Does more knowledge enhance your chance of doing better and 'original' research (in mathematics)?
Intuitively, of course the answer should be yes.  Surprisingly, however, in reality the answer is sometimes no.

A common saying, which to the best of my knowledge has no known attribution, goes something along the lines of: "The fools didn't know it was impossible, so they did it!"

To achieve a significant original scientific contribution, you need to know enough to have a sound basis to build upon.  You also need to avoid immersing yourself too deeply in conventional wisdom and groupthink, or else you are likely to have your originality bleed away from you.

Moreover, every hour spent reading the works of another is an hour not spent producing works of your own.  But of course, you can waste a huge amount of time if you end up reinventing another's idea or miss an important clue in somebody else's work.  So across a scientific life, you will end up wobbling back and forth on a balance between spending more time acquiring knowledge and spending more time generating it yourself.  Early in your career, you will spend most of your time acquiring knowledge, because you need to get to a point where you can understand what is unknown well enough to begin grappling with it meaningfully.  Later you may spend more time working on creating new knowledge, but must also keep up with your reading to keep from going stale.

Even in old and well established fields, however, it's surprisingly easy to get out to the edge of human knowledge and find yourself tangling with some of the interesting things we do not know.  Like, how do cats drink water? We only learned that a couple of years ago.  Heck, we're still figuring out how bicycles work!

If you don't have enough knowledge, you may not notice that there's a problem worth solving there, and you certainly won't have the tools to solve it.  If you're too saturated in the knowledge of others, you might not notice the problem either, because you might end up accepting their explanations instead.

In sum: you must know your fundamentals, know your field, and know how to go looking for specific pieces of additional knowledge.  But knowledge is not originality, and although knowledge often supports originality, it can also interfere with it.