Towards the Automatic Mathematician

The mathematician as a formalist

The well-designed young mathematician

This paper complements McCarthy’s “The well designed child”, in part by putting it in a broader context, the space of possible well designed progeny, and in part by relating design features to development of mathematical competence. I first moved into AI in an attempt to understand myself, especially hoping to understand how I could do mathematics. Over the ensuing four decades, my interactions...

The mind of the mathematician

It goes without saying that mathematicians have minds — my two universityeducated daughters may disagree with that, but of course we know better. So why write a book about the mind of mathematicians? Well the first point to note is that one of the authors, Ioan James, is a mathematician — naturally. He may be known to some as he is the editor of the Topology journal. The second author, Michael ...

John von Neumann , the Mathematician

Imagine a poll to choose the best-known mathematician of the twentieth century. No doubt the winner would be John von Neumann. Reasons are seen, for instance, in the title of the excellent biography [M] by Macrae: John von Neumann. The Scientific Genius who Pioneered the Modern Computer, Game Theory, Nuclear Deterrence, and Much More. Indeed, he was a fundamental figure not only in designing mo...

∞-Categories for the Working Mathematician

homotopy theory C.1. Lifting properties, weak factorization systems, and Leibniz closure C.1.1. Lemma. Any class of maps characterized by a right lifting property is closed under composition, product, pullback, retract, and limits of towers; see Lemma C.1.1. Proof. For now see [17, 11.1.4] and dualize. On account of the dual of Lemma C.1.1, any set of maps in a cocomplete category “cellularly g...