How do people in academia know whether their research, result, theorem or thesis is original work?

I am curious as to how academia continues itself without replication or reinventing the wheel. So many academicians in so many areas of work, how would one ever find out whether the work he or she is about to embark on can be considered an original work? That someone didn't already publish the very same result?

In engineering, we have all heard the story of Cooley-Tukey's method of Fast Fourier Transform. The story goes Tukey has been applying his own method of FFT for years without recognizing that the implementation was a fundamentally original approach. Until he brought it up in a meeting in the 1950s, he had always thought that this method was used widely given its extraordinarily simple implementation. Only later did everyone realize that Gauss had used the very same method 160 years earlier.

The same goes for the famed Wiener-Khinchin theorem in stochastic analysis. After two most ingenious mathematicians ever graced this earth came up with this theorem did they realized that Einstein had already published it a decade ago.

Doubtlessly, there are thousands of examples in all branches of natural sciences. It is less clear whether the social science encounters this problem since no two times and places are ever alike, and the social reality keeps on changing therefore novel results is always promised.

So how can one find out in the quickest way possible that his or her work is original work? Original in the sense that the end result is something that improves upon an existing result or opens up an entirely new field without duplications from other people. Does there exist a database somewhere to categorizes all recent and historic progress in a certain field? Are there people who are employed in academia or elsewhere to do this very task?

Edit: I guess same goes for asking a question without looking at the other questions first...seems like this question was resolved in another post T_T