Paul Graham defines "ambitious"-important problems differently than others have. I use Dr. Richard Hamming's version, from his talk, You and Your Research: http://www.cs.virginia.edu/~robins/YouAndYourResearch.html

And I started asking, "What are the important problems of your field?" And after a week or so, "What important problems are you working on?" And after some more time I came in one day and said, "If what you are doing is not important, and if you don't think it is going to lead to something important, why are you at Bell Labs working on it?"

Hamming constrained important problems not just to global or personal significance, but also added a factor of solvability. You had to have a way to attack a problem for it to matter, and if you didn't, you should be working on problems that would lead you there, somehow, maybe, hopefully, indirectly. Broad experience was just as important as technical chops.

If you do not work on an important problem, it's unlikely you'll do important work. It's perfectly obvious. Great scientists have thought through, in a careful way, a number of important problems in their field, and they keep an eye on wondering how to attack them. Let me warn you, "important problem" must be phrased carefully. The three outstanding problems in physics, in a certain sense, were never worked on while I was at Bell Labs. By important I mean guaranteed a Nobel Prize and any sum of money you want to mention. We didn't work on (1) time travel, (2) teleportation, and (3) antigravity. They are not important problems because we do not have an attack. It's not the consequence that makes a problem important, it is that you have a reasonable attack. That is what makes a problem important. When I say that most scientists don't work on important problems, I mean it in that sense. The average scientist, so far as I can make out, spends almost all his time working on problems which he believes will not be important and he also doesn't believe that they will lead to important problems.

I tackle important problems for designers in my recent essay, You and Your Designs, published in this quarter's issue of Distance: http://distance.cc/

I give examples of five important problems in design, and explain why:

1. Responsive web design, because it exposes content and content management as a first-order design constraint.

2. A/B testing, because intentionally and purposefully trying different things goes against how many of us were raised as designers.

3. The Internet of Things, because it means we can do away with metaphors and have physical objects that contain their own meaning.

4. "Big data" and "computational X," because they represent the event horizon for designer-as-polymath.

5. "Immersive I/O" and "natural user interfaces," because they remove our "sensory deprived and physically limited" constraints on interactions with technology.

I wrote in a different comment elsewhere, the interesting thing about entrepreneurship is, you don't have to be limited by your field of academic research, and your lunch tables of chemists and mathematicians can be those of any industry in the world. Working on important problems means your work will have long-term meaning.