Existence and reality in mathematics and natural science

In this article, which is based on a lecture delivered to the Indian Association for the Cultivation of Science, the author discusses the relations of mathematics and natural science. The author begins with a brief historical survey of their interactions, and then contrasts Platonism, according to which mathematical realities exist independent of the human mind, and constructivism, according to which mathematical realities are products of the human mind. Kantian and evolutionary views of mathematical knowledge are summarized. The author argues for a combination of Platonism and constructivism. With this view, evolution gives us the capacity to create mathematical objects, and in this way we acquire a new sense that enables us to reach aspects of nature beyond space and time