62

Assuming that somebody is not an employee of a university, just a math amateur, and makes a proper proof of some well known open math problem, what should he do with it? Publish on the internet for verification or send to some authorities? Is there a high risk that nobody will treat it seriously?

yoozer8
  • 233
  • 6
  • 14
Ztalloc
  • 627
  • 6
  • 4
  • 63
    Not to discourage anyone or anything, but it is almost certain that an untrained amateur's "proof" is erroneous and trivially erroneous at that. Before sending it for publication, they should show it to someone with mathematical training. Errors usually show up as circular reasoning, the use of invalid / undefined mathematical operations, category errors, not to mention the subtle logical errors that can happen to the best of mathematicians. – user_of_math Aug 15 '14 at 07:52
  • 1
    Here's a related question, although the questioner is an academic. It has signs attached to it that the questioner in that case might be aggressively wrong, so it's not the same but I think some parts of the answers will apply: http://academia.stackexchange.com/questions/18491 – Steve Jessop Aug 15 '14 at 10:00
  • 19
    @user_of_math The question says nothing about "untrained". I guess many former IMO medalists, for example, are not professional mathematicians, so they are amateur, but I wouldn't say it is almost certain that their proofs are trivially erroneous. – JiK Aug 15 '14 at 10:46
  • If the "amateur" has indeed found the solution to an open problem, which is something that professionals have spent years on with no success, shouldn't he/she at least consider spending a suitable amount of time and effort on it, that would perhaps mean enrolling in a university, and impressing his/her teachers enough to be taken seriously? – Boluc Papuccuoglu Aug 15 '14 at 14:05
  • 5
    If you *really* believe you have something, and fear having credit stolen should you show it to a trained, "professional" mathematician: write down your proofs, seal them, then mail them through traditional mail to yourself (if in the US, use USPS and mail it in a tamper-proof envelope). (You can also get the documents notarized before mailing.) After receiving the letter, **do not open it**. Take it to a bank, open a safety deposit box, and place the sealed unopened mail in the box. This provides a "poor man's copyright" which is better than nothing. – Doc Aug 15 '14 at 14:19
  • 15
    I hate to see academics poo-poo each other. Too much negativity in these replies!!! So, best of luck to the OP, I hope your solution makes it! – Unknown Coder Aug 15 '14 at 15:57
  • 15
    "Mail it to yourself" is advice that's often repeated, but it's likely poor advice. It does not provide any significant level of evidence of the date of authorship since seals and postmarks are both trivial to fake. If you're really concerned about this, consulting a lawyer and using a proper legal service designed for this purpose, or if not that, at least making proper use of a cryptographic notary service that could provide evidence of the date of signature, would be a much better course of action. – R.. GitHub STOP HELPING ICE Aug 15 '14 at 16:21
  • @Doc If you have a document notarized there is no point in mailing it to yourself. The post mark adds nothing over the notary's markings. – Kaz Aug 15 '14 at 18:14
  • 1
    Reading [this](http://blogs.discovermagazine.com/cosmicvariance/2007/06/19/the-alternative-science-respectability-checklist/) could be helpful too. – Ela782 Aug 15 '14 at 23:47
  • 2
    Following the footsteps of Clark Kent and Bruce Wayne, publish it anonymously in an open-source environment, and sign it *The Masked Mathematician*. :-) – Lucian Aug 16 '14 at 04:06
  • @R.. A better way would be to have the document in electronic form and publish a cryptographic hash (such as SHA512) of the document through some channel(s), where the date could not easily be forged. – kasperd Aug 16 '14 at 10:32
  • I voted to close as "too broad" because it seems to me that the correct answer to this is going to vary widely with the details of the proof (and the question it purports to solve). There is no such thing as a generic breakthrough... – Micah Aug 17 '14 at 06:12
  • 1
    @Doc Mailing something to your self proves nothing. If I'd mailed myself an unsealed, empty envelope last week, I could "prove" that you stole your comment from me by retyping it, putting a copy in my envelope and sealing it. The postmark only proves that the envelope went through the mail; it says nothing about the contents. – David Richerby Aug 17 '14 at 20:53
  • @DavidRicherby That's why I specified using a tamper-proof envelope. If such an envelope is opened you can easily tell. By mailing it USPS priority, there are records both that you have and that USPS has that the envelope was mailed. Placing it in a safety deposit box adds an extra level of dating (as banks will hold records for when the box was first opened and any time it is accessed after that). This isn't fail-proof, but it does provide some level of protection for people who really don't trust anyone else. – Doc Aug 18 '14 at 15:08
  • @Doc Using a tamper-proof envelope and sending it USPS priority make absolutely no difference. If I'd USPS priority mailed myself an **unsealed**, empty, tamper-proof envelope last week, I could still insert documents into it this week and seal it. The postmark, my receipt and the USPS's records still only prove that the envelope went through the mail. They do not prove that the documents were in the envelope when it was mailed. – David Richerby Aug 18 '14 at 16:01
  • @DavidRicherby ...Thus the additional instruction to place in a safety deposit box and not to access it again until such time that proof is necessary, at which point you can have a suitable witness with you. Also, "this isn't fail proof", "better than nothing". Yes, a deviant can fake it by various means but at least it gives some piece of mind to the paranoid. – Doc Aug 19 '14 at 11:49
  • 1
    @Doc That still doesn't help!!! I now have my fake proof in a safety deposit box and I bring you along to witness that, when the envelope was removed from the box, it was sealed and that, when I opened it, it contained the document. That still proves **nothing** about the state of the envelope on the date it was posted. The whole exercise is legally worthless. It gives no security to anyone, especially not the paranoid, who will assume that everything that could be faked has been faked. – David Richerby Aug 19 '14 at 12:08
  • @DavidRicherby The bank will have records of when the box was originally opened, and when it was accessed. I opened the box on August 18, 2009. It hasn't been accessed since. I take you with me to retrieve what's in the box. The bank confirms the box hasn't been opened since 2009. We open it, you see a sealed envelope inside which has dated postage on it. Even if you don't believe the postage, you should be able to place a moderate level of confidence in the package being from at least August 18, 2009. I'm not going to continue arguing in circles about this though. – Doc Aug 19 '14 at 13:34
  • 1
    Hash it and pay a pence to put it on a blockchain. – Mark S Jan 22 '18 at 03:15

6 Answers6

55

I'm no expert on this subject, but the impression that I have comes down to this: your work may be very worthwhile, but it's hard to be taken seriously if you cannot communicate your discoveries.

A particular difficulty in getting published in mathematics is that the subject is very technical -- to use a shaky metaphor, mathematicians speak their own language; and, within the field, each subject has its own dialect. If you're working without formal training or regular interaction with other mathematicians, it's naturally going to be difficult to gain the knowledge of terminology, notation, conventions, etc., that is needed to write research-level mathematics.

The problem is that lack of mastery of "the language" is often construed as a lack of understanding of concepts themselves. A professor of mine once mentioned that he receives many papers from amateurs, and in these there are often give-aways (like misuse of terminology and unintelligible symbolic manipulations) which indicate that reading the paper will simply be a waste of time.

With this in mind, put effort into writing your results clearly and carefully. Strive to use the vernacular of the field in which you have made a discovery. Read/skim papers on subjects close to yours to get an idea how to do this. Post on MSE with terminology questions. If you have trustworthy friends with experience in mathematics, try to get them to read over your proof and give you their candid opinions (both about your exposition and about the validity of your arguments).

Probably far more helpful than my rambling, here is a webpage with extensive advice for amateurs, including suggestions for how to go about publishing. You might also find this MSE thread helpful.

vociferous_rutabaga
  • 4,441
  • 13
  • 26
  • 7
    +1, clear communication is the most important determinant of whether or not an outsider will be heard by insiders. – whacka Aug 15 '14 at 08:25
  • 2
    There is also some [excellent advice from Terence Tao](https://terrytao.wordpress.com/career-advice/be-sceptical-of-your-own-work/) on this. – Andrew Kelley Jul 03 '15 at 18:45
24

I think that there are three things you need to do.

  1. Type it in $\LaTeX$. No matter how good your results, or how clear your exposition, if it is written in Word using Equation Editor then noone will take it seriously and it will be lost to the world. Get the source-code of some good papers off of the arXiv to see how to do this well (find a paper, then go "Other formats $\rightarrow$ Download source").

  2. Establish precedent. I have never quite understood this one thought, but perhaps that is because I am a tad naive. However, I do not think that the best way to do this is to post it on the arXiv, because doing this lets the whole mathematical community see your work and if you have a simple error then you will have lost all credibility (note: you cannot delete papers from the arXiv).

  3. Send it to someone to proofread. However, this is difficult for all involved. Chances are, no professor will have the time to look at your work (they are busy people, who barely have time for their own research!). Thinking outside the box, I think the best thing you could do would be to cherry-pick a few PhD students and send it to them. They will be flattered, and will have more time to respond (or, at least, will not be getting dozens of similar e-mails every week!). If they think the work is worthy, then they will pass it up the tree. Anyway, if a professor does decide to look at your work then they will probably fob off the checking to a PhD student. For example, during my PhD there was a very insistent man who ended up frequenting the pavement outside my department, waiting for mathematicians to leave and then thrusting copies of his work into their slightly scared hands$^{\dagger}$. In the end, one professor took one for the team, and gave his first-year PhD student the challenge of finding the error.

$^{\dagger}$This is not a good way to make friends.

user1729
  • 28,057
  • 7
  • 60
  • 128
  • 23
    You can't delegate "taking one for the team". What that professor did was jump under the crazy bus and pull a PhD student under too ;-) – Steve Jessop Aug 15 '14 at 09:05
  • 5
    +1 for this answer. I share your puzzlement about 2. Establishing priority worries "amateurs" **a lot** although, today, a preprint publicly available on the internet is all the proof one needs. // It seems 2. and 3. are both achieved by *sending the paper to a journal for refereeing*, no? In every journal whose Editorial Board I am on or whose modus operandi I am aware of, *every paper sent to the journal is looked at*, whatever the credentials of the authors. True, crackpot submissions usually require a very small amount of time to be rejected, but, ... – Did Aug 15 '14 at 09:22
  • 3
    ... despite a common myth, even they are submitted to a proper refereeing process. – Did Aug 15 '14 at 09:23
  • @SteveJessop Actually, it all depends on the time one needs to find the error. In most cases, this is infinitesimal (if the error is a priori subtle, to ask a PhD to stop her work to find it is another matter). – Did Aug 15 '14 at 09:25
  • @Did I agree about journal submissions. However, picking the right journal is hard and it help to have a mentor to guide you through this process (some ask you for suggestions of reviewers, and this mentor would perhaps advise not putting "Terry Tao and Andrew Wiles" as your top two candidates for reviewing your short proof of Fermat's Last Theorem!). Moreover, if I had such a proof then I would find it useful getting someone to look over my work before taking the journal submission plunge! – user1729 Aug 15 '14 at 09:32
  • That said, journal's do stipulate submissions be typeset, so maybe the answer should be simply "submit to a journal". *However*, some journals are dodgy... – user1729 Aug 15 '14 at 09:32
  • @Did: yes, in reality if the professor undertook to sit between the PhD student and the amateur (and not tell the amateur who is doing the review), then it is indeed the professor doing the hard part. The hard part is taking on the risk that it will be necessary to put in months or years of correspondence to convince the amateur that the proof truly is flawed, they have not trisected the angle, that there is no conspiracy to silence them in order to prop up the incorrect assertions of "big math", etc. – Steve Jessop Aug 15 '14 at 09:33
  • 1
    @SteveJessop To include in the flowchart the task of *convincing the author* strikes me as quite unreasonable (and this is never a task journals embark on with authors, is it?). – Did Aug 15 '14 at 09:41
  • 1
    @user1729 I agree with the content of your two last comments. – Did Aug 15 '14 at 09:43
  • 5
    @Did: that's why it's (potentially) a crazy bus. Once you've first taken on a "very insistent man", they're not standing outside the department thrusting papers at people, they're thrusting papers *at you*! You may not think you've made a long-term commitment to persuade them of anything, but short of moving cities it's not necessarily clear what will terminate the correspondence. So in the professor's position and given there's a warning sign in evidence, I think it would be *grossly* unethical to instruct the PhD student to speak directly to the amateur! – Steve Jessop Aug 15 '14 at 09:46
  • @SteveJessop I may have omitted a non-trivial fact in my anecdote: the maths department in question had a back door. – user1729 Aug 15 '14 at 09:47
  • @SteveJessop Like what, sending you repeated, insistent, obnoxious even, emails? Spam filters are (also) made for these cases... To use your metaphor, a crazy bus you can walk down from at any time looks not very crazy to me. // Meanwhile you expanded your comment: "I think it would be grossly unethical to instruct the PhD student to speak directly to the amateur!" DEFINITELY! – Did Aug 15 '14 at 09:50
  • My spam filters don't sweep the pavement outside the department (not that I have a department, but even if I did they wouldn't). And checking outside the windows every day to see which door you can use unmolested is hardly "walking down from the crazy bus" ;-) – Steve Jessop Aug 15 '14 at 09:51
  • @SteveJessop Ah, you mean, *physical* contact? Eeeeagh! Sorry, my comments do not apply to this case... – Did Aug 15 '14 at 09:53
  • This is ridiculous. Taking papers from some guy isn't jumping under a crazy bus. You're not a high security research compound and he's not a spy or terrorist. You're just academics, and he's just an enthusiast. Of course he has poor social skills, (thrusting papers at people and all) but how are the average social skills of those who work *in* the building? I bet a few of them have thrust flowers at a woman and ran away, haha. It's like you're rock stars and he's a shy groupie. – Kaz Aug 15 '14 at 18:20
  • @Did Re: "it seems 2. and 3. are achieved by submitting for refereeing:" I don't know what happened to [this case](http://academia.stackexchange.com/questions/3124/what-to-do-if-a-referee-plagiarises-the-result-after-rejecting-a-paper?rq=1) from Academia.SE, but it underscores the importance of establishing precedent through more than just journal submission. – apnorton Aug 15 '14 at 18:33
  • @anorton In most journals I know, journal submission establishes precedent since every exchange between the authors and the journal are stored on the (private) website of the journal accessible to the whole Editorial board. – Did Aug 15 '14 at 21:24
  • Side question, but how bad is a mistake on a paper on arXiv in terms of affecting your credibility? Like if I was trying to disprove something with a counterexample but I made a mistake in writing the numbers that form the counterexample, will that make me lose my credibility? – user541686 Aug 15 '14 at 22:37
  • proof verification services, while quite inconvenient as of Dec 22, 2020 would be able to solve the "proof read" problem without bothering another human. Since if you had a easy to use proof assistant you could just write the proof in computer readable format, and it would be able to check your work and confirm validity. At that point, if the open problem is documented online, and you can prove that your proof solves this problem, people have no choice but to acknowledge your work, even if you had no academic credentials. (for the record i still think the premise of this question is unlikely) – Sidharth Ghoshal Dec 23 '20 at 03:43
22

Hardy to Ramanujan: 'Let me put the matter plainly to you. You have in your possession now 3 [Ramanujan had only two] long letters of mine, in which I speak quite plainly about what you have proved or claim to be able to prove. I have shown your letters to Mr. Littlewood, Dr. Barnes, Mr. Berry, and other mathematicians. Surely it is obvious that, if I were to attempt to make any illegitimate use of your results, nothing would be easier for you than to expose me. You will, I am sure, excuse me stating the case with such bluntness. I should not do so if I were not genuinely anxious to see what can be done to give you a better chance of making the best of your obvious mathematical gifts.' Quoted - p181, The Man Who Knew Infinity, Robert Kanigel.

  • 10
    Along the lines of this quote (+1), it's worth noting that [Ramanuajan](http://en.wikipedia.org/wiki/Srinivasa_Ramanujan#Contacting_English_mathematicians) sent two failed letters (returned without comment) to English mathematicians before contacting Hardy, who realized his potential. In the book, the author suggests that the reason for these first failures might have been that the mathematicians Ramanujan chose were older and better-established, hence less open to going out on a limb for an unknown. – vociferous_rutabaga Aug 15 '14 at 14:01
9

There's a list out there that I'm sure someone else will be able to attribute that assigns crackpot points to a paper to determine whether or not it's worth reading ( I think John Baez? ). Explicitly or not, most professionals decide whether or not to read a proof based on the ideas in that list.

At any rate, regardless of what you've proved, and regardless of whether you're professional or amateur, your best bet to get your paper read is write a good summary introduction that introduces the main ideas and insights in your proof. Your first couple pages should lay out the new ideas, the main technical tools used, etc If your insight is obviously flawed, this will help an expert to quickly pick it out and point it out to you. If it's an old idea known not to work ( but maybe this isn't known to you ), an expert will also be able to pick that up quickly and suggest you make sure you have addressed the old attempts. If it's a genuinely new idea, though, then that's what's going to make the expert reader continue reading to the body of your proof.

Agree with frogeyedpeas that arXiv is the best approach. I think going directly to a journal would be very difficult. You can try reaching out directly to some professional academics as well, but I strongly recommend you do not send it to the top people at top Universities. Someone at a local college or University is a good bet. If you've been able to formulate the new idea yourself without professional training, probably anyone at any University working in math will be able to follow it.

Also, maybe goes without saying, but do write it up in LaTeX. No one is going to read a Word document proof.

6

If an amateur has created a proof of a problem the natural step is to publish it on either arXiv (or if you don't have access) viXra.

At that point you have documented you were the first to get the idea at a certain time. Now if you think it's material worthy of appearing in a paper you should attempt to reach out to relevant journals (which will have a standard method of submitting articles, etc.) and then submit your proof.

Additionally, you may want to reach out to relevant professors and researchers in that particular area to have them look over your stuff (this may take some time to coordinate so be patient!).

Again to be taken seriously in both areas is tricky. If the proof is nothing massively groundbreaking it shouldn't be a problem, but if you hypothetically did prove something huge like P=NP then chances are a good 99.9% of people will laugh you off (if you are an unestablished amateur) regardless whether you are correct or not.

This shouldn't be taken negatively, it has nothing to do with the mathematics community, it is human nature.

Peter Mortensen
  • 627
  • 5
  • 11
Sidharth Ghoshal
  • 14,653
  • 8
  • 33
  • 81
  • If it's just for documentation purposes I'd rather go with scribd than vixra. – whacka Aug 15 '14 at 07:46
  • 7
    I would not recommend vixra. If the OP is concerned with protecting a claim, one can put the paper on one own website. Although vixra philosophy of allowing open publication is commendable, the experts are usually not in the audience of vixra so vixra is not a good place for dissemination. Moreover, there are many very low quality papers on vixra. Usually, the purpose of publishing in a good journal is to earn the distinction of being among reputable works. It is not usually a good idea to put a paper among the terrible ones on vixra. – William Aug 15 '14 at 07:50
  • @William I must disagree, as a high schooler ViXrA was my goto place for documenting work that I am continuing to develop. It offered me @ the time the piece of mind of "this idea has been publicly proven mine first" now I can share it without worry others may adapt for their own purposes. Obviously something like scribd also works but I wouldn't bash ViXrA so quickly, as a repository it does an excellent job, as a peer referred source of high quality material, no way!, but isn't that obviously not its job today even if original intent when it was created? – Sidharth Ghoshal Aug 15 '14 at 07:53
  • 5
    The founding idea of vixra is interesting and there may indeed be some good papers on vixra. However, there are numerous papers with serious flaws and error. You may disagree with this point, but this is actually irrelevant. What is important is that vixra has an awful reputation. If the OP is an amateur having difficulty getting recognition, why would you shoot yourself in the foot by putting a paper on a place which a significant number people view unfavorable, especially when there are numerous other venues, like scribd, with a positive or at least neutral reputation. – William Aug 15 '14 at 08:03
  • 2
    @William: the amateur will get recognition if their proof of a "well-known open problem" is confirmed. They're hardly going to be known as "that guy who solved the Collatz conjecture, but then threw it all away by publishing on vixra so I'm not going to bother reading what he has to say about Goldbach" ;-) Journal rep is for when your result is obscure or otherwise difficult to evaluate directly. – Steve Jessop Aug 15 '14 at 08:52
  • @SteveJessop Your point depends on whether anyone will read that paper to confirm the result. The issue is depending on the nature of the question, there may be less than five people in the world who have the ability to confirm a proof. These are busy people. If even three of them think poorly of vixra, you now have only two people left to convince to look at your paper. Your chance of getting confirmed has just decreased. – William Aug 15 '14 at 08:55
  • 1
    Also, they would still be known as "the guy who solved it and put it on vixra." If I were the type to fantasize about being the guy who solves the Riemann Hypothesis out of nowhere (*cough*), my major worry would be the loss of style points inherent in neighboring with 75% crazy train. – whacka Aug 15 '14 at 08:58
  • 1
    @William: I don't really believe your hypotheticals. It's almost totally implausible for an amateur to come up with a correct proof that only 5 people can understand, because the thing that causes proofs to be understood by only a small number of people is their use of existing obscure results with complex pre-conditions, that an amateur would unlikely be exposed to and able to correctly use (in effect you're positing that the amateur is the sixth). But supposing it happens, you'd correspond with the 5 directly, they won't read it because they spot it on vixra. – Steve Jessop Aug 15 '14 at 08:59
  • @SteveJessop I don't really believe your hypotheticals. It's almost totally implausible for an amateur to come up with a correct proof of the "Collatz conjecture" or some other famous result which is not "obscure or otherwise difficult to evaluate directly" using technique anyone can understand or within length that most people would be willing to take the time to read. – William Aug 15 '14 at 09:04
  • 5
    @Steve while the exact number of five may be an exaggeration, it's certainly no exaggeration to claim that the solution of any famous open problem will almost surely only be understandable by a relatively small community of busy elites. And indeed, I'm pretty sure the name "vixra" *will* influence most mathematicians' decision of whether or not to seriously read something. They have to make these choices, and they have to base these choices off of something, after all. (One of my friends used to go on vixra literally just for teh lulz.) – whacka Aug 15 '14 at 09:07
  • @William: but the hypothetical reviewer doesn't need to read the whole thing, only as far as the first error. Almost certainly that's quite early, but if the questioner truly is a genius then the reader will become more interested as they go. The difficulty is in finding someone with time and inclination to read almost-certainly-wrong submissions. I guess the question is this: supposing you can get such a person to read your email, will they search vixra for your name and reject as soon as they find it? – Steve Jessop Aug 15 '14 at 09:11
  • 1
    @whacka: supposing what you say is true, and also that the questioner understands their own proof, then it follows *the questioner is a member of the small community of busy elites* already. The whole situation is wildly speculative, of course. What pertains, is that the proof can only be given the stamp of authority by someone in authority. Realistically it will in fact be understandable by a larger group, so like user1729 says you want it passed upwards. The questioner can resolve this issue using info we don't have -- what non-well-known *techniques* does the proof use? – Steve Jessop Aug 15 '14 at 09:15
  • @Steve Membership in this community is more than just having a proof in your head - by that logic, an alien with such a proof would be a member without even knowing of planet Earth. Rather, membership is defined by publishing, reading, and social networking. When big new results eventually make their way to mainstream media, it's because the experts could authenticate that a paper was sufficiently plausible based on certain heuristics, and given the volume of work they usually deal with, this will be stringent. – whacka Aug 15 '14 at 09:23
  • In summary, while it's true that an ideal, perfect paper will *mitigate* presence on vixra, it doesn't change the fact that vixra weighs against you, not for you. – whacka Aug 15 '14 at 09:24
  • @SteveJessop I am not really that oppose to the central concept of vixra, but the OP main concern is the "high risk that nobody will treat it seriously". My point is vixra is viewed unfavorably by many people, and it will needlessly harm an amateur already struggling to get confirmation. I think the benefit of vixra does not outweigh the harm when it comes to the OP main concern. Perhaps you disagree, but you have not actually said anything positive about vixra which could mitigate these issues. – William Aug 15 '14 at 09:32
  • @William: no, I agree that vixra doesn't serve any great purpose here that couldn't equally be served by any open publishing platform (scribd like you said). I'm just sceptical how many people will pay attention to or care what an amateur has done with their paper. For an *academic* to publish on vixra has certain implications about their ability to publish in a journal or at least arxiv, and those may be damning. – Steve Jessop Aug 15 '14 at 09:42
4

If you have solved an open problem and can monetize it then this question is easy. For example, consider factorization.

If you really developed an algorithm for efficiently factoring large numbers, you could write a paper in latex describing your algorithm and proving its correctness. You could send that paper to me. It is likely I will not understand your paper and nothing will happen. You could send it to leading researchers in the field and they will probably think you are a crank and not read your paper and nothing will happen.

Or you could try some of the RSA challenges. Collect a bunch of prizes and likely people will be coming to you asking you questions.

emory
  • 239
  • 1
  • 7
  • 2
    If you left out the money part, I'd say this was a good suggestion. A lot of open problems are constructive, such as factorization, P=NP, discrete logarithm in polytime, etc. If someone said they had a constructive solution to one of these problems, I wouldn't pay any attention to it without an implementation, regardless of how intractable it might be for large cases. – DanielV Aug 17 '14 at 19:49
  • 1
    @DanielV Exactly. People at my level can evaluate constructive implementations. Otherwise you are restricting yourself to a small elite group who probably don't have time for you. – emory Aug 17 '14 at 20:20
  • The RSA challenges were ended years before this answer was posted. Source: https://en.wikipedia.org/wiki/RSA_Factoring_Challenge – Albert Hendriks Jul 14 '21 at 09:07