The Great Math War

A stirring account of the mathematicians who went looking for the bedrock philosophical foundations of their field and witnessed a house of cards collapse instead 

As the nineteenth century ended, mathematicians were celebrating a century of triumphs that—surprisingly—made clear how little they knew: What is the nature of infinity? Is math free from self-contradiction? And what does math have to do with reality? This was the Foundational Crisis in mathematics.  

In The Great Math War, Jason Socrates Bardi tells the story of three competing efforts by mathematicians to resolve it—and the firefight that ensued. Bertrand Russell thought we could achieve certainty if we treated math as an extension of logic. David Hilbert believed redemption lay in accepting mathematics as a formal game of arbitrary rules, no different from the moves and pieces in chess. And L. E. J. Brouwer argued math is entirely rooted in human intuition—and that math is not based on logic but rather logic is based on math. It was a bitter struggle, intellectually and personally, as the three vied to set the course for mathematics in the twentieth century.   

Set against the backdrop of international warfare unfolding alongside it, The Great Math War brings the Foundational Crisis to radiant life—and shows how it indelibly shaped twentieth-century intellectual life.