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Mind blown twice by maths on the internet 🤯🤯

"An infinitely large napkins" on an abstract background

I've come across a couple of things recently that have blown my mathematical mind. The first is the Infinitely Large Napkin, a 1000+ page PDF of all sorts of maths. It's just at the level I'm at at the moment. I don't want to see proofs of stuff, I just want to furnish my mind with mathematical constructs. It has the right level of explanation and examples, with a few questions in case I want to dig a bit further. And it's free. ðŸ¤¯

Secondly I was trying out ChatGPT with some maths questions. My experience of Google search results AI, which is the only AI I regularly use, is that it's unhelpful and sometimes completely wrong. ChatGPT has been useful on the odd occasion. I tried out its maths knowlege. When I asked it a factual question it seemed to get (according to my comparison with the §1.6 of Napkin) the right answer. I guess because the internet is full of concise and true statements about maths it's highly likely to get the answer right. Here's what I asked, and the reply:

List all the groups of order less than or equal to ten

Order 1 (Trivial Group)

  • G={e}
  • Only one possible group: the trivial group.

Order 2 (Cyclic Group)

  • Z2 (Cyclic group of order 2, Abelian).
etc. up to Order 10.

It then offered to tell me more, show examples etc. ðŸ¤¯ It seems like with the Napkin document and by asking ChatGPT questions as I go along I can really dig deeply into maths.

Update 11 March 2025. It's not so hot at diagrams though. Here's "a visual representation of compactness in topology".


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