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> ... six of the fundamental concepts in mathematics ... and how they connect with our real-world intuition While the connections are interesting, I would be a
by boerseth 7mo ago
> ... six of the fundamental concepts in mathematics ... and how they connect with our real-world intuition
While the connections are interesting, I would be as interested in the disconnects, as there's a bunch of cases where our human intuitions can fail us in subtle ways. This is actually one of the lessons I treasure from mathematics: it has helped me grow a healthy set of alarm bells for those unintuitive cases. Especially for probability and statistics.
- rramadass 7mo ago> Especially for probability and statistics. For the general reader, two books by David Spiegelhalter (https://en.wikipedia.org/wiki/David_Spiegelhalter https://en.wikipedia.org/wiki/David_Spiegelhalter) are relevant here; 1) The Art of Uncertainty: How to Navigate Chance, Ignorance, Risk and Luck. 2) The Art of Statistics: Learning from Data. And of course, all the books by Nassim Taleb.
- leethargo 7mo agoThere's also the argument that human intuition can and should be trained, rather than just dismissing it, in particular when it comes to mathematics. See, for example, the book "Mathematica" by David Bessis, or this blog post: https://davidbessis.substack.com/p/thinking-fast-slow-and-super-slow https://davidbessis.substack.com/p/thinking-fast-slow-and-su...
- socalgal2 7mo agoInterview with the author about that book https://www.econtalk.org/a-mind-blowing-way-of-looking-at-math-with-david-bessis/ https://www.econtalk.org/a-mind-blowing-way-of-looking-at-ma...
- rramadass 7mo agoNice. There is also Intuition in Science and Mathematics: An Educational Approach by Efraim Fischbein - https://link.springer.com/book/10.1007/0-306-47237-6 https://link.springer.com/book/10.1007/0-306-47237-6