Friday, July 23, 2021

A Timeline of Mathematics and Gödel’s Incompleteness Theorem

This week TED-Ed published a new video about Gödel's Incompleteness Theorem. This is the latest in a long list of mathematics video lessons produced by TED-Ed. The timing of the video was perfect for me as I had planned on writing about Mathigon's Timeline of Mathematics this week. That timeline includes an entry about Gödel's incompleteness theorems.  

Mathigon's Timeline of Mathematics is an interactive timeline of developments in mathematics throughout history. The timeline begins with the development of the first counting systems and progresses through today. Throughout the timeline there are images and names to click on to learn more about each development. For example, at the beginning of the timeline you can click on an image of the Ishango Bone to learn that this artifact is the oldest representation of early counting systems. Much later in the timeline you can click on the image of Kurt Gödel to learn about his contributions to mathematics and click on examples of his theorems in practice. 




Applications for Education
The Timeline of Mathematics provides a good opportunity to combine mathematics and history into the same lesson. The early artifacts in the timeline are appropriate for use as an introduction to the development of counting and basic arthimetic. Items later in the timeline are more appropriate for conversations in middle school and high school settings.