I personally think that scientific papers offer a lot of good ideas. They will often talk about what useful applications that certain mathematical concepts have and the state of the art of what can be done with a certain technology, you will be amazed how many applications there are for something as simple as linear regression. A lot of the times they will outright publish open source libraries that have achieved state of the art performance in certain specific applications and can be integrated in your own product demo.

Also, watch some lectures (and do problems if you really want to understand the material) from MIT open courseware on challenging subjects like Linear Algebra or Statistical Inferencing. If you can combine fields from web crawling/page ranking and linear algebra (like Google did), you could have a really great idea.