Gnomes in the fog

This book looks at the development of Brouwer's Intuitionism, and its reception by the mathematics community. Is mathematics just axioms, or is there more to it? How are we to think of infinite sets? The book will certainly be of interest to students of the history of mathematics. It might also be of interest to those wanting to know about the culture in the 1920's - how the war had introduced uncertainty everywhere. It certainly requires some knowledge of university level mathematics, but was more readable than I expected. Readers who topped up what they learned at school with some reading about mathematical axiomatics would probably be able to follow it, in particular chapters 1, 2, and 6. It would also be of use to those considering research into the foundations of mathematics - possibly as a warning of the quagmire that this can become.

Hesseling puts the resolution of the debate around 1928, when Intutionism was axiomatised, but I'm not convinced - axiomatisation somewhat defeats the point. I would say that the results of Gödel and Skolem at the start of the 1930's played a significant rôle. Having definite results showed the shallowness of the philosophical posturing which preceded them.

The title comes from Kundera's observation that hindsight makes history seem clearer than it really was. Personally, I think that patches of the fog are still around.