To forget your pride, your subjective biases, and to be merciless to your own result.

They you only believe you after you have found more ways to disprove your result than they themselves can think of, tried them all, and failed in all of them. And your paper has to clearly show that this is what you did. Anything else will earn you the crackpot title.

Answer 7

May I add to Nate Eldredge's comprehensive answer that, if your work shakes or shatters the commonly held views in your community, then it is very important that you reconcile those views with yours, by which I mean: show exactly where the community is "wrong" or "not exactly right" and why. Offer counterexamples, predictions, all you can.

Relativity would be nowhere if it didn't reduce to good old Newtonean mechanics where the latter performed perfectly!

Answer 8

Some advice is to very carefully check that the proofs are correct, ask one's supervisor for advice, and seek third opinions. Perhaps the supervisor has colleagues in the research area who would be willing to read the draft and offer concrete feedback.

If the journal submitted to is good, yet the reviewers did not give any useful feedback at all, then there is almost certainly a problem with the abstract and introduction.

The abstract and introduction should make clear the new idea that allows this "breakthrough". Presumably many have approached this problem in the past and failed; there may be widespread beliefs about why it is difficult to prove or perhaps even known "barriers" to attempted proofs. The abstract and introduction should clearly and briefly mention why such beliefs, objections, or barriers do not apply or how they were overcome.

In short, the abstract and introduction must give the skeptical reader reason to believe the paper could be correct, given the reader's background knowledge. If this is done, I would hope that reviewers would at least mention why they do not believe the result.

Answer 9

While most of the answers seems to have much confidence in the academic system, I would like to offer another viewpoint.

I think it is in fact much harder for an unknown (to a specific field) to present a solution to the scientic community than normally expected.

Scientists do screw up and sometimes royally.
First example: The infamous Monty Hall problem.
More than 65% of all professional answers to Marilyn (with all sorts of academic grades including statisticians) strongly rejected their answers, sometimes with outright jeers and taunts. This included Paul Erdos and Straight Dope Cecil Adams. So even the majority of experts can fail.

Second example: The also infamous neutrino anomaly. The interesting thing here is not the error itself, but the reaction on Arxiv. Anyone who would have dared to offer superluminal theories before the announcement would have been immediately declared as relativity crank. After the announcement papers came flooding in offering all sorts of superluminal theories explaining what we know now to be simply a bad cable.

What are the problems an unknown may face ?

1. Arxiv. You need an affiliation from an university or research institute and/or an endorsement from a know author. Arxiv can revoke or limit your access without explanation. This requirement also applies to fully qualified scientists which are working in companies.

2. Journals. Too many people are trying to get their results published in too few respectable journals. Journals also pretty scale bad, you have to wait a long time to get published. Lesser known journals may have lower barriers, but you have the real danger that the contribution is missed. And even the lower journals may reject the paper.

3. Scientists. The situation is different in various countries, but normally scientists are overworked and underpaid. They have not the time nor the resources to review contributions with the very slim chance to get a scientific jackpot.

If someone thinks the viewpoint is not valid, try just for fun to supply a normal paper under a pseudonym and the home address.

The only viable option I see is to get contact to the scientists in the field and try to work with them over the contribution which may be harder than it sounds. The list provided by Kaveh is a good resource to start with.

Answer 10

Despite what people will say it is true that journals will reject papers using author profiling without a proper review. It is hard to say how many papers are rejected this way but Elsevier say that they reject 30 to 50 percent of papers without a review for other "technical reasons". See also this paper about how editors can save time by looking at author attributes such as affiliation to reject papers without looking at them.

I have personal experience of this because I recently made significant progress on a well known 100 year old open problem after experts in the field had said that future progress was likely to be very slow. The journal I submitted the paper to rejected it as soon as I confirmed that I had no affiliation. There was no reviewer report and they did not give any specific reason. I had complied with all their technical requirements for submission.

However, I pointed out to them that according to the code of conduct of the committee on publication ethics to which the journal claims to adhere "Editorial decisions should not be affected by the origins of the manuscript" and "Journals should have a declared mechanism for authors to appeal against editorial decisions." To my surprise they responded after a delay to tell me that they would look at it again.

It is true that there are many claimed resolutions of problems such as P vs NP that can be dismissed at a moments glance. This can be done because there are well understood reasons why these problem are hard and a solution would need to address that. Many claimed proofs of open problems by non-academics descend quickly into non-standard language that makes it hard to even address why they are wrong so they are just ignored by the community. It is up to the authors to make sure they communicate their ideas correctly.

If you do have a solution to an open problem my advice is to submit to an open repository such as arXiv. If you can't get an endorser use viXra or figshare (full disclosure: I am viXra admin) Do not pay attention to negative things said about viXra. It's purpose is just to give you an independent time-stamp and an archived copy you can point to. It does not attempt to review or give your work credibility in any way. The last thing you should do is submit to journals or send to experts without having a verified public copy because if it really is a breakthrough there is a real risk of plagiarism that can only be averted by having a prior copy archived.

Answer 11

From my experience as a graduate student, it seems that researchers who are passionate about their work do approximately the same thing regardless of its supposed importance.

Here's what to do:

(1) Write up your work as best you can while also discussing the ideas and concepts with your friends, collaborators, co-workers, etc.

(2) Promote your work to other researches, friends, collaborators, etc. But, often people are busy so keep your expectations low and courtesy high.

(3) Pinpoint your audience and seek out the appropriate journals, workshops, and conferences to submit to.

(4) If you have any questions or concerns before submitting, contact someone affiliated with the conference. I've had a positive experience doing this, but sometimes you get ignored.

(5) Be ready for rejection because you are more likely than not to get rejected (even if your results are important, actually especially if they are important).

Remarks:

(a) I like to think that the quality of reviews is associated with the clarity of the paper, but I've received some questionable reviews in the past that seem like scattered words that may or may not be related to my work. Just don't hold a grudge and happily try again.

(b) If something's important to you and you're financially capable, then getting rejected once or twice is alright as long as you keep trying to improve your presentation and keep communicating with others.

(c) You don't want to go off the face of the earth and live like a hermit. That's not going to help anyone and especially not you.

(d) Finally, be open minded. People do make mistakes and sometimes the thing that caused the mistake is meaningful.

Answer 12

Some very important papers have been rejected first, some were not even published.

If you are sufficiently sure about your result, and want to set a date for your discovery, and are not afraid that it sometimes takes time to demonstrate and convince people of the correctness, put your paper online on some open archive, while you work at an hopefully published version.

Some readers may discover a flaw, and perhaps help you publish.

Answer 13

First of all, "solving famous open problems" does not happen in a vacuum. There must be a good reason why the solution occurred to you after having eluded many others.

A possible reason is that you are an expert in some new technique or method of analysis. Then the trick is to establish yourself as an expert in this "new" field. Once you've done that, it is easier to claim that your mastery of this one area enabled you to solve the "unsolved" problem (providing you can demonstrate the relevance of your field). For instance, if you were a pioneer in subatomic physics who discovered that Newtonian physics didn't work in the subatomic area, acceptance of your "proof" would hinge on people's acceptance of you as a subatomic expert.

The other thing is if you have really discovered a new solution to a problem, the implication is that a lot of what is currently written in the field in relation to this problem is wrong, or at least needs to be re-thought. The way to prove yourself is to start identifying at a low level, and rising to progressively higher levels, applications that are now "voided" by your discovery. If you can prove that a whole "stream" of ideas needs to be re-thought, and then present your discovery as a "common" solution, people will take you much more seriously. An example was when people figured out that you could create a new system of "non-Euclidean" geometry just by changing a few assumptions.

Answer 14

Obviously, it will depend on the context of your discovery but one way to go around is to make an application based on the implications of your ideas. E.g. if you proved p = np, then go make a webpage and dare people to test your application to solve any np problem of any size in seconds. This way it will take them seconds or minutes to figure out if you're a crank or a genius. This approach won't work in all cases, e.g. if you actually proved that p != np.

Answer 15

Prepare for your fearlessness. You will need to use it frequently.

---

Let's say our goal is to accomplish Kaveh's list. Assuming he has some experience in academic research, then each of these statements are equivalent:

• His priority is not really to have his work accepted, but actually about not being misunderstood (the actual premise of the question is about having productive feedback)
• For him she is just stating the obvious (the upper part of the list), and telling him to do things he is already doing (the lower part)
• She needs him to accomplish the list, but he cannot do that if she accuses him for doing the thing he didn't do
• The problem of convincing her that he is not a crank is reduced to the emotional and misunderstanding problems

I think that in all discussions about cranks the overwhelming assumption is that he is hubris. This is, unfortunately, one-sided, because the actual emotions should be guilt and frustration . He is guilty for worrying he is hubris, and frustrated for her misjudge that he is hubris. With all my respect, think most experts lack the necessary experience to give an efficient advice.

^{Because this answer doesn't attempt to answer the problems that most established experts want to address, it is basically a frame challenge answer.}

The rest of the answer is just an elaboration on how to deal with emotional reactions and misunderstandings in each specific case. Here is the table of content for this answer:

• Dealing with your emotions
• Dealing with their reactions
• Other problems
• For those who want to help
• Links

You can also read an answer for a generalized question (what challenges one may face during the project, not just how to convince the experts). I will assume that your platform to get feedback on your work is Reddit, but it's not a big deal.

Dealing with your emotions

First, there are two things to begin with:

• Epistemologically, it seems that in order to solve a hard problem, you need to be aware to the solution a priori
  ^{Epistemology is a field in philosophy studying about the nature of knowledge and how we acquire it. I haven't read much about this though.}
• Psychologically, when you are aware of yourself, these self-conscious emotions will evoke: pride, shame, guilt, and embarrassment

Because doing research is to prove that you are wrong before proving you are right, a natural thing when you think you know something is have skepticism about yourself. So alongside with the specific problem you are working with you will ask these self-conscious questions:

• Am I claiming a thing that I haven't proved it yet?
• Am I claiming that I know better than the experts, when I lack formal education?

Since the answers to those questions should be yes, they will evoke self-conscious emotions, drifting you from the one and only thing you should focus on: the problem you are working at. You will enter a feedback loop of questioning yourself: the answer for those questions is the reason you questioning yourself at the first place. The real answer lies in the work you are researching, not about whether you are sane or not.

To deal with fantasy (a kind of pride), try to imagine how a life of a famous person would actually be. For every kind of success you are dreaming of, there are people who have already got it. So say you dream about the Nobel prize, ask yourself this question: how did Einstein live with his fame and money? When you realize that in fact all famous persons are annoyed for being famous, then your fantasy is cut. By being able to put yourself into their shoes, you can detach to your emotions, and get back to reality. At that time, if you still wonder what you will do when you become famous, then the only thing you want is a dark and quiet place to have a dreamless sleep through it.

Please be aware that you may have messiah complex. You may not have grandiose delusion, but the thinking that (1) only you can provide a solution that no one seems to see, and (2) in other to deliver that solution, you have to overcome the skepticism regardless how harsh it is, can develop this complex. People may also accuse you for performing gaslighting as well. All of these will make the guilt about yourself even stronger.

^{To distinguish them with true psychological problems, whose root is insecurity, I will call them as "intellectual messiah complex" and "intellectual gaslighting".}

Because the fear that you are delusional only continue when in fact you see that you still have fantasy, so when you have successfully cut it, then the fear itself will disappear. You will not feel shame, guilt or embarrass about your work anymore.

In general, the emotions are only intense when your research is still at the vague phase. The more knowledge you acquire, the less frequent they show up.

Dealing with their reactions

In my experience, there are these types of unproductive response: labeling and sarcasm.

Labeling

When they tell that you are crank, just give them this crackpot index, list all the points that may apply to you, and explain how they are wrong. If they accuse you for being arrogant, tell them that confidently walking into a storm with a smile is different to seeking for attention. If they think that you are insane (walking into a storm with a smile is insane obviously), it would be much easier if you can have the conversation face-to-face. Only by seeing how your eyes are determinate but your mind is not closed at all, that they can assume that you are not. Don't be embarrass for telling them how you have prepared for the project.

Let's discuss more about insanity. I think it is best to "help" them reach the conclusion that you are insane, because it is no longer a label on your behavior, but a label on your rationality. When you reach that stage, they will have a strong motivation to continue the conversation, and your evidences will be listened carefully. If you can create a cognitive dissonance in their mind, then their pattern-matching will be silent, and they will not be locked in their perspective anymore.

Respond to their labelling (crank, arrogant, insane, stupid, high, bias, spam, word salad, not even wrong, woowoo, pseudoscience, time- wasting, etc.) by giving the definition of the word and show why it doesn't apply to you. Have a note listing all your prepared answers for each label, so that you don't need to rely on your poor memory. To deal with skepticism, you need to immediately form perfect combination of words, and your brain will put you down. (More details later.)

Sarcasm

If they simply making some jokes, it may be true that it is actually funny. In that case, perhaps it is best to continue the joke. Seeing how you actually enjoy their jokes will make them see that it doesn't affect you at all. Like if you are a fat person, then joking on your fatness will make them see that you are aware of your shortcoming, and it's just that you don't have time to solve it yet. If you are a blind, then having a joke involving your disability will make the non-blinds astonishingly surprised. They will perceived you as invincible now.

If it's really hurt and you can't think of a clever thing to say, then perhaps it's best to remind them that they are in a place that mocking is not acceptable. Like a smack down show, they literally see you as the arrogant prideful guy who need to be taught. Note down links to comedic shows, where making fun of others is the goal, like WWE shows, higaniga conspiracy theory videos, or mocking subreddits, and show them how hilarious their actions are. For example, you can say:

Wow, r/Buddhism becomes r/WWE now?

Or you can invite an authority to deal with this:

I don't think this behavior is appropriate. I'll report the mods/I believe others don't find this appropriate as well.

In short, be clever when dealing with ad hominem. The problem is that you can't be clever when your mind is clouded with anger. So you need to prepare for clever moments. When you can do that, then their next response will likely be productive again.

But in all, don't interact with them because you feel misunderstood, but because of the knowledge they have. Try to convert questions about your identity/self (e.g. "am I crank?") to question about definition (e.g. "what is crank?"). Show how you possess a rigid body of knowledge of what they are trying to convey, with phrases like "psychologically speaking", "what you are talking about is called ______ in philosophy", "in the field of informal logic", etc. They are relevant interesting academic fields that they don't know of. If you think that they have knowledge on what you need, only focus on that, and ignore any unreasonable critique at you.

When you have solved all of the emotional problems, then 90% of the conversations now are productive. But there will still other problems.

Other problems

Memorial problem

You may have wasted so much time to read about crackpotism, conspiracy theories, delusion, etc. You may have wasted so much time on conversations that at first people strongly disagree with you, but after some talks it turns out that they don't really disagree with what you actual mean, and all of this is just misunderstanding. Take note on every evidence that that make you feel you are on the right track. Don't let your research about your sanity gone.

The problem of being unable to explain yourself is because of tacit knowledge and the tip of the tongue phenomenon. When you have a very strong evidence that you are not a crank, then after a week or so what is left is just a feeling that you are not. Lacking the evidence, you will be dragged into the loop again. You need to immediately make a perfect combination of words to get out of this.

Misunderstanding

Even when miracle happens (they spend their time and energy to analyze what you say), there will be a very strange phenomenon that you just can't understand: you always feel that they implicitly agree with what you say, but you two can't settle to a consensus, and thus just going circular.

I think, all conflicts in the world come down to the problem of priority. Usually the situation is like this: person 1 can see that problem A is more important than problem B, and person 2 see that B is more important than A. The problem is that, most of the time both A and B have to be solved together, or else none of them can be achieved. But because both insist that their point is more important, both will miss and pass each other point. Both will feel the conversation is unproductive, and sooner or later one will drop it.

When this happens, it is just a blind leading a blind, or worse, a blind fight. Investigating the nature of this phenomenon and how to deal with it is my research interest. My advice to deal with misunderstanding is to use negation, not explanation.

Egocentricism

Egocentrism is not about being selfish or have a huge ego, but about being unable to differentiate your mind with others' minds. When you find something interesting, then you will automatically assign that others will find it interesting as well, and will be confused when in fact they don't really care. However you remind yourself about this, this tendency will still activate.

Don't assume that they will assume that their feedback is wrong. You may be open minded, and they are too, but in practice both of you can't. If you assume that they are curious to know why they are wrong (a kind of trust), then you will tend to give explanation. But in fact they just see that you are defensive. They accuse you for things you have never done, and then either passively drop the conversation or actively block you from further explanation. I term this as "intellectual silent treatment".

Seeking feedback

When an idea pop up and you feel wonderful, your gut will still tell you that there are much more fields you need to read carefully. Although you don't mind spending more effort on researching, you just want to ask for feedback because it would be much more efficient. Your egocentricism assumes that people will get what you get too. If you want to finish the project as soon as possible to move on to other important things, then your urge to share it will be higher. But STOP! Posting it now will only receive harsh, unreasonable critiques. Listen to your gut, and read all the fields you need first. Good questions only come when your mind is in the ignorance stage, which is the result of understanding the field as it is.

Having said that, at some point you will see that there is no point to ask questions, and you just want them to read your work as it is. If you have the necessary requirements (literary review, inline citation, methodology, etc.), then you can now submit to an academic journal, and you don't have to be afraid for being misunderstood as a crank anymore.

Receiving feedback

In case your first and foremost audience of your work is the popular audience, making your writing style necessarily un-academic, then the situation will be complicated, because your most important audience is the academic one. (Yes, sometimes the important thing is not the one you should prioritize – see the Eisenhower method.) Because your work has to serve two different kinds of audience, who have different background, knowledge and expectation, you will have mixed feelings when receiving their feedback:

• Popular audience cannot provide useful feedback, but their excitements indicate that you have touched a big problem that they are looking for
• More knowledgeable readers or even academics from distant fields can give useful knowledge, and can play the role of initial gatekeepers. But once they say good luck to you, you know that they cannot help you anymore
• Academics from relevant fields will feel it's vague or wishy washy, because they expect your work to truly be presented in academic form. But if you explicitly say that this is just the phase to capture what you have in your mind, then their attitude will flip 180 degrees

Let's talk more about the last point. In your mind, having no literary review, methodology or dataset is not important, because you already accept that you don't have one. Therefore, you must say explicitly that the article is just a cursory research to sketch a roadmap for your study, and list all of your shortcomings as best as you can remember. Without this part their expectation will lock their minds, and any of your explanation from now on will be perceived as defensive.

For those who want to help

Here is my advice for those who want to help. Hopefully it can reduce wasted effort, and bring you maximum happiness:

• Always assume that the person you are talking at has something interesting that you can learn
• Be conscious that although they may not know what they are talking about, you may not know what they really want to convey either
• Confirm their correct observations before address your concerns
• Use Socratic questioning

Don't feel threaten when they show signs of crankiness. The fact that they accept to be labeled as crank indicates that they have something more important to do. Like you, they are rational creatures, and they have already run cost-benefit analysis before starting the project. When you want to give them advices, you may want to frame it like this:

• I don't think there is another option to do X / The best way to do this is Y. But since it seems that you know this too, can you explain why you don't think it suits you?
• I don't think you understand concept Z as it is. In my opinion, Z is about a, b, or c, and perhaps c is closer to what you mean. Is that correct?

You may want to learn about conceptual metaphors if you want to know why sometimes serious ideas are hilariously crazy. I recommend the book Metaphors we live by by Lakoff and Johnson.

Links

Kletische has some good articles about this:

• How to Handle False Accusations in Everyday Life
• Why You Win When You Forgive
• How to Handle, and Grow From, Hateful Criticism

You can also read my research: A theory of perspective. It discusses about various things, two of which are intellectual betrayal, and cold gaze, which are relevant to this answer.