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THE GREAT MATH WAR

Jason Socrates Bardi

How Three Brilliant Minds Fought for the Foundations of Mathematics

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 thatsurprisinglymade 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 itand 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 intuitionand 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 lifeand shows how it indelibly shaped twentieth-century intellectual life.

Jason Socrates Bardi is an award-winning journalist in DC who has written two books about the history of math: The Calculus Wars and The Fifth Postulate. He has published hundreds of articles about modern science and medicine in outlets including the San Francisco Chronicle, Good Morning America, US News & World Report, and The Lancet. He lives in Bethesda, Maryland.
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Published 2025-11-04 by Basic Books

Comments

Is Bardi's The Great Math War a history of early 20th century mathematics, or a cultural history of the early 20th century, or an intellectual biography of three brilliant minds David Hilbert, Bertie Russell, and L. E. J. Brouwer? Similarly to a fairy tale, Bardi's book operates on multiple levels and will be an inspiration to a wide range of readers. You will see the early 20th century in a new way zaniness, aesthetic innovation, and utopic vision suffused it, painted so wonderfully by Bardi. Although this world brims with books, and while this is a well-researched chapter in the history of mathematics and in culture at large, Bardi's book is a gem. It surprises, is beautifully written, and enlivens difficult and even odd material in a 'show don't tell' manner. Sit down comfortably and get ready for a lovely and entertaining intellectual and historical ride.

Bardi's The Great Math War provides a fascinating romp through one of the most consequential conflicts of the early 20th century, fought, not on the battlefield but within the ivory tower of mathematical theory. Its outcome helped to shape our world.

The Great Math War reads like one long, revelatory conversation with a brilliant friend, as Jason Bardi leads us through the story of how the greatest minds of the modern age slugged it out over the foundations of mathematics and so reality, against a background of passion, ambition, treachery and war.