Imagine a world in which Andrew Wiles instead of working in secret on Fermat's Last Theorem, published early and often. Would things have turned out differently? If so, how?
Perhaps someone would have beaten him to the proof, or at least, completed first whatever ended up being the final step.
Perhaps academic ridicule for working on such a silly project (because of so many previous failures) would have resulted in incentives, perhaps financial, to abandon it long before even getting close to the solution.