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Ep. 287 Ian Deters Defends the Use of Infinity in Higher Mathematics

Back on BMS ep. 229, Bob invited Steve Patterson back to the show to discuss Riemann’s Rearrangement Theorem, which was such a counterintuitive result that Bob changed his mind and agreed with Steve that mathematicians had smuggled nonsense into their field. Math PhD Ian Deters now joins Bob to defend the use of infinity in higher mathematics.

Mentioned in the Episode and Other Links of Interest:

The audio production for this episode was provided by Podsworth Media.

About the author, Robert

Christian and economist, Chief Economist at infineo, and Senior Fellow with the Mises Institute.


  1. Bill on 09/08/2023 at 12:30 AM

    My defense of Riemann’s rearrangement theorem that I gave in a comment on episode 229 is similar to Deters’. I feel vindicated, lol.

  2. Charles Rosa on 09/08/2023 at 12:32 PM

    Great podcast. Deter did a superb job of leading your listeners through the arguments. Thank you for having him on.

  3. John DeRosa on 09/15/2023 at 7:03 AM

    This was a delight to listen to. Thanks, Bob, for hosting this thoughtful rebuttal.

  4. Bernie Jackson on 09/21/2023 at 4:26 AM

    Wonderful episode! Please have a look at my response:

    Unscrambling infinity and chronicling math’s forbidden numbers
    A reply to The Bob Murphy Show, Episode 287

    While listening, I discovered a way to see the essence of these rearrangement issues without infinity or convergence. I wrote a fun story to explain it.

    Also linked from my reply is a talk I have given to high school students about the violent history of the square root of two and related themes that get pretty deep. Some of them were touched on and wondered about in this episode. The full story gets a lot weirder than it should!

    • Robert Murphy on 09/25/2023 at 12:19 PM

      I’ll take a look, thanks Mr. Jackson.

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