I'm a math student and I find that coming up with original ideas and being creative is very important in the field. I love math and I'm also a voracious reader and I like to learn about many things including physics, philosophy, history, music, etc. but math is on the top. So I like to think about these areas, however, sometimes I get this worry that because I'm investing my thinking into something other than math that my creative abilities will "run-out" and I won't be able to contribute creative ideas in math . Is there any validity to this idea? I know my question sounds weird, but it's been bugging me especially that I'm not aware of any research regarding this. Thanks
There are two sources of creativity, the within-domain analogies and the between-domain analogies. Within-domain analogies are less original but more easy to apply and use. Between-domain analogies are far more original but usually need a lot of work to apply them in the target domain. (see this book for more info)
Within-domain analogies may be quite effective in making the resulting design solutions more useful, since the sources may be industry standards that are effective and tested. But the resulting solutions are less original.
Between-domain analogy. Random between-domain cues have a positive affect on originality.
In the community of innovation T-shaped persons are highly valued. These individuals are very specialized in one area (the vertical line of T) and also have a broad but shallow knowledge of many other disciplines (the horizontal line of T).
The vertical bar on the T represents the depth of related skills and expertise in a single field, whereas the horizontal bar is the ability to collaborate across disciplines with experts in other areas and to apply knowledge in areas of expertise other than one's own.
You will not "run-out" of creativity, it is simply a matter of resource allocation. You should spend most of your time at your specialized field, but at the same time you must allocate a significant proportion of your time in other fields like physics, philosophy, history, music, engineering, biology or even to more diverse domains like fishing, sports etc. This way you will create a T-shape knowledge which according to the above references, will make you more creative and more usefull.
In order to be creative in some areas, you should be bothered by some problems. It is important to have relevant knowledge because creativity in math is not similar to creativity in art, where rules can be broken. Relevant knowledge is essential also because it offers tools. What is relevant is not always easy to identify. Asking related questions might also be good.
It is important, however, to take breaks in dealing with the questions that bother you. It helps to lose the ties that tie you to specific ways of thinking. Sleeping also contributes because it helps to lose existing ties and build new ties - some of them might be surprising. Dealing with other fields may or may not help directly, depending on how the deep structure of things might be transferred, but the breaks themselves are important, so in general, it is not a bad thing to spread on various different issues, as long as you find the time for the "dry" things.