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As a very new researcher who is exploring the best way to generate ideas, some guidance on this question would be very helpful. I have found that this is NOT easy. Ideas seem to pop out of my Professor every day and I wonder how he does it. This question is broad;

  • How do you tend to come up with initial/seed ideas? What is your search method (if you have one)?

  • What proportion of your ideas for past papers come from; (i) colleagues, (ii) intentionally browsing the literature for ideas, (iii) on the spot inspiration, (iv) conferences, (v) other?

  • How do you prioritize research ideas?

  • Is there any special, generalizable method that you've discovered to sift out those ideas that are likely to be unrealistic early on in the process of idea generation?

Based on small amounts of anecdotal evidence I have reason to believe that there is vast heterogeneity among professors regarding the above questions. For example, economist Steven Levitt says he works on 22 papers at once. A professor I know will have maybe 25% of this at any one time.

Related but not duplicate: Is there any software or tools for managing developing research ideas?

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Anecdotally - for me it just happens (and I have much more ideas than time to develop them), while either reading or (much more) solving other problems. Just sparks of "what if?" or "can I generalized it?". For me it rarely happens on purpose - it it not hard, but impossible to force myself to be creative (on research or anything else). Related - Paul Graham, "How to get startup ideas". –  Piotr Migdal Dec 18 '12 at 18:53
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8 Answers

up vote 29 down vote accepted
+50

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 discoveries, is not “Eureka!” but rather, “hmm... that's funny...” — Isaac Asimov

It's probably very akin to asking a large number of artists “how do you come up with inspiration?”, i.e. you can probably get one thousand different answers, and yet not useful answer at the same time. However, there are some elements that I think are common to all. You can't “trigger” new ideas to come into your mind, but you can put your mind into the right disposition to host these new ideas: recognize them and welcome them. Below is a list, certainly partial and limited, trying to detail my perspective in this matter:

  • Be challenged! Nothing sparks ideas more than being confronted with contradiction, healthy criticism, a spirited debate, maybe a bit of competition. Some people manage to do that by themselves, arguing against their ideas and improving them. I myself (and most of the colleagues and students I have seen) need an echo chamber, someone to discuss things with. If they're not exactly from your field, all the better, as they may have unusual/naïve/silly questions or expectations.

    To give an example, some of the most “successful” ideas I have had came while answering questions, for example from a PhD student or colleague, and replying by “no, it doesn't work like that… in fact, it's probably always guaranteed to be false, because… see, it's linked to X… or maybe it's not? hum…”

  • Be curious! Ideas come from problems. Identifying worthy problems in your field of research, and dissecting larger issues into of specific problems of manageable scope, is at least as hard as coming up with new ideas. In the end my feeling is that, especially for a researcher, all ideas are the result of one’s curiosity.

  • Manage to get some free time for thinking (and not: teaching, supervising, tutoring, reviewing, writing, sleeping, …). Body and mind. Sure, an idea can pop into your head any time, but it's probably less likely to happen when you teach basic calculus all day that when you get some time to really think.

  • Know your field, know where a new development need to occur, what is currently missing. Read review papers, search for such ideas through people's articles or blog posts, discuss with senior colleagues who have a comprehensive view of the field, …

    One of the ways you can come with ideas is by analyzing how different groups work in your fields, seeing what has been addressed and avoided, what big questions are still open, and how you can link between different works to build a coherent global picture… This is not always successful, but it usually generates some good ideas along the way!

  • Explore more or less closely related fields, and see if there is something from your background that you could apply to their problems, or ways you could build something together. Such ideas tend to be very strong, because you can oftentimes apply an entire branch of knowledge (ideas, methods, algorithms, etc.) to a very different problem. In that case, the added value comes from your different perspective, as you might try things that others would not think of.

  • Ways have been devised to come up with new ideas on a given topic, either alone or in group sessions. Brainstorming is probably the best know such method (and might be the most popular, in one form or another), but a really large number of creativity techniques have been developed. They can be applied both to enhance creativity or to boost problem solving efficiency.


Organizing ideas

A quote often attributed to Kant: “someone’s intelligence can be measured by the quantity of uncertainties that he can bear”. If that true, that has serious consequences for research. Accepting that your mind can only efficiently support a finite number of ongoing research ideas, you have to come up with ways to write them down, organize them, prioritize them, come back to them later, etc. Just as you cannot juggle with as many balls as you'd like, such “external” tools will help your brain focus on the ones that you assign high priority (or the ones to which it gives high priority; the brain works in funny ways).

Most people use very low-tech tools for that:

  • Notebooks, either sorted chronologically or thematically; in the later case, open a series of blanks pages for each new project/idea, and flip through the book whenever you want to check on them. I use a Moleskine (WP) for that purpose; having a nice, leather-bound notebook somehow helps me “value” it more and treat it with care (always have it with me, actually use it).

  • Post-it’s scattered through one’s (real or virtual) desktop. Downsides are obvious.

  • More people than I thought actually don't use any tools, and just keep all in their mind. Apparently it can be done, but I don't advise it.

But more complicated methodologies have been devised, that are supposed to help you with it:

  • Mind mapping, either on paper or software-based.
  • Using todo-list flat or two-dimensional todo-list software, or more complex task-tracking software (see, e.g. Trello).
  • The software side of this question is already covered (though possibly not extensively) here on this very Q&A site.

Finally, don't underestimate the possibilities opened by delegating: people in charge of a specific project or sub-project (PhD students or post-docs) can be tasked with maintaining a list of ideas by all contributors of the project, to come to later on.


Answers to your miscellaneous smaller questions:

What proportion of your ideas for past papers come from; (i) colleagues, (ii) intentionally browsing the literature for ideas, (iii) on the spot inspiration, (iv) conferences, (v) other?

Most ideas are hardly “traceable” to one source or another. A given idea might have formed in my head during a conference, seeing how people were failing to address a certain issue, then crystallized during a discussion with colleagues, but would never have occurred to me if not for a literature review I had performed a few months before.


I'll come back a bit later and continue working on this answer :)

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+1 for the Asimov quotation. I had this as an epigram in my PhD thesis. –  Nicholas Dec 19 '12 at 9:37
    
Agreed! +1 for Asimov! –  Ben Norris Dec 19 '12 at 11:44
    
What do you think of using something like OneNote as a surrogate to the physical notebooks you were recommending? Latex equation typesetting websites can effortlessly generate .gif pictures of your equations that you can copy into OneNote. Wouldn't this do the same thing with the same level of efficiency (or even more because you won't have any clutter) as a physical notebook? –  Jase Dec 23 '12 at 3:26
    
+1 for an epic answer. –  Jonathan Landrum Aug 13 '13 at 15:12
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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 something in a clumsy way and you have learnt a better way to do it, and so on.

    I wouldn't worry too much about this: it's a matter of time and experience, and will happen on its own. You're not evaluated on the number of ideas you have in any case. You might want to check how many of these ideas are actually good ones :).

  • How do you tend to come up with initial/seed ideas?: When you're first staring at a problem, it can be intimidating and difficult. While there's no single strategy for getting a "leg up", some useful techniques (and these might be very math/CS specific) are:

    • simplify the problem: can you solve a simpler version ? if not, can you simplify even further ? Often, finding the largest solvable element starts to get your mind rolling
    • pattern match: does this problem look like something related that has been solved ? can you borrow a method from there ? if not, why not ? again, the goal is to get your mind off the "ZOMG THIS PROBLEM IS TEH HARD" and onto "Here's a tiny piece that I can chew on".

I'm sure others will have useful ideas as well. Ultimately, you'll find that getting ideas isn't the problem: it's getting GOOD ideas that is hard.

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+1 for pattern match; found it very effective specially among different graph-like representations. –  seteropere Dec 20 '12 at 7:15
    
+100 because I expect that your simplify the problem and pattern match advice will be very helpful. –  Jase Dec 24 '12 at 5:04
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Here is some things I found useful:

  1. Attending public seminars at the department could spark nice ideas (even if it seems not related to your research).

  2. Chatting with other graduate students.

  3. Reading deeply with why? in mind. This means reading a lot and also means stopping more than usual in the assumptions hypothesis and results for different papers.
  4. Read future work and conclusions of the papers. Some papers have a real list of future research ideas.
  5. Capture the Big Picture. This usually will result in many whys for what you encountered.
  6. Ask Questions.. Even what seems as silly and fundamental questions for some can be the key for good ideas.
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Do you, when presented with anything related to your research, routinely ask, "Why is that? How can I tell if that is the case?"

If not, try doing so.

If so, you probably won't be short on ideas. Your problem will be sorting the good ones from the bad ones.

Then start asking "Is this important? How can I explain why it is important?"

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Be open/curious to what related disciplines are doing. In some you'll see that the way they solve their problems could also applied to your field but hasn't been tried yet.

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The most practical way is to go to the Library and look through journals for articles that interest you.

When you have found a selection, then sort them by a) Is this a current concern in your field? b) Is the prevailing methodology/technique practical - have you the resources? c) Will your supervisor(s) find this project interesting?

When you can answer all three questions as Yes, then do a deeper literature research and assess again whether the project is doable in the time available and publishable (sound and interesting to people in your field).

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I think it would be much more efficient to do it over the internet where every single journal article can be accessed instantly (which is not the case in the library where some references are inaccessible or take 5 minutes of wasted time to find). –  Jase Dec 30 '12 at 1:21
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Maybe you could try approaching the problem from another direction,

"What is it that you would like to achieve? what is the purpose of your research?"

There are millions of problems in life at the moment, and finding things to research is not the problem at all, even though it may seem that way. Inspiration is not purely found in a textbook, but are a function of the mind and soul and body.

Experience is what probably allows your professor to come up with constant questions. He probably practices free thinking, whereby he doesn't feel constrained in any way by other people and current belief systems. Maybe a lot of the problems that actually need to be understood, such as mental health and problems that people and our planet, experience everyday, just aren't being taken into your current world-view.

Science in itself is not an end. Science is a state of being, including understanding; and is a way that you as an intelligent, caring and investigative person (I presume) approach problems. A classic example of a problem is, that we don't understand. However, simply not understanding something is not a problem. A problem is something that has effects in the real world, such as, how can we help infertile couples reproduce and have children? Although it appears that now that we have resolved this in some detail, that it was the problem of not understanding DNA and the details of reproduction that probably is what resulted, with in vitro fertilisation, and even in vivo transplants etc. If one were to take the time to step out of this 'curiosity breeds progress' mindset, it would appear that these problems weren't purely driven by a quest for knowledge, but from real world problems, that have fortunately been solved.

I'd be interested in further discussion, as I have only this evening come up with an idea myself!

There's always a thirst for improvement, and this won't cease until people realize that happiness doesn't come from materials. Happiness is within all of us, all we have to do is tap into it. Being only 24 I have seen some truly eye-opening things and I am very humble to each of our personal strengths, but I do feel its a shame that research has become so fascinated with one-upmanship, and away from the real potential and benefit of being so intelligent.

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I would recommend Pragmatic Thinking and Learning: Refactor Your Wetware by Andy Hunt. This book has some very good tips for coming up with ideas, research or otherwise.

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I don't think this is very useful without giving some indication of what is actually in the book. –  David Z Dec 21 '12 at 2:09
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