The unreasonable effectiveness of mathematics in the natural sciences

The title of the post is the title of an article written by Eugene Wigner in 1960 (you can find it here). I remember that article when I watched interestellar. I am amazed with the power of that artificial language that we call mathematics, its axiomatic method, the formal logic and the theory that lies in its foundations. I am even more amazed by the way it is used to investigate, formally, the nature of physical phenomena. The ontological true of the objects and its relations as described by the theory are debatable. What is incredible and uncontestable is the fruitfulness of such abstract representation. Even more misterious are the connections that appear here and there in mathematics. To cite one example, think about Robert Sedgewick and Flajolet. They deveolped a formula that are quite close to each other, although they were studying completely different topics.

For Social Sciences, it is true, that effectiveness is less pronounced, as this article discuss.

In the same vein, we have others:

In natural sciences

For social sciences

Why (un)reasonable?

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