In the 1800s, it seemed like mathematics was a solved problem. The paradoxes in the field were resolved, and even areas like advanced calculus could be taught consistently and reliably at any school. It was clearly understandable in a way that abstract fields like philosophy weren’t, and it was on its way to solving humanity’s problems. Mathematical work on electromagnetism made modern electrical engineering and power systems possible. New research in algebra created the logical basis for future computer science and digital circuits.

But then new problems appeared. In the early 20th century, mathematicians made discoveries that showed them enough to know how little they really knew. Bertrand Russell showed that at its edges, math fell apart. It couldn’t fully define itself on its own terms without becoming logically inconsistent. He gave the analogy of a small-town barber who shaves everyone who doesn't shave himself; the question is, who shaves the barber—if he shaves himself, he breaks the rule, but if he doesn't shave himself, he must, by the rule, shave himself?

 In today’s episode, I’m speaking to Jason Bardi, author of The Great Math War: How Three Brilliant Minds Fought for the Foundations of Mathematics and we explore the story of three competing efforts by mathematicians to resolve this crisis. What do you do if math, the most logical of all sciences, becomes illogical at a certain point? Bertrand Russell thought the problem could be solved with even more logic, we just hadn’t tried hard enough. David Hilbert thought 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. Set against the backdrop of one of the most turbulent periods of European history (from the late 19th century through World War I, the 1920s, the Great Depression, and the early days of World War II), we look at what happens when rock-solid truths don’t seem so rock solid anymore.

In the 1800s, it seemed like mathematics was a solved problem. The paradoxes in the field were resolved, and even areas like advanced calculus could be taught consistently and reliably at any school. It was clearly understandable in a way that abstract fields like philosophy weren&rsquo;t, and it was on its way to solving humanity&rsquo;s problems. Mathematical work on electromagnetism made modern electrical engineering and power systems possible. New research in algebra created the logical basis for future computer science and digital circuits.
But then new problems appeared. In the early 20th century, mathematicians made discoveries that showed them enough to know how little they really knew. Bertrand Russell showed that at its edges, math fell apart. It couldn&rsquo;t fully define itself on its own terms without becoming logically inconsistent. He gave the analogy of a small-town barber who shaves everyone who doesn't shave himself; the question is, who shaves the barber&mdash;if he shaves himself, he breaks the rule, but if he doesn't shave himself, he must, by the rule, shave himself?
&nbsp;In today&rsquo;s episode, I&rsquo;m speaking to Jason Bardi, author of The Great Math War: How Three Brilliant Minds Fought for the Foundations of Mathematics and we explore the story of three competing efforts by mathematicians to resolve this crisis. What do you do if math, the most logical of all sciences, becomes illogical at a certain point? Bertrand Russell thought the problem could be solved with even more logic, we just hadn&rsquo;t tried hard enough. David Hilbert thought 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&mdash;and that math is not based on logic but rather logic is based on math. Set against the backdrop of one of the most turbulent periods of European history (from the late 19th century through World&nbsp;War&nbsp;I, the 1920s,&nbsp;the Great&nbsp;Depression, and the early days of World&nbsp;War&nbsp;II), we look at what happens when rock-solid truths don&rsquo;t seem so rock solid anymore.

For history lovers who listen to podcasts, History Unplugged is the most comprehensive show of its kind. It's the only show that dedicates episodes to both interviewing experts and answering questions from its audience. First, it features a call-in show where you can ask our resident historian (Scott Rank, PhD) absolutely anything (What was it like to be a Turkish sultan with four wives and twelve concubines? If you were sent back in time, how would you kill Hitler?). Second, it features long-form interviews with best-selling authors who have written about everything. Topics include gruff World War II generals who flew with airmen on bombing raids, a war horse who gained the rank of sergeant, and presidents who gave their best speeches while drunk.

A show about American history, world history, World Wars 1 & 2, the Civil War, and much more.

History Unplugged Podcast

For history lovers who listen to podcasts, History Unplugged is the most comprehensive show of its kind. It's the only show that dedicates episodes to both interviewing experts and answering questions from its audience. First, it features a call-in show where you can ask our resident historian (Scott Rank, PhD) absolutely anything (What was it like to be a Turkish sultan with four wives and twelve concubines? If you were sent back in time, how would you kill Hitler?). Second, it features long-form interviews with best-selling authors who have written about everything. Topics include gruff World War II generals who flew with airmen on bombing raids, a war horse who gained the rank of sergeant, and presidents who gave their best speeches while drunk.

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