2017-10-19

[public] 913K views, 24.5K likes, 1.19K dislikes audio only

PBS Infinite Series

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What if the foundation that all of mathematics is built upon isn't as firm as we thought it was?

Note: The natural numbers sometimes include zero and sometimes don't -- it depends on how you define it. Within logic, zero is always included as a natural number.

Correction - The image shown at 8:15 is of Netwon's Principia and not Russell and Whitehead's Principia Mathematica as was intended.

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Mathematics is cumulative -- it builds on itself. That’s part of why you take math courses in a fairly prescribed order. To learn about matrices - big blocks of numbers - and the procedure for multiplying matrices, you need to know about numbers. Matrices are defined in terms of - in other words, constructed from - more fundamental objects: numbers.

References::

Probability website mentioned in comments: http://people.ischool.berkeley.edu/~nick/aaronson-oracle/index.html

https://plato.stanford.edu/entries/philosophy-mathematics/

https://plato.stanford.edu/entries/logicism/

Ernst Snapper :: https://www.maa.org/sites/default/files/pdf/upload_library/22/Allendoerfer/1980/0025570x.di021111.02p0048m.pdf

Philosophy of mathematics (Selected readings) edited by Paul Benacerraf and Hilary Putnam

Written and Hosted by Kelsey Houston-Edwards

Produced by Rusty Ward

Graphics by Ray Lux

Assistant Editing and Sound Design by Mike Petrow

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