Steve Patterson | The Historical Context for Modern Mathematics @StevePatterson | Uploaded August 2018 | Updated October 2024, 4 hours ago.
Most people do not understand the history or context of modern mathematics. They do not realize just how many assumptions were made around the turn of the 20th century, as mathematics was undergoing a foundational crisis.
Instead, your average PhD has a strong opinion about the rigor of modern mathematics and has never conceived of alternative structures of math. They passionately believe the very first thing they were taught - no different than a religion.
Euclidean geometry served as the foundation for mathematics for nearly two thousand years, with the supposed "best minds" considering it indubitable. Until it wasn't. When non-Euclidean geometries were discovered, they shook the literal foundations of mathematics - a crisis that has never been fully resolved.
In this video, I go through some of the attempts to re-found higher mathematics. Different philosophies will yield different mathematical structures - especially with regard to the notion of "completed infinities."
Comments and corrections welcome. I don't expect this story is 100% accurate, as it's just a brain dump to get it out while working on other things. When editing, I already know I misspoke. Still, this should be a good enough story to serve as a starting point to learn about the context for modern math. I do intend to write significantly on this topic.
Check out more at: steve-patterson.com
If you think this content is worth $1, please check out my Patreon page to support the creation of more videos like this:
patreon.com/stevepatterson
Or you can enter Amazon through: goo.gl/ftfFLg
Or, you can support with Bitcoin Cash: qp35pt4qlgskgg05zjuuy84udnnhw4ma7vrn05qjfz
Most people do not understand the history or context of modern mathematics. They do not realize just how many assumptions were made around the turn of the 20th century, as mathematics was undergoing a foundational crisis.
Instead, your average PhD has a strong opinion about the rigor of modern mathematics and has never conceived of alternative structures of math. They passionately believe the very first thing they were taught - no different than a religion.
Euclidean geometry served as the foundation for mathematics for nearly two thousand years, with the supposed "best minds" considering it indubitable. Until it wasn't. When non-Euclidean geometries were discovered, they shook the literal foundations of mathematics - a crisis that has never been fully resolved.
In this video, I go through some of the attempts to re-found higher mathematics. Different philosophies will yield different mathematical structures - especially with regard to the notion of "completed infinities."
Comments and corrections welcome. I don't expect this story is 100% accurate, as it's just a brain dump to get it out while working on other things. When editing, I already know I misspoke. Still, this should be a good enough story to serve as a starting point to learn about the context for modern math. I do intend to write significantly on this topic.
Check out more at: steve-patterson.com
If you think this content is worth $1, please check out my Patreon page to support the creation of more videos like this:
patreon.com/stevepatterson
Or you can enter Amazon through: goo.gl/ftfFLg
Or, you can support with Bitcoin Cash: qp35pt4qlgskgg05zjuuy84udnnhw4ma7vrn05qjfz
