325

Your question has some issues. Given some of the 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 ...


210

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 ...


200

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 ...


136

Dan's answer is very good, and I want to add one more point: Accept that on the first pass you will not be able to fully understand the topic. Appreciate that there are decades and sometimes centuries (for the math, at least) of research supporting the topic you're learning. Thinking you can "get to the bottom" of it in a few months, let alone a week or two,...


129

There should be a celebration of general topology being alive, but this does not happen. What is wrong? The people who say general topology is dead are generally not unhappy about this conclusion: they feel it died a well-deserved death due to a lack of important connections with the rest of mathematics. (They are wrong, both about whether it in fact died ...


120

Here is a brand new mathematical theory I have invented just now (in the last 30 seconds): A Gobleflump is a set together with a ternary operation Star(a,b,c), and a binary operation Spade(a,b) satisfying Star(Spade(a,b),Spade(c,d),Spade(e,f)) = Spade(Star(a,b,c),Star(d,e,f)). I could now devote my life to the study of Gobleflumps. I could publish papers ...


88

Indeed, funding agencies require authors to acknowledge their funding, but it's not mandatory to acknowledge personal resources. To me, however, that footnote doesn't sound like a joke at all, but a sincere acknowledgement of those who have supported him during previous years allowing him to have savings (and during those visits he might have worked on ...


84

Absolutely not. Affiliations do not matter; what matters is the value and the fit of the contribution to the journal or the conference to which you are submitting.


70

Unfortunately, I expect it will be difficult to find a supervisor who will take you on under these circumstances. It's not impossible, but it will require finding exactly the right match, and that will require a lot of luck. Here are some of the issues that will worry potential advisors: What if the problem is too easy, and turns out not to be substantial ...


66

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 ...


65

Publishing papers about psychology experiments does present an additional issue, human subject research ethics. A reputable journal is likely to require assurance that the rights and welfare of the research subjects were protected during the research. If you were working or studying at a research university in many countries the university would have some ...


64

Be very wary of doing mathematical research on your own. Even if you read all the books there are, you will most likely go off on a tangent and reinvent a theory that has been known in math for decades or centuries - simply because you never heard about it and did not know the commonly accepted names of the structures you have been working with. Or, as ...


63

While it is not true that you should be in academia to publish papers, I'll give my two cents on what I learned so far: If you work in industry and you write technical papers, your contributions are well-accepted, although they're typically more focused on certain practical aspects. Authors writing by themselves are welcome, but they somehow are not very ...


63

A good and fair question. I took a brief look at your materials, and it seems like you introduce a host of new terminology and notation. It would take a tremendous effort for anyone to learn it. What is the payoff? Why should anyone take the trouble? I don't mean to cause offense, but these are questions that you must anticipate and be prepared to ...


61

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 ...


57

My impression is that the likelihood of this is proportional to how theoretical the field that you have in mind is. In math or theoretical physics, it's at least imaginable for an outsider to produce an important new discovery. In High Energy Physics the idea alone seems outlandish. That said, even in math the ratio of cranks (deluded amateurs who are ...


53

What's wrong with my actions and speaking? Nothing's wrong with your actions, although they are not likely to lead to success. As for your speaking, the paragraph you quote is not ideal, but I don't think that's why you are getting turned down. Instead, the problem is that the system is just not set up to provide research mentors for high school students. ...


51

An article is not about you. It is not a reward of effort. In an article you try to communicate to the readers, so it needs to contain something that your readers want to read. If something is already done, then why would I want to read it? Maybe, you have variation, or a special case, or a more general case, that makes your equation or your derivation ...


46

I recommend that you record your failures and not just your successes. In your case, I suggest you write a technical report giving all the details (the implementation, the comparison, the conclusion). It may not be considered as a publication worthy of your resumé, but at least it serves to document your efforts and may prove to be useful in the future (in ...


43

Technically, Maurice is right. You really don't have to be in academia to publish (even in academic journals). One famous example is Paul Erdos ( http://en.wikipedia.org/wiki/Paul_Erd%C5%91s#Career ), who I believe had no affiliation (at least in practice) for much of his life. However, most cultures have certain standard ways of doing things. Academia, ...


43

What you should do right now depends on the nature of the improvements that you have made: If your new algorithm achieves its improvement due to some shift in how you represent or think about the problem, then it's probably worth publishing. You don't need to be in any special position to publish: anybody can write a paper. Look at where the competing ...


42

The question you seem to be asking is "Can I be paid to do research, without any formal education, if I am very good?" The likely answer is no. I know many serious researchers across countless fields, and the only ones I am aware of who can make a living without any formal training are inventors who got quite lucky in terms of their ideas and their ...


42

I find the dichotomy of your title question a bit strange. No, one is not required to acknowledge personal funding sources, but in academic papers one often acknowledges / otherwise thanks people and things in the absence of any requirement to do so. Though I do not know Perelman personally, I know him by reputation: he is a person of great integrity. ...


41

As Nunoxic noted, doing research as a part of your job is possible. Also, doing research at a graduate program that isn't at a top school is possible. But doing research on your own, and hoping to bring innovations to a field... is highly unlikely to work, in my opinion. My opinion is based on experience with a bad schooling system (undergrad and Masters in ...


41

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 ...


41

Nowadays, you can get feedback and answers to questions from places like MathStackExchange, and MathOverflow. Most of the responses are (in my observation) either entirely competent or quickly corrected by others. Good quality control. No, that wouldn't be the same as having a good advisor (ideally a world-class scholar on your subject) that you talk to in ...


39

It sounds like you have a singular focus on achieving the following two goals: Getting into a fully funded, high quality pure math PhD program. Using your position as a funded PhD student to solve a particular math problem you have formulated, and nothing else. Let's start by thinking how you can achieve the first of these two goals. The thing to keep in ...


39

Good question! If you are a total layman popular scientific magazines or blogs like the Scientific American from Nature Publishing Group or scienceblogs.com are a first source to spot which kind of views are represented in the community. Articles therein are mostly written by current or former academics and scientists with educational background in a ...


38

If you know someone at the university, you can discuss getting an adjunct appointment, which is probably the closest thing to what you're looking for.


Only top voted, non community-wiki answers of a minimum length are eligible