MATHEMATICS: DISCOVERY OR INVENTION?

Invention Versus Discovery

because they have not experienced any necessity to achieve such an evolution in their natural environments. At this moment, the cognitive processes that lead to the invention and modification of new tool-use behavior remain for further investigation. Since the first observation of wild chimpanzees was achieved by Jane Goodall in 1960, the study of nonhuman animals’ tool use does not have a long...

Discovery, invention, and development: human creative thinking.

Scheme-based theorem discovery and concept invention

We describe an approach to automatically invent/explore new mathematical theories, with the goal of producing results comparable to those produced by humans, as represented, for example, in the libraries of the Isabelle proof assistant. Our approach is based on ‘schemes’, which are terms in higher-order logic. We show that it is possible to automate the instantiation process of schemes to gener...

Invention vs. Discovery A critical discussion

The paper proposes an epistemological analysis of the dichotomy discovery/invention. In particular, we argue in favor of the idea that science does not discover facts by induction but rather invents theories that are then checked against experience.

Discovery and Reasoning in Mathematics

We discuss the automation of mathematical reasoning, surveying the abilities displayed by human mathematicians and the computational techniques available for automating these abilities. We argue the importance of the simultaneous study of these techniques, because problems inherent in one technique can often be solved if it is able to interact with others.