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96

Generally speaking, you need to do more than develop software (any software) to get a PhD. Even creating a new Operating System isn't quite "enough". But the reason is subtle. An many people base their doctoral degrees on software they develop. The issue is that, in most cases, people will, like myself, have the belief that you get a doctorate by advancing ...


87

From your question it seems that the only reason you chose computational mechanics was because it was "hot", and you are now regretting your decision because the field is no longer "hot" and thus it's hard to publish in high-impact journals. This is the wrong approach, not just because it's impossible to predict what topic will be "hot" when you enter the ...


72

Okay, as you say, this is very broad, and possibly argumentative. So, I'll try to section off my answer for your various sub-questions, and talk not so much about how I do come up (and organize) research ideas, but how I see it done by everyone (including me). Coming up with ideas The most exciting phrase to hear in science, the one that heralds new ...


72

Novelty is a basic requirement in research because without novel results, the work is of at best limited usefulness. It's not useless - review papers are useful - but it's less interesting to the people at the frontier. In the case of a PhD, it is supposed to signify a student is now capable of doing research. Research (as opposed to literature review) ...


63

This might be a good research topic for a Ph.D. in mathematics education, which is a thing that you can get a Ph. D. in (see for example this list of schools offering that degrees). However, it would not be a good topic for a Ph. D. in mathematics.


60

The whole point of scientific debate is to refine our knowledge. Go into the discussion with a mentality to learn, not to win. Keeping this in mind will help you keep the discussion not adversarial and not emotional. On unresolved disagreements, try to find a way to falsify either hypothesis. If it is not possible, consider that which option is correct is ...


59

Only my personal experience, but I hope it will help you a little bit: I am almost in the exact situation you describe in your question. I finished my PhD in Algebra (coding theory, lot's of linear algebra and representation theory) and am now working as a software developer. As a fun fact, this wasn't always planned. When I started my PhD, I was still ...


44

Perhaps the best route is to split the difference. Note the concern of one professor, but take heart from the support of your advisor. There are a lot of possible explanations. Perhaps the professor making the comment is overlooking some aspects that are harder than they think. Some things that look easy from the outside are harder when you get into the ...


41

One approach is follows: Find one or two good recent PhD theses in your chosen area. Read these thoroughly. As you read, write down every question that pops into your mind, write down every time the author states that something is left for future work or needs further investigation. This will have a dual effect. Firstly, you will get a good introduction to ...


41

"Insulated" is a strange word to use there, but that reads for all the world like "This was a one-off project for me I don't really work on anymore". Many academics end up having those. It doesn't mean anything about your research, and definitely isn't "shocking". To respond to your edit, one-off or isolated projects aren't inherently better or worse ...


39

I completely agree with ff524's criteria, but here are some further considerations: A good thesis topic should not be all or nothing. Instead, it should accommodate a range of levels of ambition. There should be fallback options that would be enough to graduate even if things go poorly, moderately ambitious outcomes that you could reasonably aim for, and ...


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 ...


39

A single point of feedback says nothing about your future prospects. There are just too many possible sources of noise in the data. Maybe the professor had a paper rejected, or a scoop of his favorite ice cream dropped from the cone just before your talk. If the same feedback would arise repeatedly, that might be an issue.


35

This answer will be a bit different and not limited to the sciences as the other current answers seem to be. It will also apply to many similar degrees not designated PhD. I'll use the term "doctorate" as an abbreviation for "research doctorate" to distinguish it from other degrees such as those that are clinically focused, for example. Study for a ...


34

I'll address two points in your question (the overall question is quite broad): Ideas seem to pop out of my Professor every day: If you've worked on enough problems, you amass a collection of tools and mental shorthands that you can apply to a new problem. It's a matter of experience. You also might see someone else's paper and realize that they are doing ...


33

My take on this: yes your feelings are normal, but Hotness is overrated (by definition). Researchers who are only passionate about "hot" topics are, many times, not good researchers scientifically, and professionally. The reason is that "hotness" is not intrinsic to the scientific subject you research, rather an external, almost purely social phenomenon. ...


33

Your situation is quite common with MS theses (in the US at least). There are several people who are given ideas from their advisors which either turn out to be dead-ends or take up much more than the allotted time. In EECS, the MS thesis defense is more about displaying your ability to conduct research than having significant results. Clearly describe the ...


30

I believe the most 'formal' way to share these would be to write a survey of the area that your open problems relate to, highlighting each problem. This adds a publication, and anyone who solves one of the problems is likely to cite it. Moreover, if the survey is sufficiently in-depth, it can generate a large number of citations as an introduction to the ...


28

The interaction between student and professor should not be a one-shot set-a-problem. Instead, they should be talking frequently, often once a week, and adjusting the nature and direction of the project based on what is being learned during it. The project starts with some idea, from either the professor or the student, that the professor thinks likely to ...


27

I think you need to do some reading up on the path towards getting a PhD. In general, an idea that you have on your own based on knowledge you acquired during your undergraduate studies is extremely unlikely to be suitable as a thesis topic. Rather, to get a PhD you’d need to apply and get accepted to a PhD program, take classes, and find an advisor who ...


26

Your best option, in my opinion, is to discuss it with him. You may need to wait a bit until he feels well enough to think about it, but you really need his advice about how to proceed. He may be able to help you in your current studies, or not. Depending on the illness he may also never return to work. But, if you need to change professors and projects, he ...


25

You'll be amazed at how much the choice of Master's thesis will influence your long-term interest in the field, prospects for jobs within and outside of academia. I'd suggest picking up some mainstream journals or magazines in your field and see what is currently trendy in the field, and what are bread and butter topics. Having a birds eye view of what's ...


25

Jot down your interests. Future goals (long term and short term). Doesn't have to be accurate but just to give you the "big picture". Speak with your PhD advisor (if you already have one). Align his/her interests with yours and see if you have common ground (you may need to lean towards his interests or find another advisor) Once you have a list of topics ...


24

It is easy to discharge your ethical obligations here: you treat the unpublished paper like you would any other source, i.e., citing it carefully and making sure not to rewrite sentences or rehash ideas without explicit attribution (include direct quotes if necessary, and probably don't include too many of those without a very compelling reason). As you ...


23

You're thinking about this the wrong way; if do not have a topic you want to write about - then don't write. I'm not being flippant: You should write and publish something if you feel it's important to express in writing and to disseminate. Don't try to produce publications for publication's sake. But maybe it's the other way around: You're frustrated ...


22

A "good" thesis topic is one that's a good research topic in general (moves the field forward, publishable, etc.), interesting to you specifically (you'll be spending a LOT of time on it), a topic that (you and your advisor believe with some degree of confidence) can be addressed with the resources that are available to complete the thesis. ("Resources" ...


22

In most fields in the US, coming to a potential advisor with a proposal isn't necessary. But with an MS, you should have the area you want to study narrowed quite a bit. I don't know specifically about how it works in applied math, but in theoretical math, you generally work out the project details with your advisor given some common interest. The advisor, ...


21

At least for most graduate programs in pure mathematics in the US, there's no need to have a specialization in mind when applying. [This may be very different in other countries.] It's valuable to demonstrate in your application that you have studied some serious mathematics, by discussing undergraduate research or advanced coursework. However, there's no ...


21

An incentive you should recognize is time: worrying about these problems takes time away from what you do want to prioritize. I recommend the following experiment, and will assume for sake of discussion that the ideas lie within mathematics. Take one or two of the ideas that you consider expendable, and spend 30 minutes writing a MathOverflow post about ...


21

Any of the scenarios you describe can happen, in practice. (I am in the United States; this may differ in other countries.) It depends on the student's interests and abilities, the advisor's interests and advising style, how broad advisor's interests are, whether the advisor has funding for a particular project and needs a student to work on that problem, ...


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