In machine learning, people have been more and more letting go of the idea that they should understand how a particular algorithm works, and accepting it on the basis that it "just works".
Are there other examples in the history of science where people started to achieve success by transitioning to methods that are less clearly understood than the previously used methods?
The emergence of infinitesimal methods in the 17th century led to just such a situation. The old-fashioned methods sometimes called "method by exhaustion" worked to calculate areas and solve other geometric problems, but they were cumbersome and less effective than the new infinitesimal methods. On the other hand, it was less clear how exactly the infinitesimal methods work. Moreover infinitesimals posed something of a philosophical if not theological challenge, in that they were entities you can't pin down the way you can pin down ordinary numbers. A major battle raged that had talented mathematicians on both sides, and it took decades before the new techniques were accepted.
